Misplaced Pages

#192807

89-574: Astolat Dollhouse Castle (also known as Astolat Castle or Dollhouse Castle ) is a museum-quality dollhouse , which was appraised as "the most valuable dollhouse in the world," at $ 8.5 million in 2015. Its great value is attributable to its hand-made intricate 800 pounds (360 kg), 9 feet (2.7 m) tall, 29 room structure, and its extensive collection of high-quality miniatures including extravagant furnishings, with working fireplaces, stained glass panels, and 10,000 handcrafted miniature pieces that include original works of art, gold chandeliers, and

178-414: A = 0 {\displaystyle a=0} . While not explicitly studied by Hamilton, this indirectly introduced notions of basis, here given by the quaternion elements i , j , k {\displaystyle i,j,k} , as well as the dot product and cross product , which correspond to (the negative of) the scalar part and the vector part of the product of two vector quaternions. It

267-487: A parallelogram , and hence are coplanar. A sphere in 3-space (also called a 2-sphere because it is a 2-dimensional object) consists of the set of all points in 3-space at a fixed distance r from a central point P . The solid enclosed by the sphere is called a ball (or, more precisely a 3-ball ). The volume of the ball is given by V = 4 3 π r 3 , {\displaystyle V={\frac {4}{3}}\pi r^{3},} and

356-565: A 1:18 (or 2/3") scale, while a 1:12 (or 1") scale is common for dollhouses made for adult collectors. Miniature homes, furnished with domestic articles and resident inhabitants, both people and animals, have been made for thousands of years. The earliest known examples were found in the Egyptian tombs of the Old Kingdom , created nearly five thousand years ago. These wooden models of servants, furnishings, boats, livestock and pets placed in

445-522: A choice of basis, corresponding to a set of axes. But in rotational symmetry, there is no reason why one set of axes is preferred to say, the same set of axes which has been rotated arbitrarily. Stated another way, a preferred choice of axes breaks the rotational symmetry of physical space. Computationally, it is necessary to work with the more concrete description R 3 {\displaystyle \mathbb {R} ^{3}} in order to do concrete computations. A more abstract description still

534-529: A custom basis by individual craftsmen. With the advent of the Industrial Revolution, factories began mass producing toys, including dollhouses and miniatures suitable for furnishing them. German companies noted for their dollhouses included Christian Hacker, Moritz Gottschalk , Elastolin , and Moritz Reichel. The list of important English companies includes Silber & Fleming, Evans & Cartwright, and Lines Brothers (which became Tri-ang). By

623-528: A field , which is not commutative nor associative , but is a Lie algebra with the cross product being the Lie bracket. Specifically, the space together with the product, ( R 3 , × ) {\displaystyle (\mathbb {R} ^{3},\times )} is isomorphic to the Lie algebra of three-dimensional rotations, denoted s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} . In order to satisfy

712-412: A given plane, intersect that plane in a unique point, or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line. A hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a three-dimensional space are the two-dimensional subspaces, that is, the planes. In terms of Cartesian coordinates, the points of

801-558: A hobby is due largely to the publications of two experts, Vivien Greene (1904-2003) in the UK, and Flora Gill Jacobs (1918-2006) in the US. Vivien Greene's first book, English Dolls' Houses of the 18th and 19th Centuries , was published in 1955; in the same year, an exhibition of period dolls houses from several countries was held in London. Flora Gill Jacobs' first book, A History of Dolls’ Houses ,

890-400: A hyperplane satisfy a single linear equation , so planes in this 3-space are described by linear equations. A line can be described by a pair of independent linear equations—each representing a plane having this line as a common intersection. Varignon's theorem states that the midpoints of any quadrilateral in R 3 {\displaystyle \mathbb {R} ^{3}} form

979-681: A photo presentation of the Astolat Dollhouse Castle was released courtesy of the Nassau County Museum of Art, an updated version released in 2009 showed some of the upgraded interior furnishings and acquisitions, and a video presentation that previewed a charity tour of the dollhouse. Other notable dollhouses include Titania's Palace , which is on display in Denmark, Tara's Palace, which is on display in Ireland at

SECTION 10

#1732780965193

1068-419: A plane curve about a fixed line in its plane as an axis is called a surface of revolution . The plane curve is called the generatrix of the surface. A section of the surface, made by intersecting the surface with a plane that is perpendicular (orthogonal) to the axis, is a circle. Simple examples occur when the generatrix is a line. If the generatrix line intersects the axis line, the surface of revolution

1157-442: A subtle way. By definition, there exists a basis B = { e 1 , e 2 , e 3 } {\displaystyle {\mathcal {B}}=\{e_{1},e_{2},e_{3}\}} for V {\displaystyle V} . This corresponds to an isomorphism between V {\displaystyle V} and R 3 {\displaystyle \mathbb {R} ^{3}} :

1246-686: A thinner plywood and are held together by a system of tabs and slots (plus glue). These houses are usually light-weight and lower cost but often require siding, shingles, or other exterior treatments to look realistic. Kits made from heavier plywood or MDF are held together with nails and glue. The dolls house hobby has two main focuses: construction and/or purchase of dolls houses made by or for adult enthusiasts, and collection of contemporary, vintage or antique dolls houses which were often originally made for children. Dollhouses for hobbyists and collectors are available in different forms, from ready made and decorated houses to kits to custom built houses made to

1335-445: A unique plane, so skew lines are lines that do not meet and do not lie in a common plane. Two distinct planes can either meet in a common line or are parallel (i.e., do not meet). Three distinct planes, no pair of which are parallel, can either meet in a common line, meet in a unique common point, or have no point in common. In the last case, the three lines of intersection of each pair of planes are mutually parallel. A line can lie in

1424-477: A vector A is denoted by || A || . The dot product of a vector A = [ A 1 , A 2 , A 3 ] with itself is which gives the formula for the Euclidean length of the vector. Without reference to the components of the vectors, the dot product of two non-zero Euclidean vectors A and B is given by where θ is the angle between A and B . The cross product or vector product

1513-644: Is 1:12 scale, also called 1" or one inch scale (where 1 foot is represented by 1 inch.) Among adult collectors there are also smaller scales which are much more common in the United States than in Britain. 1:24 or half inch scale (1 foot is 1/2") was popular in Marx dollhouses in the 1950s but only became widely available in collectible houses after 2002, about the same time that even smaller scales became more popular, like 1:48 or quarter inch scale (1 foot

1602-404: Is 1/4") and 1:144 or "dollhouse for a dollhouse" scale. 1/24th scale dolls houses, and those in smaller scales, may be considered as just one species of miniature houses of this size. 1/24th (or the almost indistinguishable 1/25th) is used for a variety of models including display models and what are coming to be known as 'house portraits'. These typically focus on the exterior detail rather than

1691-567: Is 4' 1" tall, contains 18 rooms, and required 15 years to construct. It was built in Ireland but was won by Denmark in a bidding war in 1978 at Sotheby's London Auction house. Tara's Palace is located in the Tara's Palace Museum of Childhood in the grounds of Powerscourt Estate near Enniskerry , Ireland . It required 10 years to build, is 4'6" in height, contains 22 rooms, and was built by Ron McDonnell beginning in 1978 after he failed to secure

1780-627: Is a binary operation on two vectors in three-dimensional space and is denoted by the symbol ×. The cross product A × B of the vectors A and B is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics , and engineering . In function language, the cross product is a function × : R 3 × R 3 → R 3 {\displaystyle \times :\mathbb {R} ^{3}\times \mathbb {R} ^{3}\rightarrow \mathbb {R} ^{3}} . The components of

1869-758: Is a right circular cone with vertex (apex) the point of intersection. However, if the generatrix and axis are parallel, then the surface of revolution is a circular cylinder . In analogy with the conic sections , the set of points whose Cartesian coordinates satisfy the general equation of the second degree, namely, A x 2 + B y 2 + C z 2 + F x y + G y z + H x z + J x + K y + L z + M = 0 , {\displaystyle Ax^{2}+By^{2}+Cz^{2}+Fxy+Gyz+Hxz+Jx+Ky+Lz+M=0,} where A , B , C , F , G , H , J , K , L and M are real numbers and not all of A , B , C , F , G and H are zero,

SECTION 20

#1732780965193

1958-466: Is called a quadric surface . There are six types of non-degenerate quadric surfaces: The degenerate quadric surfaces are the empty set, a single point, a single line, a single plane, a pair of planes or a quadratic cylinder (a surface consisting of a non-degenerate conic section in a plane π and all the lines of R through that conic that are normal to π ). Elliptic cones are sometimes considered to be degenerate quadric surfaces as well. Both

2047-625: Is called the Fairy Castle . It is 7' tall, has twelve rooms, and required 7 years to construct, beginning in 1928. In 2012 dollars, the fairy Castle would cost $ 7 million and when first put on tour it generated $ 9 million in revenue over a four-year period. It has been on display since the 1950s at the Museum of Science and Industry in Chicago, Illinois and is visited by an estimated 1.5 million people each year. The Astolat Dollhouse Castle

2136-400: Is commonly denoted R n , {\displaystyle \mathbb {R} ^{n},} and can be identified to the pair formed by a n -dimensional Euclidean space and a Cartesian coordinate system . When n = 3 , this space is called the three-dimensional Euclidean space (or simply "Euclidean space" when the context is clear). In classical physics , it serves as a model of

2225-564: Is filled with miniature items of the finest and most modern goods of the period. Writers like Sir Arthur Conan Doyle and Rudyard Kipling contributed special books which were written and bound in scale size. Titania's Palace is on display in Egeskov Castle in Denmark , a miniature castle that was hand-built by James Hicks & Sons, Irish Cabinet Makers who were commissioned by Sir Neville Wilkinson from 1907 to 1922. The palace

2314-406: Is found in linear algebra , where the idea of independence is crucial. Space has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is three-dimensional because every point in space can be described by a linear combination of three independent vectors . A vector can be pictured as an arrow. The vector's magnitude

2403-425: Is its length, and its direction is the direction the arrow points. A vector in R 3 {\displaystyle \mathbb {R} ^{3}} can be represented by an ordered triple of real numbers. These numbers are called the components of the vector. The dot product of two vectors A = [ A 1 , A 2 , A 3 ] and B = [ B 1 , B 2 , B 3 ] is defined as: The magnitude of

2492-720: Is now located at the Museum of the City of New York. The 68 miniature Thorne Rooms room boxes , each with a different theme, were designed by Narcissa Niblack Thorne and furniture for them was created by craftsmen in the 1930s and 40s. They are now at the Art Institute of Chicago , Phoenix Art Museum and the Knoxville Museum of Art in Knoxville, Tennessee. American silent film actress Colleen Moore's dollhouse

2581-551: Is on exhibit in the Museum of Childhood in London, England . Queen Mary's Dolls' House was designed for Queen Mary in 1924 by Sir Edwin Lutyens , a leading architect of the time, and is on display at Windsor Castle . When first put on display it was visited by 1.6 million people in seven months. It is approximately 5' tall, contains 16 rooms, and required 4 years to construct. The dollhouse has working plumbing and lights and

2670-506: Is rotated. The Astolat Dollhouse Castle was on rare public display at the Time-Warner Center at Columbus Circle, New York City from 12 November to 8 December 2015. All proceeds from this exhibition benefited charities for children, including St Jude's Children's Hospital , Orphans International , and others. Consisting of seven levels, stairways, and hallways, Astolat Dollhouse Castle was created for 360 degree viewing. As with

2759-669: Is the Kronecker delta . Written out in full, the standard basis is E 1 = ( 1 0 0 ) , E 2 = ( 0 1 0 ) , E 3 = ( 0 0 1 ) . {\displaystyle E_{1}={\begin{pmatrix}1\\0\\0\end{pmatrix}},E_{2}={\begin{pmatrix}0\\1\\0\end{pmatrix}},E_{3}={\begin{pmatrix}0\\0\\1\end{pmatrix}}.} Therefore R 3 {\displaystyle \mathbb {R} ^{3}} can be viewed as

Astolat Dollhouse Castle - Misplaced Pages Continue

2848-534: Is the Levi-Civita symbol . It has the property that A × B = − B × A {\displaystyle \mathbf {A} \times \mathbf {B} =-\mathbf {B} \times \mathbf {A} } . Its magnitude is related to the angle θ {\displaystyle \theta } between A {\displaystyle \mathbf {A} } and B {\displaystyle \mathbf {B} } by

2937-638: Is the largest museum of its kind in Europe. In Russia, the most famous dollhouse was made for Pavel Naschekin (1830s, now in the collection of National Pushkin Museum ). In the United Kingdom, the Uppark Baby-house (ca. 1730) is on exhibit at Uppark , West Sussex, owned by The National Trust. The Nostell Priory Baby-house (ca. 1730) is on exhibit at Nostell Priory , Yorkshire, also owned by The National Trust. The Tate House (1760)

3026-418: Is to model physical space as a three-dimensional affine space E ( 3 ) {\displaystyle E(3)} over the real numbers. This is unique up to affine isomorphism. It is sometimes referred to as three-dimensional Euclidean space. Just as the vector space description came from 'forgetting the preferred basis' of R 3 {\displaystyle \mathbb {R} ^{3}} ,

3115-540: The Colleen Moore dollhouse certain exterior walls are fixed to create a 3-D viewing experience. The basement level consists of the Knights Of Columbus room, wine cellar, kitchens, and the armory. The main floor contains the entrance foyer, main stairway, and butler's closet. Next level up contains the formal living room, dining room, and music room and its audience balcony. The fourth level contains

3204-499: The Euclidean space of dimension three, which models physical space . More general three-dimensional spaces are called 3-manifolds . The term may also refer colloquially to a subset of space, a three-dimensional region (or 3D domain ), a solid figure . Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n -dimensional Euclidean space. The set of these n -tuples

3293-573: The Moomin Museum displays the Moomin house , a dollhouse created around the Moomin characters of Tove Jansson . The house was built by Jansson, Tuulikki Pietilä and Pentti Eistola and later donated to the town of Tampere. The museum also contains dozens of roomboxes with Moomin characters, all made by Tuulikki Pietilä. The Dollhouse Museum ( German : Puppenhausmuseum ) in Basel , Switzerland

3382-704: The Tara's Palace Museum of Childhood in Powerscourt , and the Stettheimer dollhouse in New York City which is primarily known for its original miniature artwork. Queen Mary's Dolls' House in Windsor Castle in England includes contributions from many notable artists and craftsmen of the 1920s. Dollhouse The history of today's dollhouses can be traced back about four hundred years to

3471-611: The baby house display cases of Europe, which showed idealized interiors. Smaller dollhouses with more realistic exteriors appeared in Europe in the 18th century. Early dollhouses were all handmade, but following the Industrial Revolution and World War II , they were increasingly mass-produced and became more standardized and affordable. Dollhouses can range from simple boxes stacked together used as rooms for play, to multi-million dollar structures displayed in museums. Contemporary children's play dollhouses are mostly on

3560-465: The "wizard’s tower" outfitted with telescopes and zodiacal signs. The furnishings include seven periods and styles, including Spanish, Oriental, Tudor , 18th-century English, and Victorian . The Dollhouse Castle's namesake was inspired by the fantasy castle "Astolat" in Alfred Tennyson ’s poem Lady of Shalott . Astolat Castle has a copper roof and structural wood walls that are finished on

3649-513: The 19th century, developments of the geometry of three-dimensional space came with William Rowan Hamilton 's development of the quaternions . In fact, it was Hamilton who coined the terms scalar and vector , and they were first defined within his geometric framework for quaternions . Three dimensional space could then be described by quaternions q = a + u i + v j + w k {\displaystyle q=a+ui+vj+wk} which had vanishing scalar component, that is,

Astolat Dollhouse Castle - Misplaced Pages Continue

3738-473: The 19th century, the products were not made to a strict scale. Children's play dollhouses from most of the 20th and 21st centuries are 1:18 or two third inch scale (where 1 foot is represented by 2/3 of an inch). Common brands include Lundby (Sweden), Renwal, Plasco, Marx , Petite Princess, and T. Cohn (all American) and Caroline's Home, Barton, Dol-Toi and Tri-ang (English). A few brands use 1:16 or 3/4"-scale. The most common standard for adult collectors

3827-565: The Astolat Dollhouse Castle were designed with fixed contiguous exterior walls to create a three-dimensional viewing effect. As interest in doll houses expanded during the seventeenth century, there was also a shift in the gender-oriented organization of the miniature houses towards a more feminine focus. There is a shift of viewing doll houses as a collectible “male-oriented artefact to a female-organized model of domesticity”. Dutch doll houses resembled cabinets with separate compartments of fully furnished rooms than actual houses, which represented

3916-495: The Nassau County Museum of Art. Freeman is an avid collector of dollhouses and since her acquisition of the Astolat Dollhouse Castle she has continually upgraded its interiors with additional one-of-a-kind antique miniatures, tiny antique furniture, and paintings in addition to those that already existed within the structure. There are reportedly now about 30,000 miniatures pieces in the Astolat Dollhouse Castle collection, but only about 10,000 are displayed at any one time. The inventory

4005-626: The Pyramids almost certainly were made for religious purposes. The earliest known European dollhouses were the baby houses from the 16th century, which consisted of cabinet display cases made up of individual rooms. The term “baby” in baby house is coined from the old English word meaning doll. Dollhouses of this period showed idealized interiors complete with detailed furnishings and accessories. The cabinets were built by hand with architectural details, filled with miniature household items and were solely intended for adults. The baby moniker referred to

4094-564: The United States, most houses have an open back and a fancy facade, while British houses are more likely to have a hinged front that opens to reveal the rooms. Children's dollhouses during the 20th century have been made from a variety of materials, including metal ( tin litho ), fibreboard, plastic, and wood. With the exception of Lundby , 1:18 scale furniture for children's dollhouses has most often been made of plastic. Contemporary kit and fully built houses are typically made of plywood or medium-density fiberboard (MDF). Tab-and-slot kits use

4183-533: The Wisconsin Toy Co. Dollhouse dolls and miniatures were also produced in Japan, mostly by copying original German designs. After World War II, dollshouses were mass-produced in factories on a much larger scale with less detailed craftsmanship than before. By the 1950s, the typical dollhouse sold commercially was made of painted sheet metal filled with plastic furniture. Such houses cost little enough that

4272-399: The above-mentioned systems. Two distinct points always determine a (straight) line . Three distinct points are either collinear or determine a unique plane . On the other hand, four distinct points can either be collinear, coplanar , or determine the entire space. Two distinct lines can either intersect, be parallel or be skew . Two parallel lines, or two intersecting lines , lie in

4361-495: The abstract vector space, together with the additional structure of a choice of basis. Conversely, V {\displaystyle V} can be obtained by starting with R 3 {\displaystyle \mathbb {R} ^{3}} and 'forgetting' the Cartesian product structure, or equivalently the standard choice of basis. As opposed to a general vector space V {\displaystyle V} ,

4450-775: The axioms of a Lie algebra, instead of associativity the cross product satisfies the Jacobi identity . For any three vectors A , B {\displaystyle \mathbf {A} ,\mathbf {B} } and C {\displaystyle \mathbf {C} } A × ( B × C ) + B × ( C × A ) + C × ( A × B ) = 0 {\displaystyle \mathbf {A} \times (\mathbf {B} \times \mathbf {C} )+\mathbf {B} \times (\mathbf {C} \times \mathbf {A} )+\mathbf {C} \times (\mathbf {A} \times \mathbf {B} )=0} One can in n dimensions take

4539-630: The construction for the isomorphism is found here . However, there is no 'preferred' or 'canonical basis' for V {\displaystyle V} . On the other hand, there is a preferred basis for R 3 {\displaystyle \mathbb {R} ^{3}} , which is due to its description as a Cartesian product of copies of R {\displaystyle \mathbb {R} } , that is, R 3 = R × R × R {\displaystyle \mathbb {R} ^{3}=\mathbb {R} \times \mathbb {R} \times \mathbb {R} } . This allows

SECTION 50

#1732780965193

4628-491: The construction of the five regular Platonic solids in a sphere. In the 17th century, three-dimensional space was described with Cartesian coordinates , with the advent of analytic geometry developed by René Descartes in his work La Géométrie and Pierre de Fermat in the manuscript Ad locos planos et solidos isagoge (Introduction to Plane and Solid Loci), which was unpublished during Fermat's lifetime. However, only Fermat's work dealt with three-dimensional space. In

4717-880: The cross product are A × B = [ A 2 B 3 − B 2 A 3 , A 3 B 1 − B 3 A 1 , A 1 B 2 − B 1 A 2 ] {\displaystyle \mathbf {A} \times \mathbf {B} =[A_{2}B_{3}-B_{2}A_{3},A_{3}B_{1}-B_{3}A_{1},A_{1}B_{2}-B_{1}A_{2}]} , and can also be written in components, using Einstein summation convention as ( A × B ) i = ε i j k A j B k {\displaystyle (\mathbf {A} \times \mathbf {B} )_{i}=\varepsilon _{ijk}A_{j}B_{k}} where ε i j k {\displaystyle \varepsilon _{ijk}}

4806-591: The customer's design. Some design and build their own dollhouse. Simpler designs might consist of boxes stacked together and used as rooms. Miniature objects used for decoration inside dollhouses include furniture , interior decorations , dolls and items like books , couches, furniture, wallpaper, and even clocks . Some include functional kitchen appliances to create miniature food . Dollhouses for enthusiasts are available ready made and in kits, but may also be homemade. Dozens of miniature trade shows are held by various miniature organizations and enthusiasts throughout

4895-516: The definition of canonical projections, π i : R 3 → R {\displaystyle \pi _{i}:\mathbb {R} ^{3}\rightarrow \mathbb {R} } , where 1 ≤ i ≤ 3 {\displaystyle 1\leq i\leq 3} . For example, π 1 ( x 1 , x 2 , x 3 ) = x {\displaystyle \pi _{1}(x_{1},x_{2},x_{3})=x} . This then allows

4984-493: The definition of the standard basis B Standard = { E 1 , E 2 , E 3 } {\displaystyle {\mathcal {B}}_{\text{Standard}}=\{E_{1},E_{2},E_{3}\}} defined by π i ( E j ) = δ i j {\displaystyle \pi _{i}(E_{j})=\delta _{ij}} where δ i j {\displaystyle \delta _{ij}}

5073-528: The dollhouse of Petronella Oortman in the Rijksmuseum Amsterdam . The Rijksmuseum estimates that Petronella Oortman spent twenty to thirty thousand guilders on her miniature house, which was nearly the price of a real house along one of Amsterdam's canals at that time. All these dollhouses shows the linen room (laundry room), kitchen, and bedrooms in great detail. In Tampere in Finland ,

5162-579: The dollhouses known as Deauville Dollhouses. They were made by the VILLARD & WEILL company, mainly between 1905 and 1925. This toys manufacturer won prizes in Sydney, Paris and St Louis World Fairs. The TynieToy Company of Providence, Rhode Island, made authentic replicas of American antique houses and furniture in a uniform scale beginning in about 1917. Other American companies of the early 20th century were Roger Williams Toys, Tootsietoy , Schoenhut, and

5251-427: The domestic household, “through the inclusion of amply-stocked linen rooms and kitchens”.   Three-dimensional space In geometry , a three-dimensional space ( 3D space , 3-space or, rarely, tri-dimensional space ) is a mathematical space in which three values ( coordinates ) are required to determine the position of a point . Most commonly, it is the three-dimensional Euclidean space , that is,

5340-526: The end of the 19th century American dollhouses were being made in the United States by The Bliss Manufacturing Company. In France, the Deauville dollhouses were made by the manufacturer Villard & Weill in the first quarter of the 20th century. Germany produced the most prized dollhouses and doll house miniatures up until World War I . The doll houses were produced in Nuremberg, Germany ; which, since

5429-446: The exterior with papier-mâché and then sculpted to a rough faux stone finish. Some of these exterior wall panels are fixed to create a three-dimensional effect when viewers peer into the castle. Other walls can be opened or removed for group viewing. The structure was built to a 25.4 mm to 304.8 mm scale (one inch to one foot) (1:12) scale . The Astolat Dollhouse Castle was acquired by collector L. Freeman in 1996 and moved to

SECTION 60

#1732780965193

5518-411: The great majority of girls from the developed western countries which were not struggling with rebuilding after World War II could own one. The baby houses of the 17th and 18th centuries, and the toy dollhouses of the 19th and early 20th century rarely had uniform scales, even for the features or contents of any individual house. Although a number of manufacturers made lines of miniature toy furniture in

5607-421: The hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces , meaning that they can be made up from a family of straight lines. In fact, each has two families of generating lines, the members of each family are disjoint and each member one family intersects, with just one exception, every member of the other family. Each family is called a regulus . Another way of viewing three-dimensional space

5696-460: The identity ‖ A × B ‖ = ‖ A ‖ ⋅ ‖ B ‖ ⋅ | sin ⁡ θ | . {\displaystyle \left\|\mathbf {A} \times \mathbf {B} \right\|=\left\|\mathbf {A} \right\|\cdot \left\|\mathbf {B} \right\|\cdot \left|\sin \theta \right|.} The space and product form an algebra over

5785-404: The interior furnishings and artwork are original and were purchased at auctions from private collectors, or commissioned from known miniaturists and artisans. Such artists include Eric Pearson, George Becker, Warren Dick, Laurel Coulon, Mary McGrath, among others. The lighting features fully illuminate all areas of Astolat and separate day and night-time lighting systems automatically adjust based on

5874-491: The physical universe , in which all known matter exists. When relativity theory is considered, it can be considered a local subspace of space-time . While this space remains the most compelling and useful way to model the world as it is experienced, it is only one example of a 3-manifold. In this classical example, when the three values refer to measurements in different directions ( coordinates ), any three directions can be chosen, provided that these directions do not lie in

5963-555: The position of any point in three-dimensional space is given by an ordered triple of real numbers , each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two axes. Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates , though there are an infinite number of possible methods. For more, see Euclidean space . Below are images of

6052-925: The private library containing duelling pistols , a library of miniature books , fireplace, miniature daguerreotypes , and the oil painting display area. Fifth level contains the sleeping quarters. Sixth floor contains the grand ballroom, musician's alcove, bar area and sitting rooms. Wizards's tower is on the top level and contains hand painted zodiac signs, telescope, observatory and astronomical depictions. The interior spaces include miniature fittings and furniture most of which are antique, hand-crafted, and one-of-a kind. Some are even artifacts from Pompeii . Other furnishings, and ancillary art includes sculptures, original oil paintings, portrait miniatures , hand sewn tapestries, carved wood moldings, chandeliers, sconces, framed mirrors, and accessories. These include miniature inlaid marble bathrooms, parquet floors, gold chandeliers, hand etched wood panels, and pieces made of gold. Most of

6141-472: The product of n − 1 vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions . It can be useful to describe three-dimensional space as a three-dimensional vector space V {\displaystyle V} over the real numbers. This differs from R 3 {\displaystyle \mathbb {R} ^{3}} in

6230-434: The return of Titania's Palace to Ireland. It is furnished with miniature antiques. The Stettheimer Dollhouse was constructed in New York City by Carrie Walter Stettheimer between 1916 and 1935. Many contemporary artists made miniatures of their art for the dollhouse, including Marcel Duchamp , Alexander Archipenko , George Bellows , Gaston Lachaise , and Marguerite Zorach . It is 28" high and contains 12 rooms, and

6319-532: The rooms inside, though there is no reason why a dolls house should not have a realistic exterior or a house portrait include interior details. In Germany during the middle part of the 20th century 1:10 scale became popular based on the metric system . Dollhouses coming out of Germany today remain closer in scale to 1:10 than 1:12. The largest common size for dollhouses is 1:6 which is proportionate for Barbie , Ken , Blythe and other dolls 11-12 inches tall, and furniture and accessories such as Re-Ment . In

6408-523: The same plane . Furthermore, if these directions are pairwise perpendicular , the three values are often labeled by the terms width /breadth , height /depth , and length . Books XI to XIII of Euclid's Elements dealt with three-dimensional geometry. Book XI develops notions of orthogonality and parallelism of lines and planes, and defines solids including parallelpipeds, pyramids, prisms, spheres, octahedra, icosahedra and dodecahedra. Book XII develops notions of similarity of solids. Book XIII describes

6497-468: The scale of the houses rather than the demographic it was aimed at. They were off-limits to children, not because of safety concerns for the child but to protect the dollhouse. Such cabinet houses were trophy collections owned by the few matrons living in the cities of Holland, England and Germany who were wealthy enough to afford them and, fully furnished, were worth the price of a modest full-size house's construction. The earliest known recorded baby house

6586-606: The sixteenth century, was coined as the 'toy city'. Their baby houses were thought to be the origin for the basic standards of contemporary doll houses. Notable German miniature companies included Märklin , Rock and Graner and others. Their products were not only avidly collected in Central Europe, but regularly exported to Britain and North America. Germany's involvement in WWI seriously impeded both production and export. New manufacturers arose in other countries. France produced

6675-679: The smallest antique Bible in the world. Many of its miniatures, including some made of gold, sterling silver, are antique and one of a kind. Few other museum quality dollhouses meet such criteria. The Astolat Dollhouse Castle was once on display at the Tee Ridder division of the Nassau County Museum of Art in Roslyn Harbor, New York . Inspired by Alfred Tennyson 's poetry about the Lady of Astolat , Astolat Dollhouse Castle

6764-530: The space R 3 {\displaystyle \mathbb {R} ^{3}} is sometimes referred to as a coordinate space. Physically, it is conceptually desirable to use the abstract formalism in order to assume as little structure as possible if it is not given by the parameters of a particular problem. For example, in a problem with rotational symmetry, working with the more concrete description of three-dimensional space R 3 {\displaystyle \mathbb {R} ^{3}} assumes

6853-418: The surface area of the sphere is A = 4 π r 2 . {\displaystyle A=4\pi r^{2}.} Another type of sphere arises from a 4-ball, whose three-dimensional surface is the 3-sphere : points equidistant to the origin of the euclidean space R . If a point has coordinates, P ( x , y , z , w ) , then x + y + z + w = 1 characterizes those points on

6942-447: The time of day. "The Castle is worth so much because of the structure itself," said Paula Gilhooley, the museum's curator. Furthermore, "Astolat is one of the finest miniature structures in the world exhibiting a rare combination of sculpture, art, engineering and detail that sets it apart from anything in existence to date." Astolat "is a massive feat of construction and when you see it, it will leave you absolutely speechless". In 2006,

7031-446: The unit 3-sphere centered at the origin. This 3-sphere is an example of a 3-manifold: a space which is 'looks locally' like 3-D space. In precise topological terms, each point of the 3-sphere has a neighborhood which is homeomorphic to an open subset of 3-D space. In three dimensions, there are nine regular polytopes: the five convex Platonic solids and the four nonconvex Kepler-Poinsot polyhedra . A surface generated by revolving

7120-491: The work of Hermann Grassmann and Giuseppe Peano , the latter of whom first gave the modern definition of vector spaces as an algebraic structure. In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, each perpendicular to the other two at the origin , the point at which they cross. They are usually labeled x , y , and z . Relative to these axes,

7209-418: The year, where artisans and dealers display and sell miniatures. Often, how-to seminars and workshops are part of the show features. Stores that sell miniatures also hold classes. Enthusiasts share images online and use Internet forums, blogs and other online social media to share information about dollhouses and miniatures. Recognition of the value and enjoyment of collecting vintage and antique dolls houses as

7298-607: Was built over a thirteen-year period. The exterior took a year to sculpt to the final finish. The interiors and adjoining areas were each constructed to the highest standards of that time. When Astolat was first installed, the museum's curator stated "each room is decorated with furniture, tables, chairs, artwork and lighting made by artisans from around the world, and the materials are unique and expensive." It weighs approximately 800 pounds (360 kg). The interior consists of 29 rooms and adjacent areas that contain approximately 10,000 separate interior pieces. Astolat Dollhouse Castle

7387-584: Was commissioned from 1557-1558 by Albrecht V, Duke of Bavaria .   Smaller doll houses, such as the Tate house with more realistic exteriors, appeared in Europe in the 18th century. Nuremberg kitchens , a type of single-room dollhouse, date back at least to 1572, when one was given to Dorothea and Anna , the Princesses of Saxony, daughters of Augustus, Elector of Saxony aged five and ten. The early European dollhouses were each unique, constructed on

7476-683: Was commissioned in 1631 and was publicly displayed and advertised by Köferlin in the form of original verses composed on broadsheet. Surviving Dutch 17th century notable cabinet dollhouses include the Amsterdam, Netherlands 18th century dollhouses of Sara Rothé ; one is in the Frans Hals Museum , and one is in the Gemeentemuseum Den Haag ; the dollhouse of Petronella de la Court in Centraal Museum , and

7565-435: Was created between 1974 and 1987 primarily by master miniaturist Elaine Diehl with support and assistance from artisans throughout the world. In addition to its 9 feet (2.7 m) height, it has 29 rooms, hallways, corridors, sitting areas, and windows. The Colleen Moore fairy Castle Dollhouse and the Astolat Dollhouse Castle were designed with fixed contiguous exterior walls to create a three-dimensional viewing effect. Astolat

7654-591: Was initially displayed in Diehl's museum shop in Sedona, Arizona , until her retirement in 1996. It was a popular tourist attraction which drew people from around the world. On 10 May 1982, dollhouse creator Colleen Moore took a trip to view the Astolat Dollhouse and met with Diehl. Unique parquet floors, framed mirrors, tapestries, gold chandeliers, oil paintings, and fireplaces lead up to the top floor housing

7743-474: Was inspired by Alfred Tennyson 's poetry about the Lady of the Lake and built between 1974 and 1987 by miniaturist Elaine Diehl. It was appraised over $ 1 million in 2006 and at $ 8.5 million in 2015 primarily because of the upgrade to the interiors and pieces. It is 9' tall, has 29 rooms and is on display at the Nassau County Museum of Art on Long Island, New York. The Colleen Moore fairy Castle Dollhouse and

7832-473: Was not until Josiah Willard Gibbs that these two products were identified in their own right, and the modern notation for the dot and cross product were introduced in his classroom teaching notes, found also in the 1901 textbook Vector Analysis written by Edwin Bidwell Wilson based on Gibbs' lectures. Also during the 19th century came developments in the abstract formalism of vector spaces, with

7921-908: Was published in 1953. Both collectors opened museums dedicated to dolls houses, the Rotunda (1962-1998) in Oxford , England, and the Washington Dolls’ House & Toy Museum (1975-2004), in Washington D.C. , US. Through print publications such as the International Dolls' House News (c 1969-2002) American Miniaturist , and Dolls House and Miniature Scene , collectors around the world shared photos, tips, queries and information; today, websites, blogs, social media, and online forums allow even more collectors to share their hobby. Anna Köferlin’s (no longer existing) Nuremberg doll house

#192807