Misplaced Pages

#699300

86-480: The wide beach of fine sand is popular with sunbathers , swimmers and surfers . A local landmark is Contis Lighthouse ( Contis Phare ). The lighthouse stands 38 metres high and has 192 steps. It is painted white with a spiralling dark stripe, like a sucre d'orge . It is the only lighthouse from Capbreton to Cap Ferret . Contis village also has shops and services fulfilling the needs of holidaymakers. The French television drama series La Dernière Vague

172-466: A spiral . Archimedes' other mathematical achievements include deriving an approximation of pi ( π ) , defining and investigating the Archimedean spiral , and devising a system using exponentiation for expressing very large numbers . He was also one of the first to apply mathematics to physical phenomena , working on statics and hydrostatics . Archimedes' achievements in this area include

258-470: A Circle . The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results." It

344-441: A ball into a container after each mile traveled. As legend has it, Archimedes arranged mirrors as a parabolic reflector to burn ships attacking Syracuse using focused sunlight. While there is no extant contemporary evidence of this feat and modern scholars believe it did not happen, Archimedes may have written a work on mirrors entitled Catoptrica , and Lucian and Galen , writing in the second century AD, mentioned that during

430-497: A circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 3 ⁠ 1 / 7 ⁠ (approx. 3.1429) and 3 ⁠ 10 / 71 ⁠ (approx. 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle ( π r 2 {\displaystyle \pi r^{2}} ). In On

516-434: A diameter of between 0.074 and 4.75 millimeters. By another definition, in terms of particle size as used by geologists , sand particles range in diameter from 0.0625 mm (or 1 ⁄ 16  mm) a volume of approximately 0.00012 cubic millimetres, to 2 mm, a volume of approximately 4.2 cubic millimetres, the difference in volumes being 34,688 measures difference. Any particle falling within this range of sizes

602-434: A documentary called " Sand Wars " about the impact of the lack of construction sand. It shows the ecological and economic effects of both legal and illegal trade in construction sand. To retrieve the sand, the method of hydraulic dredging is used. This works by pumping the top few meters of sand out of the water and filling it into a boat, which is then transported back to land for processing. All marine life mixed in with

688-610: A high olivine content. Many sands, especially those found extensively in Southern Europe , have iron impurities within the quartz crystals of the sand, giving a deep yellow color. Sand deposits in some areas contain garnets and other resistant minerals, including some small gemstones . Rocks erode or weather over a long period of time, mainly by water and wind, and their sediments are transported downstream. These sediments continue to break apart into smaller pieces until they become fine grains of sand. The type of rock

774-408: A line which rotates with constant angular velocity . Equivalently, in modern polar coordinates ( r , θ ), it can be described by the equation r = a + b θ {\displaystyle \,r=a+b\theta } with real numbers a and b . This is an early example of a mechanical curve (a curve traced by a moving point ) considered by a Greek mathematician. This

860-435: A mischaracterization. Archimedes was able to use indivisibles (a precursor to infinitesimals ) in a way that is similar to modern integral calculus . Through proof by contradiction ( reductio ad absurdum ), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion , and he employed it to approximate

946-460: A number that was greater than the grains of sand needed to fill the universe. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: There are some, King Gelo , who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. To solve

SECTION 10

#1732779869700

1032-740: A person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. Polybius remarks how, during the Second Punic War , Syracuse switched allegiances from Rome to Carthage , resulting in a military campaign under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher , who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved catapults , crane-like machines that could be swung around in an arc, and other stone-throwers . Although

1118-411: A proof of the law of the lever , the widespread use of the concept of center of gravity , and the enunciation of the law of buoyancy known as Archimedes' principle . He is also credited with designing innovative machines , such as his screw pump , compound pulleys , and defensive war machines to protect his native Syracuse from invasion. Archimedes died during the siege of Syracuse , when he

1204-620: A reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account. A similar quotation is found in the work of Valerius Maximus (fl. 30 AD), who wrote in Memorable Doings and Sayings , " ... sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare' " ("... but protecting

1290-489: A result. People sometimes dig holes in the sand at beaches for recreational purposes, but if too deep they can result in serious injury or death in the event of a collapse. Manufactured sand (M sand) is sand made from rock by artificial processes, usually for construction purposes in cement or concrete. It differs from river sand by being more angular, and has somewhat different properties. In Dubai , United Arab Emirates , sand needed to construct infrastructure and create

1376-483: A significant dredging industry, raising environmental concerns over fish depletion, landslides, and flooding. Countries such as China, Indonesia, Malaysia, and Cambodia ban sand exports, citing these issues as a major factor. It is estimated that the annual consumption of sand and gravel is 40 billion tons and sand is a US$ 70 billion global industry. With increasing use, more is expected to come from recycling and alternatives to sand. The global demand for sand in 2017

1462-408: A solution that applied the hydrostatics principle known as Archimedes' principle , found in his treatise On Floating Bodies : a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of

1548-404: A temple dedicated to the goddess Aphrodite among its facilities. The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes. Archimedes' screw was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The screw

1634-420: Is silica (silicon dioxide, or SiO 2 ), usually in the form of quartz . Calcium carbonate is the second most common type of sand. One such example of this is aragonite , which has been created over the past 500   million years by various forms of life, such as coral and shellfish . It is the primary form of sand apparent in areas where reefs have dominated the ecosystem for millions of years, as in

1720-410: Is 4 π r for the sphere, and 6 π r for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral . It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along

1806-508: Is called grus in geology or sharp sand in the building trade where it is preferred for concrete, and in gardening where it is used as a soil amendment to loosen clay soils. Sand that is transported long distances by water or wind will be rounded, with characteristic abrasion patterns on the grain surface. Desert sand is typically rounded. People who collect sand as a hobby are known as arenophiles . Organisms that thrive in sandy environments are psammophiles. Only some sands are suitable for

SECTION 20

#1732779869700

1892-427: Is defined by its grain size. Sand grains are smaller than gravel and coarser than silt . Sand can also refer to a textural class of soil or soil type; i.e., a soil containing more than 85 percent sand-sized particles by mass. The composition of sand varies, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non- tropical coastal settings

1978-504: Is possible that he used an iterative procedure to calculate these values. In Quadrature of the Parabola , Archimedes proved that the area enclosed by a parabola and a straight line is ⁠ 4 / 3 ⁠ times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio ⁠ 1 / 4 ⁠ : If

2064-532: Is still in use today for pumping liquids and granulated solids such as coal and grain. Described by Vitruvius , Archimedes' device may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon . The world's first seagoing steamship with a screw propeller was the SS Archimedes , which was launched in 1839 and named in honor of Archimedes and his work on

2150-433: Is termed a sand grain . Sand grains are between gravel (with particles ranging from 2 mm up to 64 mm by the latter system, and from 4.75 mm up to 75 mm in the former) and silt (particles smaller than 0.0625 mm down to 0.004 mm). The size specification between sand and gravel has remained constant for more than a century, but particle diameters as small as 0.02 mm were considered sand under

2236-474: Is the most common mineral resistant to weathering . The composition of mineral sand is highly variable, depending on the local rock sources and conditions. The bright white sands found in tropical and subtropical coastal settings are eroded limestone and may contain coral and shell fragments in addition to other organic or organically derived fragmental material, suggesting that sand formation depends on living organisms, too. The gypsum sand dunes of

2322-738: The Albert Atterberg standard in use during the early 20th century. The grains of sand in Archimedes ' The Sand Reckoner written around 240 BCE, were 0.02 mm in diameter. A 1938 specification of the United States Department of Agriculture was 0.05 mm. A 1953 engineering standard published by the American Association of State Highway and Transportation Officials set the minimum sand size at 0.074 mm. Sand feels gritty when rubbed between

2408-566: The Byzantine Greek architect Isidore of Miletus ( c.  530 AD ), while commentaries on the works of Archimedes written by Eutocius in the same century helped bring his work to a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and into Latin via Arabic by Gerard of Cremona (c. 1114–1187). Direct Greek to Latin translations were later done by William of Moerbeke (c. 1215–1286) and Iacobus Cremonensis (c. 1400–1453). During

2494-748: The Caribbean . Somewhat more rarely, sand may be composed of calcium sulfate , such as gypsum and selenite , as is found in places such as White Sands National Park and Salt Plains National Wildlife Refuge in the U.S. Sand is a non-renewable resource over human timescales, and sand suitable for making concrete is in high demand. Desert sand, although plentiful, is not suitable for concrete. Fifty billion tons of beach sand and fossil sand are used each year for construction. The exact definition of sand varies. The scientific Unified Soil Classification System used in engineering and geology corresponds to US Standard Sieves, and defines sand as particles with

2580-470: The Dubai Islands exceeds local supplies, requiring sand from Australia . The artificial islands required more than 835 million tonnes of sand, at a cost greater than $ 26 billion USD. [REDACTED] Earth Sciences portal Archimedes Archimedes of Syracuse ( / ˌ ɑːr k ɪ ˈ m iː d iː z / AR -kim- EE -deez ; c.  287  – c.  212   BC )

2666-514: The Krumbein phi scale , where size is Φ = -log 2 D; D being the particle size in mm. On this scale, for sand the value of Φ varies from −1 to +4, with the divisions between sub-categories at whole numbers. The most common constituent of sand, in inland continental settings and non-tropical coastal settings, is silica (silicon dioxide, or SiO 2 ), usually in the form of quartz , which, because of its chemical inertness and considerable hardness,

Contis - Misplaced Pages Continue

2752-595: The Renaissance and again in the 17th century , while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results. Archimedes was born c. 287 BC in the seaport city of Syracuse , Sicily , at that time a self-governing colony in Magna Graecia . The date of birth is based on a statement by

2838-586: The Renaissance , the Editio princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin. The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986). This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who

2924-687: The White Sands National Park in New Mexico are famous for their bright, white color. Arkose is a sand or sandstone with considerable feldspar content, derived from weathering and erosion of a (usually nearby) granitic rock outcrop. Some sands contain magnetite , chlorite , glauconite , or gypsum . Sands rich in magnetite are dark to black in color, as are sands derived from volcanic basalts and obsidian . Chlorite - glauconite bearing sands are typically green in color, as are sands derived from basaltic lava with

3010-479: The heliocentric theory of the solar system proposed by Aristarchus of Samos , as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies . By using a system of numbers based on powers of the myriad , Archimedes concludes that the number of grains of sand required to fill the universe is 8 × 10 in modern notation. The introductory letter states that Archimedes' father

3096-643: The lever , he gave a mathematical proof of the principle involved in his work On the Equilibrium of Planes . Earlier descriptions of the principle of the lever are found in a work by Euclid and in the Mechanical Problems , belonging to the Peripatetic school of the followers of Aristotle , the authorship of which has been attributed by some to Archytas . There are several, often conflicting, reports regarding Archimedes' feats using

3182-439: The siege of Syracuse Archimedes had burned enemy ships. Nearly four hundred years later, Anthemius , despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry. The purported device, sometimes called " Archimedes' heat ray ", has been the subject of an ongoing debate about its credibility since the Renaissance . René Descartes rejected it as false, while modern researchers have attempted to recreate

3268-549: The Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II , the ruler of Syracuse, although Cicero suggests he was of humble origin. In the Sand-Reckoner , Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes

3354-478: The Earth" ( Greek : δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ). Olympiodorus later attributed the same boast to Archimedes' invention of the baroulkos , a kind of windlass , rather than the lever. A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse . Athenaeus of Naucratis quotes a certain Moschion in a description on how King Hiero II commissioned

3440-519: The Earth, Sun, and Moon, as well as Aristarchus ' heliocentric model of the universe, in the Sand-Reckoner . Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves), applying correction factors to these measurements, and finally giving

3526-581: The Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness. Cicero (106–43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see

Contis - Misplaced Pages Continue

3612-487: The Sahara is sand dunes, while 70% is bare rock. The wind is responsible for creating these different environments and shaping the sand to be round and smooth. These properties make desert sand unusable for construction. Beach sand is also formed by erosion. Over thousands of years, rocks are eroded near the shoreline from the constant motion of waves and the sediments build up. Weathering and river deposition also accelerate

3698-528: The Sphere and Cylinder , Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. Archimedes gives the value of the square root of 3 as lying between ⁠ 265 / 153 ⁠ (approximately 1.7320261) and ⁠ 1351 / 780 ⁠ (approximately 1.7320512) in Measurement of

3784-412: The areas of figures and the value of π . In Measurement of a Circle , he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon , calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of

3870-416: The capture of Syracuse and Archimedes' role in it. Plutarch (45–119 AD) provides at least two accounts on how Archimedes died after Syracuse was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged

3956-419: The capture of Syracuse in the Second Punic War , Marcellus is said to have taken back to Rome two mechanisms which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets. Cicero also mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus . The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated

4042-431: The carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof , that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built. The Roman historian Livy (59 BC–17 AD) retells Polybius's story of

4128-410: The concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems . These include the area of a circle , the surface area and volume of a sphere , the area of an ellipse , the area under a parabola , the volume of a segment of a paraboloid of revolution , the volume of a segment of a hyperboloid of revolution , and the area of

4214-441: The construction industry, for example for making concrete . Grains of desert sand are rounded by being blown in the wind, and for this reason do not produce solid concrete, unlike the rough sand from the sea. Because of the growth of population and of cities and the consequent construction activity there is a huge demand for these special kinds of sand, and natural sources are running low. In 2012 French director Denis Delestrac made

4300-503: The construction of these mechanisms entitled On Sphere-Making . Modern research in this area has been focused on the Antikythera mechanism , another device built c.  100 BC probably designed with a similar purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing . This was once thought to have been beyond the range of the technology available in ancient times, but

4386-470: The density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in. The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement . Archimedes may have instead sought

SECTION 50

#1732779869700

4472-456: The design of a huge ship, the Syracusia , which could be used for luxury travel, carrying supplies, and as a display of naval power . The Syracusia is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. The ship presumably was capable of carrying 600 people and included garden decorations, a gymnasium , and

4558-616: The dialect of ancient Syracuse. Many written works by Archimedes have not survived or are only extant in heavily edited fragments; at least seven of his treatises are known to have existed due to references made by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra , while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica . Archimedes made his work known through correspondence with mathematicians in Alexandria . The writings of Archimedes were first collected by

4644-524: The discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics . Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", though some scholars believe this may be

4730-426: The dust with his hands, said 'I beg of you, do not disturb this ' "). The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a crown for a temple had been made for King Hiero II of Syracuse , who supplied the pure gold to be used. The crown was likely made in the shape of a votive wreath . Archimedes

4816-609: The effect using only the means that would have been available to Archimedes, mostly with negative results. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship, but the overall effect would have been blinding, dazzling , or distracting the crew of the ship rather than fire. Using modern materials and larger scale, sunlight-concentrating solar furnaces can reach very high temperatures, and are sometimes used for generating electricity . Archimedes discusses astronomical measurements of

4902-438: The extracted sand is killed and the ecosystem can continue to suffer for years after the mining is complete. Not only does this affect marine life, but also the local fishing industries because of the loss of life, and communities living close to the water's edge. When sand is taken out of the water it increases the risk of landslides, which can lead to loss of agricultural land and/or damage to dwellings. Sand's many uses require

4988-541: The feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device. Archimedes has also been credited with improving the power and accuracy of the catapult , and with inventing the odometer during the First Punic War . The odometer was described as a cart with a gear mechanism that dropped

5074-660: The fingers. Silt , by comparison, feels like flour . ISO 14688 grades sands as fine, medium, and coarse with ranges 0.063 mm to 0.2 mm to 0.63 mm to 2.0 mm. In the United States, sand is commonly divided into five sub-categories based on size: very fine sand ( 1 ⁄ 16 – 1 ⁄ 8  mm diameter), fine sand ( 1 ⁄ 8  mm – 1 ⁄ 4  mm), medium sand ( 1 ⁄ 4  mm – 1 ⁄ 2  mm), coarse sand ( 1 ⁄ 2  mm – 1 mm), and very coarse sand (1 mm – 2 mm). These sizes are based on

5160-551: The first comprehensive compilation was not made until c.  530   AD by Isidore of Miletus in Byzantine Constantinople , while Eutocius ' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during

5246-519: The first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines , and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to  ⁠ 1 / 3 ⁠ . In The Sand Reckoner , Archimedes set out to calculate

SECTION 60

#1732779869700

5332-477: The globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth when the Sun was in line. This is a description of a small planetarium . Pappus of Alexandria reports on a now lost treatise by Archimedes dealing with

5418-416: The lever to lift very heavy objects. Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. According to Pappus of Alexandria , Archimedes' work on levers and his understanding of mechanical advantage caused him to remark: "Give me a place to stand on, and I will move

5504-584: The other to the Temple of Virtue in Rome. Marcellus's mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus , who described it thus: Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. When Gallus moved

5590-420: The principles derived to calculate the areas and centers of gravity of various geometric figures including triangles , parallelograms and parabolas . In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He achieves this in one of his proofs by calculating

5676-496: The problem, Archimedes devised a system of counting based on the myriad . The word itself derives from the Greek μυριάς , murias , for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion , or 8 × 10 . The works of Archimedes were written in Doric Greek ,

5762-437: The process of creating a beach, along with marine animals interacting with rocks, such as eating the algae off of them. Once there is a sufficient amount of sand, the beach acts as a barrier to keep the land from eroding any further. This sand is ideal for construction as it is angular and of various sizes. Marine sand (or ocean sand) comes from sediments transported into the ocean and the erosion of ocean rocks. The thickness of

5848-461: The rate the sand can replenish, making it a non-renewable resource. Sand dunes are a consequence of dry conditions or wind deposition. The Sahara Desert is very dry because of its geographic location and proximity to the equator . It is known for its vast sand dunes, which exist mainly due to a lack of vegetation and water. Over time, wind blows away fine particles, such as clay and dead organic matter, leaving only sand and larger rocks. Only 15% of

5934-457: The result in the form of upper and lower bounds to account for observational error. Ptolemy , quoting Hipparchus, also references Archimedes' solstice observations in the Almagest . This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years. Cicero's De re publica portrays a fictional conversation taking place in 129 BC. After

6020-453: The same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo Galilei , who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." While Archimedes did not invent

6106-460: The sand because they do not have as much time to dissolve away. The term for sand formed by weathering is "epiclastic." Sand from rivers are collected either from the river itself or its flood plain and accounts for the majority of the sand used in the construction industry. Because of this, many small rivers have been depleted, causing environmental concern and economic losses to adjacent land. The rate of sand mining in such areas greatly outweighs

6192-480: The sand layer varies, however it is common to have more sand closer to land; this type of sand is ideal for construction and is a very valuable commodity. Europe is the main miners of marine sand, which greatly hurts ecosystems and local fisheries. The study of individual grains can reveal much historical information as to the origin and kind of transport of the grain. Quartz sand that is recently weathered from granite or gneiss quartz crystals will be angular. It

6278-416: The screw. Archimedes is said to have designed a claw as a weapon to defend the city of Syracuse. Also known as " the ship shaker ", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test

6364-411: The sediment originated from and the intensity of the environment give different compositions of sand. The most common rock to form sand is granite , where the feldspar minerals dissolve faster than the quartz , causing the rock to break apart into small pieces. In high energy environments rocks break apart much faster than in more calm settings. In granite rocks this results in more feldspar minerals in

6450-559: The soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus ") and had ordered that he should not be harmed. The last words attributed to Archimedes are " Do not disturb my circles " ( Latin , " Noli turbare circulos meos "; Katharevousa Greek , "μὴ μου τοὺς κύκλους τάραττε"),

6536-493: The user to wear respiratory protection to avoid breathing the resulting fine silica dust . Safety data sheets for silica sand state that "excessive inhalation of crystalline silica is a serious health concern." In areas of high pore water pressure , sand and salt water can form quicksand , which is a colloid hydrogel that behaves like a liquid. Quicksand produces a considerable barrier to escape for creatures caught within, who often die from exposure (not from submersion) as

6622-418: The value of a geometric series that sums to infinity with the ratio 1/4. In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter . The volume is ⁠ 4 / 3 ⁠ π r for the sphere, and 2 π r for the cylinder. The surface area

6708-635: Was 9.55 billion tons as part of a $ 99.5 billion industry. In April 2022, the United Nations Environment Programme (UNEP) published a report stating that 50 billion tons of sand and gravel were being used every year. The report made 10 recommendations, including a ban on beach extraction, to avert a crisis, and move toward a circular economy for the two resources. While sand is generally non-toxic, sand-using activities such as sandblasting require precautions. Bags of silica sand used for sandblasting now carry labels warning

6794-411: Was a student of Conon of Samos . In Proposition II, Archimedes gives an approximation of the value of pi ( π ), showing that it is greater than ⁠ 223 / 71 ⁠ (3.1408...) and less than ⁠ 22 / 7 ⁠ (3.1428...). In this treatise, also known as Psammites , Archimedes finds a number that is greater than the grains of sand needed to fill the universe. This book mentions

6880-480: Was an Ancient Greek mathematician , physicist , engineer , astronomer , and inventor from the ancient city of Syracuse in Sicily . Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity . Regarded as the greatest mathematician of ancient history , and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying

6966-494: Was an astronomer named Phidias. The Sand Reckoner is the only surviving work in which Archimedes discusses his views on astronomy. There are two books to On the Equilibrium of Planes : the first contains seven postulates and fifteen propositions , while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever , which states that: Magnitudes are in equilibrium at distances reciprocally proportional to their weights. Archimedes uses

7052-417: Was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density . In this account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the golden crown's volume . Archimedes

7138-407: Was filmed around Contis, making use of the distinctive lighthouse. 44°5′32″N 1°19′15″W  /  44.09222°N 1.32083°W  / 44.09222; -1.32083 This Landes geographical article is a stub . You can help Misplaced Pages by expanding it . Sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but

7224-412: Was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his most valued mathematical discovery. Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but

7310-471: Was so excited by this discovery that he took to the streets naked, having forgotten to dress, crying " Eureka !" ( Greek : "εὕρηκα , heúrēka !, lit.   ' I have found [it]! ' ). For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added,

7396-790: Was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria , Egypt, during his youth. From his surviving written works, it is clear that he maintained collegial relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene . The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius ( c. 200–118 BC), written about 70 years after his death. It sheds little light on Archimedes as

#699300