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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 . 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.

Squared Squares; Perfect Simples, Perfect Compounds and Imperfect Simples

All four kinds of squared square have the squares in the dissection (the 'elements') reduced by any common factor so their GCD = 1. How to make a magically appearing square. You can rearrange the polygons cut from an 8 × 8 square to form a 5 × 13 rectangle - gaining a square unit of area in the process.

how to make a magically appearing square

Where did the extra square come from? Links For instructions on how to make this project and many others check out the book Amazing Math Projects You Can Build Yourself written for kids 9 to 14 years old. Comments. How round is your circle? Giving half an ellipse constant width Circular arcs are not necessary either, although they are much easier to draw.

How round is your circle?

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. 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. Rolling discs. Slotted discs, large and small Take two identical discs and slot them together along diameters so that the discs are perpendicular.

Rolling discs

There is one separation of centres for which the compound shape has a centre of mass which remains a constant height above the surface of a table. The resulting shape rolls along in a most intriguing way. Mendocino motor. The Mendocino motor is a solar-powered magnetically levitated electric motor.

Mendocino 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.

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,

Tiling by Squares

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. Kokichi Sugihara's English Homepage. SUGIHARA Kokichi Specially Appointed Professor, Dr. of Engineering Welcome to my Homepage.

Kokichi Sugihara's English 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) 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. 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.

Le découpage de Dudeney

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 =