File:TomoyukiMogi(SquareRoot).gif

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English: Upper/right red and blue part: Geometric construction of the square x2 of a given length x and the unit length 1, using the Pythagorean theorem. If a and b and c denotes the length of the blue triangle's short and long cathetus and hypotenuse, respectively, then a2=x2+1, and b2=x4+x2. Hence, c2=a2+b2=x4+2x2+1=(x2+1)2, so c-1=x2.
Lower left green and yellow part: Applying the same construction in reverse order obtains a length of √x, given x and the unit length: If d and e and f and g denotes the length of the yellow triangle's short and long cathetus and hypotenuse and height (dotted line), respectively, then d2=g2+1 and e2=x2+g2. Hence x2+2x+1=(x+1)2=f2=d2+e2=x2+2g2+1, so g=√x.
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Made by Tomoyuki Mogi. (茂木知行)

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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Date/TimeThumbnailDimensionsUserComment
current12:16, 9 April 2016Thumbnail for version as of 12:16, 9 April 2016960 × 540 (17 KB)TOMOYUKI MOGI (talk | contribs)
11:50, 9 April 2016Thumbnail for version as of 11:50, 9 April 2016960 × 540 (17 KB)TOMOYUKI MOGI (talk | contribs)

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