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 . 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. Squared Squares; Perfect Simples, Perfect Compounds and Imperfect Simples.
There are 4 main kinds of squared squares which have been of sufficient interest to be searched for, counted and recorded; That is, the three types depicted below, and the fourth type, Mrs Perkin's Quilts, which can include those three types and in addition, squared squares which are 'imperfect' and 'compound' as well.
All four kinds of squared square have the squares in the dissection (the 'elements') reduced by any common factor so their GCD = 1. A chronology of the significant square dissection discoveries and the people who made them; How to make a magically appearing square. How round is your circle? Giving half an ellipse constant width Circular arcs are not necessary either, although they are much easier to draw.
In a square of width w draw a convex curve from top to bottom touching the left hand side, and which is tangent to the top and bottom of the square. At no point should the curvature be less than the curvature of a circle with radius w. 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. Zoetrope. A modern replica of a Victorian zoetrope A zoetrope is a device that produces the illusion of motion from a rapid succession of static pictures.
The term zoetrope is from the Greek words ζωή zoe, "life" and τρόπος tropos, "turn". It may be taken to mean "live turning" or "animation". 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. Invention The earliest known zoetrope was created in China around 180 AD by the inventor Ding Huan (丁緩).
The modern zoetrope was invented in 1833 by British mathematician William George Horner. Rolling discs. Mendocino motor. The Mendocino motor is a solar-powered magnetically levitated electric motor.
Description 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 References See also External links 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. SUGIHARA Kokichi Specially Appointed Professor, Dr. of Engineering Welcome to my Homepage.
(to my Japanese homepage) Meiji Institute for Advanced Study of Mathematical Sciences Organization for the Strategic Coordination of Research and Intellectual Property Meiji University 1-1-1 Higasimita, Tamaku, Kawasaki 214-8571, Japan E-Mail :kokichis(a)isc.meiji.ac.jp Recent Talks Geometric Software Impossible Solids and Impossible Motions PDF file of "Machine Interpretation of Line Drawings" (released in September 2006) Personal Data. 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"]
Constructions Régle - Compas - Conique. Le découpage de Dudeney. Remarque Quand on transforme le triangle, on obtient un quadrilatère convexe (les angles plats sur les côtés sont conservés par rotation de 180°) ; ce quadrilatère a par construction 4 angles droits.
Il s'agit donc d'un rectangle. Ce rectangle a même aire que le triangle initial : (le découpage conserve l'aire). Un côté de ce rectangle (jaune + bleu) mesure RS. En effet c'est RF + RG = RF + FS = RS Le calcul précédent, RS = , montre que l'aire du rectangle est égale à RS² .