By Georges Perec

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Extra resources for Les mots croises II

Example text

Let HB = x and BG = y. By the Pythagorean Theorem on HBG, x2 + y 2 = (1 − y)2 . And therefore y= Since EAH and 1 − x2 . 2 (1) HBG are similar, HB : BG = AE : AH, or x : y = √ 1 : 2−x . 2 (2) Equations (1) and (2) together lead to the quadratic equation, √ √ 2 2 5 2 3x − 4 2x + 1 = 0. Therefore, x = . 19745 . . August 11, 2008 11:23 World Scientific Book - 9in x 6in Origamics˙noline 31 EXTENSION OF THE HAGA’S THEOREMS TO SILVER RATIO RECTANGLES Fig. 9 Haga’s Third Theorem fold with A4 paper in a vertical layout.

Yoko Takamoto, a teacher of the Senior High School attached to Toshimagaoka Women’s Educational Institution, while a trainee at Tsukuba University’s Extension course entitled “Origami and Education”. August 11, 2008 11:23 World Scientific Book - 9in x 6in 41 Origamics˙noline X-LINES WITH LOTS OF SURPRISES ☎ ✄ ✟ ✆ ✡ ☛ ☞ ✍ ✠ ✌ ✝ ✞ ✁ ✂ ✍ ✌ Fig. 9 The length FH (= IG) is an interesting fact. 9). These are sides of triangles FJH and IJG respectively. Since J lies on the midline then FJ = JG and HJ = JI.

1(b)). Press the whole crease repeatedly with the finger nail to make it clear and distinct. 1(c)). Make sure that the fold is distinct. Now place the other lower vertex on the selected point and 3 These surprises come from the mathematical reasoning arise through paper folding. Through those surprises, we can find the invariant and it initiates us to inquire much more paper folding as mathematical science activity. 1(d)). 1(e)). Do you see the two creases? ✂✁☎✄ ✝✆✞✄ ✌✎✍✑✏✓✒✔✍✑✕✖✍✘✗✝✙✎✚ ✛ ✗✜✍✑✗✣✢✥✤✎✦✧✚ ✕✧✛★✦✩✕✪✛ ✫✎✒ ✬ ✤✧✤✎✒✘✗✭✒✯✮✧✰✧✒✩✱ ✂✟☎✄ ✍✵✴✯✒✶✛ ✫✓✒ ✦✩✷✥✒✑✗ ✒✯✸✹✛✓✺✓✒✑✗✣✛✹✒✑✻ ✲☛ ✦✩✕✧ ✳ ✛✹✦✼✛ ✫✓✒✽✍✑✳ ✗✾✙✎✚ ✛ ✗✡✍✘✗✣✢✥ ✳ ✤✎✦✧✚ ✕✧✛✣✱ ✡✠☛✄ ✍✵✴✯✒✶✛ ✫✓✒ ✒✽✦❀✙❁✛✹✍✯✚ ✕✖✦✩✕✓✒ ✿ ✚ ✕✓✒☎✱ ✳ ✂☞☎✄ ✦✩✷✥✒✑✗❂✗✜✚ ✰✩✫✧✛✓✺✓✒✘✗✣✛✹✒✵✻ ✚ ✕✓✍ ✲☛ ✦✩✕✧ ✳ ✛✹✦✼✛ ✫✓✒❄❃✂✍✑ ✳ ❅❆✒✽✍✘✗✝✙✎✚ ✛ ✗✡✍✑✗✝✢✥✤✎✦✧✚ ✕✧✛✣✱ ✢✩❈✯✷✪✒✽✦❀✙❁✛✹✍✯✚ ✕✪✛ ✷✪✦✪✴✑✗✜✒✯✍✯❃❉✒✯❃ ❇✚ ✕✪✛ ✫✓✳ ✒❄ ✳ ✸✝✦✩✗✝❅❊✦❁✸✎❋●✱ Fig.