Equilateral triangle dissected by equilateral triangles. Mrs. Perkins's Quilt. A Mrs. Perkins's quilt is a dissection of a square of side into a number of smaller squares. The name "Mrs. Perkins's Quilt" comes from a problem in one of Dudeney's books, where he gives a solution for . Unlike a perfect square dissection, however, the smaller squares need not be all different sizes. The smallest numbers of squares needed to create relatively prime dissections of an quilt for , 2, ... are 1, 4, 6, 7, 8, 9, 9, 10, 10, 11, 11, 11, 11, 12, ... On October 9-10, L.
Known to be needed for various side lengths , with those for (and possibly 16) proved minimal by J. For general , which Trustrum (1965) improved to order . Squared Squares; Perfect Simples, Perfect Compounds and Imperfect Simples. How to make a magically appearing square. How round is your circle? Solid Objects Representing "Impossible Objects" NEW! Impossible Motion Got the First Prize. I am happy to announce that this illusion won the first prize at the Best Illusion of the Year Contest 2010 held on May 10th, 2010 in Naples, Florida. Thank you very much for warm encouragement.
Snap Shot Images A short description is here (pdf) . A constructin kit (figures of unfolded surfaces) is here (pdf file) . Nature News Solid objects which generate anomalous pictures Copyright in 1997 by Kokichi Sugihara The following are not painting, but photographs of real paper-made objects. Escher's Endless Stairs Unfolded surface (ps file) Unfolded surface (pdf file) U and Bar Unfolded surface (ps file) Unfolded surface (pdf file) Two Rings Unfolded surface (ps file) Unfolded surface (pdf file) References Kokichi SUGIHARA: Classification of impossible objects. Kokichi SUGIHARA: Mathematical structures of line drawings of polyhedrons. --- Toward man-machine communication by means of line drawings.
Kokichi SUGIHARA: Machine Interpretation of Line Drawings. Zoetrope. A modern replica of a Victorian zoetrope A zoetrope is one of several pre-film animation devices that produce the illusion of motion by displaying a sequence of drawings or photographs showing progressive phases of that motion. The name zoetrope was composed from the Greek root words ζωή zoe, "life" and τρόπος tropos, "turning". The zoetrope consists of a cylinder with slits cut vertically in the sides. On the inner surface of the cylinder is a band with images from a set of sequenced pictures. As the cylinder spins, the user looks through the slits at the pictures across. The scanning of the slits keeps the pictures from simply blurring together, and the user sees a rapid succession of images, producing the illusion of motion.
From the late 19th century, devices working on similar principles have been developed, named analogously as linear zoetropes and 3D zoetropes, with traditional zoetropes referred to as "cylindrical zoetropes" if distinction is needed. Invention[edit] Ghibli[edit] Rolling discs. Mendocino motor. The Mendocino motor is a solar-powered magnetically levitated electric motor.
Description[edit] The motor consists of a four-, five-, six- or eight-sided rotor block in the middle of a shaft. The rotor block has two sets of windings and a solar cell attached to each side. The shaft is positioned horizontally and has a magnet at each end. The magnets on the shaft provide levitation by repelling magnets in a base under the motor. When light strikes one of the solar cells, it generates an electric current thus energizing one of the rotor windings. At present, this is a novelty; it has a very low power output. History[edit] References[edit] See also[edit] External links[edit] Detailed description of construction. Anagyre. Résultats Google Recherche d'images correspondant à. Tiling by Squares. A square or rectangle is said to be 'squared' into n squares if it is tiled into n squares of sizes s1,s2,s3,..sn. A rectangle can be squared if its sides are commensurable (in rational proportion, both being integral mutiples of the same quantity) The sizes of the squares si are shown as integers and the number of squares n is called the order.
Squared squares and squared rectangles are called simple if they do not contain a smaller squared square or rectangle, and compound if they do. Squared squares and squared rectangles are called perfect if the squares in the tiling are all of different sizes and imperfect if they are not. Most of the square tilings we are familiar with in our everyday lives use repeating squares of the same size, such as fly screens, square floor tiles, square umbrella base or stands square graph paper and the like. These repeating grid square tilings can be described using this terminology as 'imperfect' and 'compound'. Algebraic Method Figure 71; Algebraic Method. Kokichi Sugihara's English Homepage. Dissections - Construction de Dudeney. Dissections de polygones La construction de Herny Ernest Dudeney (1857 - 1930) [Transformations en croix ou étoiles] [Transformations de quadrilatères] [Transformations "fun"] [Retour Dissection(Polygones réguliers)] [Liens et références] [Panoplie du constructible] [Menu Général] La construction On considère un triangle équilatéral de côté 2.
DudOK.fig Une construction approchée On rencontre parfois, dans certains ouvrages, une construction de la racine quatrième de 3 (côté du carré de même aire que le triangle de côté 2) mentionnée comme exacte alors qu'elle n'est qu'une approximation. DudFaux.fig (on y mesure une erreur de 1%) Une superbe application en CabriJava de Eric Hakenholz Des calculs élémentaires donnent (c étant le côté du carré, comme ci-dessus) Si ce découpage permettait d'obtenir un carré, d'une manière ou d'une autre, il existerait une Q-combinaison linéaire de de somme c. .
Il est donc impossible de réaliser un carré avec les 4 pièces de ce puzzle. Menu général. Constructions Régle - Compas - Conique. Le découpage de Dudeney.