[alogo] Thabit ibn Qurra dissection

Dissect two given squares (here MZYC and YWOX) into triangles and quadrilaterals and rearrange the pieces into a square (here UVZW) [Bottema, p. 5], [YiuEGN, p.2].

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]

Notice that the ratio k = QR/ST controls the position of the square UVZW. Hence, modifying them, we change the dimensions of the squares.
The figure repesents also another proof of Pythagora's theorem (see Pythagoras.html ).

See Also



[Bottema] O. Bottema Topics in Elementary Geometry Springer Verlag Heidelberg 2007
[YiuEGN] Yiu, P. Euclidean Geometry Notes (pdf). http://www.math.fau.edu/yiu/EuclideanGeometryNotes.pdf

Return to Gallery

Produced with EucliDraw©