Archimedes character
Archimedes logo 2
english Website presentation
italiano Presentazione del sito
francais Présentation du site
german Vorstellung dieser Website
Puzzle crafting & workshops • Laboratorio di giochi d'ingegno • Atelier de puzzles
by Gianni A. Sarcone & Marie-Jo Waeber
border 1 border 2 bis

Squaring Triangle (Dudeney's Triangle)

The puzzle we'll make together starts as an equilateral triangle, but it unfolds and folds to make a square! Magic? No, simply mathematical! To make our triangular puzzle we don't need any compass or strange tools... We just need a paper sheet, a pencil, a L-shaped square and a pair of scissors.

How to make an equilateral triangle with a paper sheet
Take a standard paper sheet and fold it lengthwise in two equal parts as shown in fig. 2 below. Now, unfold your paper sheet (notice the foldmark in its middle). Then, fold back a corner of the paper sheet on the foldmark and draw a line along the corner side (see fig. 4). Repeat this operation with the opposite corner of the paper sheet. Cut your sheet along the two lines you've drawn (fig. 7). Compliments! You have now a perfect equilateral triangle.

How to transform your equilateral triangle into a square
Fold back the 3 corners of the triangle to make a rectangle as per fig. 9. Then, unfold your triangle. Important: the foldmarks define a rectangle ABCD. Trace the diagonal BD of the rectangle ABCD (fig. 11). Now, with the help of a L-shaped square trace 2 perpendiculars to the diagonal BD, one passing through point A, the other one through point C, as shown in fig. 12. Your triangle is now divided in 4 pieces. Cut them out and reassemble them as shown in fig. 15.

diagram 1
diagram 2
diagram 3
© Gianni A. Sarcone
Source: MateMagica, ISBN 88-89197-56-0

comment a comment recommend this page stumble it Rate it on StumbleUpon
border 2
border 3
border 3 bis  
border 4  
Archimedes journal ARCHIMEDES journal is an interactive review devoted to entertaining & involving the readers with puzzles, recreational mathematics and visual creativity. This journal is published for an audience without a specific math background. Each issue covers a broad range of mental and hands-on activities for the reader to enjoy! Workshop image "How to focus attention? Encourage creative exploration?" Multicultural interactive puzzle activities & workshops for museums and institutions.
Related links
arrow A large selection of puzzles books.
arrow Puzzles for publishers and editors.

border 5
border 8 border 7
A range of
puzzles for
you to make!

border 6
Home | About Us | Sponsorship | Press-clippings | Cont@ct | ©opyrights | | Link2us | Sitemap
© Archimedes' Lab | Privacy & Terms | The web's best resource for puzzles and mental activities
 
thin line

This site exists thanks to sponsorised ads and online sales of puzzle products and activities.