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117-628: The Fairbanks Museum & Planetarium is a combination natural science museum , history museum , and planetarium located in St. Johnsbury, Vermont . It was founded in 1890 by businessman, politician, naturalist, and collector Franklin Fairbanks . The museum and its buildings are on the U.S. National Register of Historic Places . The Eye on the Sky Weather Center is a meteorology and weather forecasting station operated regularly at

234-425: A beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. The maximal diameter (which corresponds to the long diagonal of the hexagon), D , is twice the maximal radius or circumradius , R , which equals the side length, t . The minimal diameter or

351-409: A hexagram . A regular hexagon can be dissected into six equilateral triangles by adding a center point. This pattern repeats within the regular triangular tiling . A regular hexagon can be extended into a regular dodecagon by adding alternating squares and equilateral triangles around it. This pattern repeats within the rhombitrihexagonal tiling . There are six self-crossing hexagons with

468-421: A triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral , and that the regular hexagon can be partitioned into six equilateral triangles. Like squares and equilateral triangles , regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations . The cells of

585-503: A truncated equilateral triangle , t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular . It is bicentric , meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle , which equals 2 3 {\displaystyle {\tfrac {2}{\sqrt {3}}}} times

702-482: A break from the past by rejecting Aristotle and his medieval followers outright, calling their approach to natural philosophy superficial. Hexagon In geometry , a hexagon (from Greek ἕξ , hex , meaning "six", and γωνία , gonía , meaning "corner, angle") is a six-sided polygon . The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A regular hexagon has Schläfli symbol {6} and can also be constructed as

819-546: A career in planetary science undergo graduate-level studies in one of the Earth sciences, astronomy, astrophysics, geophysics, or physics. They then focus their research within the discipline of planetary science. Major conferences are held annually, and numerous peer reviewed journals cater to the diverse research interests in planetary science. Some planetary scientists are employed by private research centers and frequently engage in collaborative research initiatives. Constituting

936-423: A hexagon has vertices on the circumcircle of an acute triangle at the six points (including three triangle vertices) where the extended altitudes of the triangle meet the circumcircle, then the area of the hexagon is twice the area of the triangle. Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at

1053-484: A key part of most scientific discourse. Such integrative fields, for example, include nanoscience , astrobiology , and complex system informatics . Materials science is a relatively new, interdisciplinary field that deals with the study of matter and its properties and the discovery and design of new materials. Originally developed through the field of metallurgy , the study of the properties of materials and solids has now expanded into all materials. The field covers

1170-447: A laboratory, using a series of (often well-tested) techniques for manipulating materials, as well as an understanding of the underlying processes. Chemistry is often called " the central science " because of its role in connecting the other natural sciences. Early experiments in chemistry had their roots in the system of alchemy , a set of beliefs combining mysticism with physical experiments. The science of chemistry began to develop with

1287-423: A level equal with theology and the debate of religious constructs in a scientific context, showed the persistence with which Catholic leaders resisted the development of natural philosophy even from a theological perspective. Aquinas and Albertus Magnus , another Catholic theologian of the era, sought to distance theology from science in their works. "I don't see what one's interpretation of Aristotle has to do with

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1404-630: A live night sky astronomy lesson, as well as telescope demonstrations and other educational displays. The event was certified by Guinness World Records and covered by Vermont Public Radio and local news media. In 2019, the museum's weather station surpassed its 125th anniversary, and was recognized by the World Meteorological Organization , National Weather Service , and NOAA as the second oldest regular meteorological observation station in North America, after

1521-400: A matter not only for their existence but also for their definition." There was broad agreement among scholars in medieval times that natural science was about bodies in motion. However, there was division about including fields such as medicine, music, and perspective. Philosophers pondered questions including the existence of a vacuum, whether motion could produce heat, the colors of rainbows,

1638-744: A methodical way. Still, philosophical perspectives, conjectures , and presuppositions , often overlooked, remain necessary in natural science. Systematic data collection, including discovery science , succeeded natural history , which emerged in the 16th century by describing and classifying plants, animals, minerals, and so on. Today, "natural history" suggests observational descriptions aimed at popular audiences. Philosophers of science have suggested several criteria, including Karl Popper 's controversial falsifiability criterion, to help them differentiate scientific endeavors from non-scientific ones. Validity , accuracy , and quality control , such as peer review and reproducibility of findings, are amongst

1755-434: A regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumcircle between B and C, then PE + PF = PA + PB + PC + PD . It follows from the ratio of circumradius to inradius that the height-to-width ratio of a regular hexagon is 1:1.1547005; that is, a hexagon with a long diagonal of 1.0000000 will have a distance of 0.8660254 or cos(30°) between parallel sides. For an arbitrary point in

1872-575: A regular hexagonal pattern. The two simple roots have a 120° angle between them. The 12 roots of the Exceptional Lie group G2 , represented by a Dynkin diagram [REDACTED] [REDACTED] [REDACTED] are also in a hexagonal pattern. The two simple roots of two lengths have a 150° angle between them. Coxeter states that every zonogon (a 2 m -gon whose opposite sides are parallel and of equal length) can be dissected into 1 ⁄ 2 m ( m − 1) parallelograms. In particular this

1989-480: A separate field in its own right, most modern workers in the field agree that it has matured to a state that it has its own paradigms and practices. Planetary science or planetology, is the scientific study of planets, which include terrestrial planets like the Earth, and other types of planets, such as gas giants and ice giants . Planetary science also concerns other celestial bodies, such as dwarf planets moons , asteroids , and comets . This largely includes

2106-400: A significant role in the other natural sciences, as represented by astrophysics , geophysics , chemical physics and biophysics . Likewise chemistry is represented by such fields as biochemistry , physical chemistry , geochemistry and astrochemistry . A particular example of a scientific discipline that draws upon multiple natural sciences is environmental science . This field studies

2223-476: A significant role in the world economy. Physics embodies the study of the fundamental constituents of the universe , the forces and interactions they exert on one another, and the results produced by these interactions. Physics is generally regarded as foundational because all other natural sciences use and obey the field's principles and laws. Physics relies heavily on mathematics as the logical framework for formulating and quantifying principles. The study of

2340-423: A single point. In a hexagon that is tangential to a circle and that has consecutive sides a , b , c , d , e , and f , If an equilateral triangle is constructed externally on each side of any hexagon, then the midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle. A skew hexagon is a skew polygon with six vertices and edges but not existing on

2457-410: A step closer to direct inquiry about cause and effect in nature between 600 and 400 BC. However, an element of magic and mythology remained. Natural phenomena such as earthquakes and eclipses were explained increasingly in the context of nature itself instead of being attributed to angry gods. Thales of Miletus , an early philosopher who lived from 625 to 546 BC, explained earthquakes by theorizing that

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2574-741: A treatise by the earlier Persian scholar Al-Farabi called On the Sciences into Latin, calling the study of the mechanics of nature Scientia naturalis , or natural science. Gundissalinus also proposed his classification of the natural sciences in his 1150 work On the Division of Philosophy . This was the first detailed classification of the sciences based on Greek and Arab philosophy to reach Western Europe. Gundissalinus defined natural science as "the science considering only things unabstracted and with motion," as opposed to mathematics and sciences that rely on mathematics. Following Al-Farabi, he separated

2691-580: Is a natural science that studies celestial objects and phenomena. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Astronomy is the study of everything in the universe beyond Earth's atmosphere, including objects we can see with our naked eyes. It is one of the oldest sciences. Astronomers of early civilizations performed methodical observations of the night sky, and astronomical artifacts have been found from much earlier periods. There are two types of astronomy: observational astronomy and theoretical astronomy. Observational astronomy

2808-420: Is an all-embracing term for the sciences related to the planet Earth , including geology , geography , geophysics , geochemistry , climatology , glaciology , hydrology , meteorology , and oceanography . Although mining and precious stones have been human interests throughout the history of civilization, the development of the related sciences of economic geology and mineralogy did not occur until

2925-399: Is concerned with the characteristics, classification and behaviors of organisms , as well as how species were formed and their interactions with each other and the environment . The biological fields of botany , zoology , and medicine date back to early periods of civilization, while microbiology was introduced in the 17th century with the invention of the microscope. However, it

3042-533: Is focused on acquiring and analyzing data, mainly using basic principles of physics. In contrast, Theoretical astronomy is oriented towards developing computer or analytical models to describe astronomical objects and phenomena. This discipline is the science of celestial objects and phenomena that originate outside the Earth's atmosphere . It is concerned with the evolution, physics , chemistry , meteorology , geology , and motion of celestial objects, as well as

3159-750: Is full symmetry, and a1 is no symmetry. p6 , an isogonal hexagon constructed by three mirrors can alternate long and short edges, and d6 , an isotoxal hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular hexagon. The i4 forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an elongated rhombus , while d2 and p2 can be seen as horizontally and vertically elongated kites . g2 hexagons, with opposite sides parallel are also called hexagonal parallelogons . Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only

3276-439: Is inscribed in any conic section , and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration. The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point . If

3393-447: Is no Platonic solid made of only regular hexagons, because the hexagons tessellate , not allowing the result to "fold up". The Archimedean solids with some hexagonal faces are the truncated tetrahedron , truncated octahedron , truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron . These hexagons can be considered truncated triangles, with Coxeter diagrams of

3510-519: Is sub-categorized into more specialized cross-disciplines, such as physical oceanography and marine biology . As the marine ecosystem is vast and diverse, marine biology is further divided into many subfields, including specializations in particular species . There is also a subset of cross-disciplinary fields with strong currents that run counter to specialization by the nature of the problems they address. Put another way: In some fields of integrative application, specialists in more than one field are

3627-496: Is the Petrie polygon for these higher dimensional regular , uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections : A principal diagonal of a hexagon is a diagonal which divides the hexagon into quadrilaterals. In any convex equilateral hexagon (one with all sides equal) with common side a , there exists a principal diagonal d 1 such that and a principal diagonal d 2 such that There

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3744-406: Is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. This decomposition of a regular hexagon is based on a Petrie polygon projection of a cube , with 3 of 6 square faces. Other parallelogons and projective directions of the cube are dissected within rectangular cuboids . A regular hexagon has Schläfli symbol {6}. A regular hexagon is a part of

3861-576: The Ayurvedic tradition saw health and illness as a combination of three humors: wind , bile and phlegm . A healthy life resulted from a balance among these humors. In Ayurvedic thought, the body consisted of five elements: earth, water, fire, wind, and space. Ayurvedic surgeons performed complex surgeries and developed a detailed understanding of human anatomy. Pre-Socratic philosophers in Ancient Greek culture brought natural philosophy

3978-654: The Blue Hill Meteorological Observatory , having begun a continuous streak of weather observations in early 1894. Natural science Natural science can be divided into two main branches: life science and physical science . Life science is alternatively known as biology , and physical science is subdivided into branches: physics , chemistry , earth science , and astronomy . These branches of natural science may be further divided into more specialized branches (also known as fields). As empirical sciences, natural sciences use tools from

4095-623: The International Geophysical Year , and first publicly opened in April 1961, under museum director Fred Mold. It is named after famed scientist Lyman Spitzer Jr. , a pioneer of modern astrophysics and astronomical observation. In the planetarium lobby is the space science gallery, displayed in which are astrophotographs from the Northern Skies Observatory in nearby Peacham, Vermont , images from

4212-693: The Mesopotamian and Ancient Egyptian cultures, which produced the first known written evidence of natural philosophy , the precursor of natural science. While the writings show an interest in astronomy, mathematics, and other aspects of the physical world, the ultimate aim of inquiry about nature's workings was, in all cases, religious or mythological, not scientific. A tradition of scientific inquiry also emerged in Ancient China , where Taoist alchemists and philosophers experimented with elixirs to extend life and cure ailments. They focused on

4329-707: The Solar System , but recently has started to expand to exoplanets , particularly terrestrial exoplanets . It explores various objects, spanning from micrometeoroids to gas giants, to establish their composition, movements, genesis, interrelation, and past. Planetary science is an interdisciplinary domain, having originated from astronomy and Earth science , and currently encompassing a multitude of areas, such as planetary geology , cosmochemistry , atmospheric science , physics , oceanography , hydrology , theoretical planetology , glaciology , and exoplanetology. Related fields encompass space physics , which delves into

4446-593: The Spitzer Space Telescope , as well as an iron-nickel meteorite recovered in Patagonia . Also in the gallery is a Fairbanks Scale which displays the equivalent weight of an object or person if it were in the gravitational field of the Moon or other planets in the Solar System . Live shows and presentations as well as planetarium movies cover a variety of topics, including basic backyard stargazing,

4563-529: The U.S. Department of Commerce Economic Development Administration . General building maintenance and preservation work is also being carried out during this time. The museum is organized into 6 different departments or categories, which are reflected in its logo and hexagon theme found throughout the museum: Natural History , Geoscience , Ethnology , Engineering , Meteorology , and Astronomy . The entire collection includes roughly 175,000 objects. Storage and archive spaces are maintained on site for many of

4680-427: The apothem (radius of the inscribed circle ). All internal angles are 120 degrees . A regular hexagon has six rotational symmetries ( rotational symmetry of order six ) and six reflection symmetries ( six lines of symmetry ), making up the dihedral group D 6 . The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that

4797-522: The cell or organic molecule . Modern biology is divided into subdisciplines by the type of organism and by the scale being studied. Molecular biology is the study of the fundamental chemistry of life, while cellular biology is the examination of the cell; the basic building block of all life. At a higher level, anatomy and physiology look at the internal structures, and their functions, of an organism, while ecology looks at how various organisms interrelate. Earth science (also known as geoscience)

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4914-420: The formal sciences , such as mathematics and logic , converting information about nature into measurements that can be explained as clear statements of the " laws of nature ". Modern natural science succeeded more classical approaches to natural philosophy . Galileo , Kepler , Descartes , Bacon , and Newton debated the benefits of using approaches which were more mathematical and more experimental in

5031-624: The formation and development of the universe . Astronomy includes examining, studying, and modeling stars, planets, and comets. Most of the information used by astronomers is gathered by remote observation. However, some laboratory reproduction of celestial phenomena has been performed (such as the molecular chemistry of the interstellar medium ). There is considerable overlap with physics and in some areas of earth science . There are also interdisciplinary fields such as astrophysics , planetary sciences , and cosmology , along with allied disciplines such as space physics and astrochemistry . While

5148-462: The g6 subgroup has no degrees of freedom but can be seen as directed edges . Hexagons of symmetry g2 , i4 , and r12 , as parallelogons can tessellate the Euclidean plane by translation. Other hexagon shapes can tile the plane with different orientations. The 6 roots of the simple Lie group A2 , represented by a Dynkin diagram [REDACTED] [REDACTED] [REDACTED] , are in

5265-478: The path of totality will be passing over the area of Vermont, providing a more spectacular viewing opportunity. The museum was listed on the National Register of Historic Places in 2008. The listing included one contributing building and two contributing objects . On 10 August 2018, the museum obtained the world record for the largest astronomy observation event, with over 1500 people attending

5382-542: The vertex arrangement of the regular hexagon: From bees' honeycombs to the Giant's Causeway , hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons. This means that honeycombs require less wax to construct and gain much strength under compression . Irregular hexagons with parallel opposite edges are called parallelogons and can also tile

5499-522: The yin and yang , or contrasting elements in nature; the yin was associated with femininity and coldness, while yang was associated with masculinity and warmth. The five phases – fire, earth, metal, wood, and water – described a cycle of transformations in nature. The water turned into wood, which turned into the fire when it burned. The ashes left by fire were earth. Using these principles, Chinese philosophers and doctors explored human anatomy, characterizing organs as predominantly yin or yang, and understood

5616-454: The 16th century, and he is considered to be the father of biology for his pioneering work in that science . He also presented philosophies about physics, nature, and astronomy using inductive reasoning in his works Physics and Meteorology . While Aristotle considered natural philosophy more seriously than his predecessors, he approached it as a theoretical branch of science. Still, inspired by his work, Ancient Roman philosophers of

5733-549: The 18th century. The study of the earth, particularly paleontology , blossomed in the 19th century. The growth of other disciplines, such as geophysics , in the 20th century led to the development of the theory of plate tectonics in the 1960s, which has had a similar effect on the Earth sciences as the theory of evolution had on biology. Earth sciences today are closely linked to petroleum and mineral resources , climate research, and to environmental assessment and remediation . Although sometimes considered in conjunction with

5850-757: The Guiness World Record for the "largest astronomy lesson" in 2018 when 1,580 people attended a 40 minute program held across the street from the Museum. The planetarium regularly coordinates with the Vermont Astronomical Society and the Northern Skies Observatory, an astronomy research, observation, and image and data processing center located in Peacham, Vermont , to host public outdoor astronomy events at

5967-566: The Middle Ages brought with it further advances in natural philosophy. European inventions such as the horseshoe , horse collar and crop rotation allowed for rapid population growth, eventually giving way to urbanization and the foundation of schools connected to monasteries and cathedrals in modern-day France and England . Aided by the schools, an approach to Christian theology developed that sought to answer questions about nature and other subjects using logic. This approach, however,

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6084-529: The Night Sky weekly night sky forecast for astronomy, as well as the Skywatch Almanac meteorology and astronomy newsletter and online blog. The Lyman Spitzer Jr. Planetarium and Vinton Space Science Gallery (sometimes shortened to simply the "Spitzer Planetarium"), located at the top of a spiral staircase on the second floor overhanging the front entrance, was built between 1959 and 1960 following

6201-565: The Shippee Family Eye Care Butterfly House was installed in the courtyard behind the Museum's main gallery. An open structure with a canopy cover and benches along the inside, the butterfly house is an immersive experience that invites guests to walk among native butterflies and local flora during the summer months. The Fairbanks Museum has seen continuous operation since its founding, other than annual brief closures every January for upkeep and maintenance of

6318-479: The West. Christopher Columbus 's discovery of a new world changed perceptions about the physical makeup of the world, while observations by Copernicus , Tyco Brahe and Galileo brought a more accurate picture of the solar system as heliocentric and proved many of Aristotle's theories about the heavenly bodies false. Several 17th-century philosophers, including Thomas Hobbes , John Locke and Francis Bacon , made

6435-542: The chemistry, physics, and engineering applications of materials, including metals, ceramics, artificial polymers, and many others. The field's core deals with relating the structure of materials with their properties. Materials science is at the forefront of research in science and engineering. It is an essential part of forensic engineering (the investigation of materials, products, structures, or components that fail or do not operate or function as intended, causing personal injury or damage to property) and failure analysis ,

6552-512: The conclusion that something is impossible. While an impossibility assertion in natural science can never be proved, it could be refuted by the observation of a single counterexample. Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined. This field encompasses a diverse set of disciplines that examine phenomena related to living organisms. The scale of study can range from sub-component biophysics up to complex ecologies . Biology

6669-425: The construction and launching of model rockets . Notable space themed events hosted by the museum include a series of special planetarium shows and astronomy outreach events for the 2009 International Year of Astronomy , observations of the 2012 Transit of Venus , the 2017 North American Solar Eclipse , and a 2018 world record astronomy observation. From 16 to 24 July 2019, the museum displayed exhibits celebrating

6786-516: The creation of broadcasting studios for meteorologists. Initially located in the basement of the main building (which often drew questions and criticism about the lack of windows and visibility for the forecasters to see the actual sky), the weather center's studios were relocated in 2017 to another building at the back of the museum campus. The weather center produces the Eye on the Sky daily forecast, Eye on

6903-494: The development of thermodynamics , and the quantum mechanical model of atomic and subatomic physics. The field of physics is vast and can include such diverse studies as quantum mechanics and theoretical physics , applied physics and optics . Modern physics is becoming increasingly specialized, where researchers tend to focus on a particular area rather than being "universalists" like Isaac Newton , Albert Einstein , and Lev Landau , who worked in multiple areas. Astronomy

7020-403: The diameter of the inscribed circle (separation of parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base), d , is twice the minimal radius or inradius , r . The maxima and minima are related by the same factor: The area of a regular hexagon For any regular polygon , the area can also be expressed in terms of the apothem a and the perimeter p . For

7137-575: The early 13th century, although the practice was frowned upon by the Catholic church. A 1210 decree from the Synod of Paris ordered that "no lectures are to be held in Paris either publicly or privately using Aristotle's books on natural philosophy or the commentaries, and we forbid all this under pain of ex-communication." In the late Middle Ages, Spanish philosopher Dominicus Gundissalinus translated

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7254-501: The early 1st century AD, including Lucretius , Seneca and Pliny the Elder , wrote treatises that dealt with the rules of the natural world in varying degrees of depth. Many Ancient Roman Neoplatonists of the 3rd to the 6th centuries also adapted Aristotle's teachings on the physical world to a philosophy that emphasized spiritualism. Early medieval philosophers including Macrobius , Calcidius and Martianus Capella also examined

7371-447: The earth sciences, due to the independent development of its concepts, techniques, and practices and also the fact of it having a wide range of sub-disciplines under its wing, atmospheric science is also considered a separate branch of natural science. This field studies the characteristics of different layers of the atmosphere from ground level to the edge of the space. The timescale of the study also varies from day to century. Sometimes,

7488-546: The etymology of the term. The prefix "hex-" originates from the Greek word "hex," meaning six, while "sex-" comes from the Latin "sex," also signifying six. Some linguists and mathematicians argue that since many English mathematical terms derive from Latin, the use of "sexagon" would align with this tradition. Historical discussions date back to the 19th century, when mathematicians began to standardize terminology in geometry. However,

7605-532: The exhibits and facilities, and rotation of the vast collection in and out of storage. Normal operations had the museum open 10 AM 5 PM. ET every day of the week. However, due to the COVID-19 pandemic , the museum closed in March 2020, and only partially reopened between July–December 2020, The museum reopened again in early March 2021, with the planetarium reopening, under restrictions, in late May 2021. While closed,

7722-679: The exhibits is available to visitors as well. Meteorological records by the Fairbanks family in St. Johnsbury date back to the 1870s at the Undercliffe mansion, and were then moved to the Fairbanks Museum in 1891, with regular weather recordings at the same unaltered location beginning in late 1893. In part, the museum's tradition of reporting the weather and atmospheric conditions comes from Franklin Fairbanks' own practice of doing so. The meteorological instruments are located primarily behind

7839-400: The field also includes the study of climatic patterns on planets other than Earth. The serious study of oceans began in the early- to mid-20th century. As a field of natural science, it is relatively young, but stand-alone programs offer specializations in the subject. Though some controversies remain as to the categorization of the field under earth sciences, interdisciplinary sciences, or as

7956-440: The form [REDACTED] [REDACTED] [REDACTED] [REDACTED] [REDACTED] and [REDACTED] [REDACTED] [REDACTED] [REDACTED] [REDACTED] . There are other symmetry polyhedra with stretched or flattened hexagons, like these Goldberg polyhedron G(2,0): There are also 9 Johnson solids with regular hexagons: The debate over whether hexagons should be referred to as "sexagons" has its roots in

8073-533: The history and development of astronomy, constellations and their association with various mythology and cultures, celestial navigation , artificial satellites and spacecraft missions, Lunar exploration , planetary science , heliophysics , exoplanetary science , astrodynamics , and cosmology . It is one of only two public planetaria in northern New England , along with the McAuliffe-Shepard Discovery Center . The section of

8190-888: The impact of the Sun on the bodies in the Solar System, and astrobiology . Planetary science comprises interconnected observational and theoretical branches. Observational research entails a combination of space exploration , primarily through robotic spacecraft missions utilizing remote sensing, and comparative experimental work conducted in Earth-based laboratories. The theoretical aspect involves extensive mathematical modelling and computer simulation . Typically, planetary scientists are situated within astronomy and physics or Earth sciences departments in universities or research centers. However, there are also dedicated planetary science institutes worldwide. Generally, individuals pursuing

8307-436: The interactions of physical, chemical, geological, and biological components of the environment , with particular regard to the effect of human activities and the impact on biodiversity and sustainability . This science also draws upon expertise from other fields, such as economics, law, and social sciences. A comparable discipline is oceanography , as it draws upon a similar breadth of scientific disciplines. Oceanography

8424-651: The items and artifacts had been kept beginning in the 1870s. Much of the main collection in the museum comes from Fairbanks' own pre-existing collection, for which the museum was purposefully built to contain and display. Between 1959 and 1960, the planetarium and space gallery were installed, replacing the Colonial Room exhibit gallery. It opened to the public in April 1961, becoming the only public planetarium in Vermont, and has been periodically upgraded over time, while being continuously operated ever since. In 2017,

8541-496: The items when not on display. The museum's exhibits include natural specimens, a seasonal wildflower table, a native butterfly house and flower garden, an observation beehive, artistic pieces made out of insects , taxidermy dioramas (moose, bison, flamingos, bears, birds of paradise, snakes, woodchucks and opossums), endangered and extinct species , dinosaurs and fossils, as well as geological displays, ethnographic displays, and various historical and cultural artifacts from around

8658-556: The latter being the key to understanding, for example, the cause of various aviation accidents. Many of the most pressing scientific problems that are faced today are due to the limitations of the materials that are available, and, as a result, breakthroughs in this field are likely to have a significant impact on the future of technology. The basis of materials science involves studying the structure of materials and relating them to their properties . Understanding this structure-property correlation, material scientists can then go on to study

8775-530: The location of the Fairbanks Scales headquarters and factories since the 1820s, as well as several other mansions and estates owned by members of the family. Before founding the museum, Franklin Fairbanks had served as president of the company, which his father and uncle had founded. The location for the museum, a plot of land Fairbanks already owned in the St. Johnsbury village, had been inspected, approved, cleared, and prepared in 1889. Construction on

8892-540: The main building began with a ceremony on 4 July 1890 when Frances Clapp Fairbanks laid the cornerstone. The building was finished by spring 1891, opening to the public later that year. Designed by Lambert Packard , the building features red sandstone and limestone laid in Richardsonian-Romanesque style. The museum was expanded in 1894 to house the entire growing collection, moving from its previous location, Fairbanks' own house, Undercliffe Mansion, where

9009-555: The main building, where they also serve as a weather recording exhibit, as well as on a truss affixed on top of the museum roof. The Northern New England Weather Center, also known as the Eye on the Sky Weather Center, was established at the museum in November 1981 by meteorologists Steve Maleski and Mark Breen, continuing the written weather reports for the NWS , but expanding to include local radio and print media weather forecasting, with

9126-454: The most respected criteria in today's global scientific community. In natural science, impossibility assertions come to be widely accepted as overwhelmingly probable rather than considered proven to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying theory, very successful in making predictions, whose assumptions lead logically to

9243-413: The motion of the earth, whether elemental chemicals exist, and where in the atmosphere rain is formed. In the centuries up through the end of the Middle Ages, natural science was often mingled with philosophies about magic and the occult. Natural philosophy appeared in various forms, from treatises to encyclopedias to commentaries on Aristotle. The interaction between natural philosophy and Christianity

9360-416: The museum for temporary display by NASA as part of a public science outreach initiative by the agency in observation of the event. During closure due to the COVID-19 pandemic , the planetarium hosted live online events, answering questions submitted by local residents and students about the topics, including the 2020 Winter Solstice Jupiter-Saturn Conjunction , featuring telescope views and descriptions of

9477-405: The museum now occupied by the planetarium previously contained a historical exhibit about Vermont during the colonial period . During the earlier years of its operation, the planetarium originally used simple folding chairs situated around a projection module, but in the early 1980s the chairs were replaced by rows of curved benches arranged in semicircles on either side. In 2012, the planetarium

9594-465: The museum, and produces public astronomy shows, as well as educational classes on various space science topics. Other productions of the planetarium include the Eye on the Night Sky astronomy program for radio broadcast, and the Night Owl astronomy & spaceflight news articles for online and print publication. The town of St. Johnsbury had a long history with the Fairbanks family, having been

9711-508: The observatory site and across the state. In more recent years, Spitzer Planetarium presenters also utilize a smaller, inflatable dome, called a "portable planetarium", featuring the same projection software as the main planetarium, for presentations at schools, libraries, and other indoor event spaces in the region. Annual spring astronomy camp includes astronomy lessons about planets, stars, constellations, and space probe missions, as well as basic chemistry and physics lessons, which includes

9828-409: The origins of natural science as far back as pre-literate human societies, where understanding the natural world was necessary for survival. People observed and built up knowledge about the behavior of animals and the usefulness of plants as food and medicine, which was passed down from generation to generation. These primitive understandings gave way to more formalized inquiry around 3500 to 3000 BC in

9945-603: The physical world, largely from a cosmological and cosmographical perspective, putting forth theories on the arrangement of celestial bodies and the heavens, which were posited as being composed of aether . Aristotle's works on natural philosophy continued to be translated and studied amid the rise of the Byzantine Empire and Abbasid Caliphate . In the Byzantine Empire, John Philoponus , an Alexandrian Aristotelian commentator and Christian theologian,

10062-508: The physical world; Plato criticized pre-Socratic thinkers as materialists and anti-religionists. Aristotle , however, a student of Plato who lived from 384 to 322 BC, paid closer attention to the natural world in his philosophy. In his History of Animals , he described the inner workings of 110 species, including the stingray , catfish and bee . He investigated chick embryos by breaking open eggs and observing them at various stages of development. Aristotle's works were influential through

10179-506: The plane by translation. In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation. In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane. Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon

10296-403: The plane of a regular hexagon with circumradius R {\displaystyle R} , whose distances to the centroid of the regular hexagon and its six vertices are L {\displaystyle L} and d i {\displaystyle d_{i}} respectively, we have If d i {\displaystyle d_{i}} are the distances from

10413-630: The principles of the universe has a long history and largely derives from direct observation and experimentation. The formulation of theories about the governing laws of the universe has been central to the study of physics from very early on, with philosophy gradually yielding to systematic, quantitative experimental testing and observation as the source of verification. Key historical developments in physics include Isaac Newton 's theory of universal gravitation and classical mechanics , an understanding of electricity and its relation to magnetism , Einstein 's theories of special and general relativity ,

10530-517: The regular hexagonal tiling , {6,3}, with three hexagonal faces around each vertex. A regular hexagon can also be created as a truncated equilateral triangle , with Schläfli symbol t{3}. Seen with two types (colors) of edges, this form only has D 3 symmetry. A truncated hexagon, t{6}, is a dodecagon , {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle , {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating

10647-406: The regular hexagon these are given by a = r , and p = 6 R = 4 r 3 {\displaystyle {}=6R=4r{\sqrt {3}}} , so The regular hexagon fills the fraction 3 3 2 π ≈ 0.8270 {\displaystyle {\tfrac {3{\sqrt {3}}}{2\pi }}\approx 0.8270} of its circumscribed circle . If

10764-556: The relationship between the pulse, the heart, and the flow of blood in the body centuries before it became accepted in the West. Little evidence survives of how Ancient Indian cultures around the Indus River understood nature, but some of their perspectives may be reflected in the Vedas , a set of sacred Hindu texts. They reveal a conception of the universe as ever-expanding and constantly being recycled and reformed. Surgeons in

10881-426: The relative performance of a material in a particular application. The major determinants of the structure of a material and, thus, of its properties are its constituent chemical elements and how it has been processed into its final form. These characteristics, taken together and related through the laws of thermodynamics and kinetics , govern a material's microstructure and thus its properties. Some scholars trace

10998-401: The replacement of the benches with modern seating in a more traditional theater arrangement, and rotating the hemispherical projection screen forward, both expanding audience capacity and improving comfortability of the domed theater. An elevator was also installed to improve accessibility, connecting the main museum entrance with the planetarium lobby. The Fairbanks Museum & Planetarium set

11115-485: The same occasion. In July 2021, the museum hosted an event both on-site and online with Dr. Jennifer Gruber , a program manager and engineer working on NASA's Artemis Program at the Moon, providing updates about the program including SLS , HLS , and CLPS developments, and taking questions from the audience. For the upcoming 2024 North American Solar Eclipse , the museum is expecting a greater event than that of 2017, as

11232-540: The same plane. The interior of such a hexagon is not generally defined. A skew zig-zag hexagon has vertices alternating between two parallel planes. A regular skew hexagon is vertex-transitive with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in the vertices and side edges of a triangular antiprism with the same D 3d , [2 ,6] symmetry, order 12. The cube and octahedron (same as triangular antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon

11349-504: The science that deals with bodies in motion. Roger Bacon , an English friar and philosopher, wrote that natural science dealt with "a principle of motion and rest, as in the parts of the elements of fire, air, earth, and water, and in all inanimate things made from them." These sciences also covered plants, animals and celestial bodies. Later in the 13th century, a Catholic priest and theologian Thomas Aquinas defined natural science as dealing with "mobile beings" and "things which depend on

11466-456: The sciences into eight parts, including: physics, cosmology, meteorology, minerals science, and plant and animal science. Later, philosophers made their own classifications of the natural sciences. Robert Kilwardby wrote On the Order of the Sciences in the 13th century that classed medicine as a mechanical science, along with agriculture, hunting, and theater, while defining natural science as

11583-475: The scientific study of matter at the atomic and molecular scale, chemistry deals primarily with collections of atoms, such as gases , molecules, crystals , and metals . The composition, statistical properties, transformations, and reactions of these materials are studied. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications. Most chemical processes can be studied directly in

11700-418: The semicentennial of Apollo 11 ; on 20 July, it hosted an event which featured a real-time rebroadcast of the mission, showings of contemporary documentaries from 1969, model rocket construction and launching, spaceflight simulations , planetarium shows focused on the Moon and both past and future human lunar exploration , as well as lunar regolith and rock samples from various Apollo missions obtained by

11817-402: The site since 1893. Meteorologists broadcast their unique weather forecasts for Vermont, New Hampshire, and areas immediately around the region, on Vermont Public Radio and Magic 97.7. The facility also produces daily weather forecasts for three newspapers: The Caledonian Record , Times Argus , and Rutland Herald . The Lyman Spitzer Jr. Planetarium , established in 1960, is located at

11934-415: The study of celestial features and phenomena can be traced back to antiquity, the scientific methodology of this field began to develop in the middle of the 17th century. A key factor was Galileo 's introduction of the telescope to examine the night sky in more detail. The mathematical treatment of astronomy began with Newton 's development of celestial mechanics and the laws of gravitation . However, it

12051-401: The successive sides of a cyclic hexagon are a , b , c , d , e , f , then the three main diagonals intersect in a single point if and only if ace = bdf . If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent . If

12168-491: The teaching of the faith," he wrote in 1271. By the 16th and 17th centuries, natural philosophy evolved beyond commentary on Aristotle as more early Greek philosophy was uncovered and translated. The invention of the printing press in the 15th century, the invention of the microscope and telescope, and the Protestant Reformation fundamentally altered the social context in which scientific inquiry evolved in

12285-520: The time of the Abbasid Caliphate from the 9th century onward, when Muslim scholars expanded upon Greek and Indian natural philosophy. The words alcohol , algebra and zenith all have Arabic roots. Aristotle's works and other Greek natural philosophy did not reach the West until about the middle of the 12th century, when works were translated from Greek and Arabic into Latin . The development of European civilization later in

12402-617: The two planets and their moons, live coverage of the Mars 2020 Perseverance rover landing, hosted by Fairbanks science communicators, featuring live telemetry from NASA JPL during the craft's descent, and a commemoration of Yuri's Night 2021 , the 60th anniversary of Vostok 1 , 40th anniversary of STS-1 , the first flight of the Mars 2020 Ingenuity helicopter , as well as International Space Station port relocations and crew rotations of Soyuz MS-17 / 18 and Dragon Crew-1 / 2 happening around

12519-422: The vertices of a regular hexagon to any point on its circumcircle, then The regular hexagon has D 6 symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D 6 ), 2 dihedral: (D 3, D 2 ), 4 cyclic : (Z 6 , Z 3 , Z 2 , Z 1 ) and the trivial (e) These symmetries express nine distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. r12

12636-480: The weather station and some educational programs continued to operate, holding regular online classes and science livestreams, as well as pandemic situation updates for local residents in Vermont and New Hampshire. Between 2020 and 2023, major modification and construction is taking place to expand the eastern side of main building in a project known as the "Tang Science Annex", to provide more exhibition area and greater accessibility, with major funding being provided by

12753-447: The work of Robert Boyle , the discoverer of gases , and Antoine Lavoisier , who developed the theory of the conservation of mass . The discovery of the chemical elements and atomic theory began to systematize this science, and researchers developed a fundamental understanding of states of matter , ions , chemical bonds and chemical reactions . The success of this science led to a complementary chemical industry that now plays

12870-457: The world floated on water and that water was the fundamental element in nature. In the 5th century BC, Leucippus was an early exponent of atomism , the idea that the world is made up of fundamental indivisible particles. Pythagoras applied Greek innovations in mathematics to astronomy and suggested that the earth was spherical . Later Socratic and Platonic thought focused on ethics, morals, and art and did not attempt an investigation of

12987-464: The world. On the second floor there is an exhibit about atmospheric ice crystal formation, featuring photographs by Snowflake Bentley , a friend of Franklin Fairbanks. Also displayed are 19th and 20th century manufacturing hardware and scales from the E & T Fairbanks Scales Company , founded by Franklin's father and uncle, Erastus and Thaddeus Fairbanks . Educational classes are regularly provided for local schools and tour groups. An audio tour of

13104-440: Was complex during this period; some early theologians, including Tatian and Eusebius , considered natural philosophy an outcropping of pagan Greek science and were suspicious of it. Although some later Christian philosophers, including Aquinas, came to see natural science as a means of interpreting scripture, this suspicion persisted until the 12th and 13th centuries. The Condemnation of 1277 , which forbade setting philosophy on

13221-410: Was not until the 19th century that biology became a unified science. Once scientists discovered commonalities between all living things, it was decided they were best studied as a whole. Some key developments in biology were the discovery of genetics , evolution through natural selection , the germ theory of disease , and the application of the techniques of chemistry and physics at the level of

13338-504: Was seen by some detractors as heresy . By the 12th century, Western European scholars and philosophers came into contact with a body of knowledge of which they had previously been ignorant: a large corpus of works in Greek and Arabic that were preserved by Islamic scholars. Through translation into Latin, Western Europe was introduced to Aristotle and his natural philosophy. These works were taught at new universities in Paris and Oxford by

13455-541: Was the first to question Aristotle's physics teaching. Unlike Aristotle, who based his physics on verbal argument, Philoponus instead relied on observation and argued for observation rather than resorting to a verbal argument. He introduced the theory of impetus . John Philoponus' criticism of Aristotelian principles of physics served as inspiration for Galileo Galilei during the Scientific Revolution . A revival in mathematics and science took place during

13572-435: Was triggered by earlier work of astronomers such as Kepler . By the 19th century, astronomy had developed into formal science, with the introduction of instruments such as the spectroscope and photography , along with much-improved telescopes and the creation of professional observatories. The distinctions between the natural science disciplines are not always sharp, and they share many cross-discipline fields. Physics plays

13689-447: Was upgraded with the installation of digital hardware and software, greatly increasing capabilities, and allowing for the projection of specialized 360° video. However, the analog hardware originally used in the 1960s, including a control panel and a dodecahedron with optical pinholes used for star projection, are on permanent display on the main floor of the museum. The planetarium was further renovated between 2018 and 2019, including

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