Behold!
![[Monochrome picture which says it all]](pythag-wb.gif)
The above picture is my favourite proof of Pythagoras' theorem. Filling in the details is left as an exercise to the reader.
A detailed version of the proof, for those who do not feel up to the challenge, appears in Alan M. Selby's Appetizers and Lessons for Math and Reason.
I am leaving this page in the state it had at the end of year 2000. (Except, of course, for the current paragraph. The previous edit was dated 2000-12-05 18:28:38 UTC.) I believe that monochrome screens are so rare these days that there is little point in maintaining a separate monochrome version. As web browsers improve, maybe I'll reinstate this functionality by providing an alternate style sheet for the original version. Until then, I hope you can make do with the colored version.
This proof is sometimes referred to as the Chinese square proof, or just the Chinese proof. It is supposed to have appeared in the Chou pei suan ching (ca. 1100 B.C.E.), according to Ralph H. Abraham [see ``Dead links'' below,] who attributes this information to the book by Frank J. Swetz and T. I. Kao, Was Pythagoras Chinese?.
According to David E. Joyce's A brief outline of the history of Chinese mathematics, however, the earliest known proof of Pythagoras is given by Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.)
I have been told that this proof, with the exclamation `Behold!', is due to the Indian mathematician Bhaskara II (approx. 1114-1185). A web page at the Aurora University's Mathematics department attributes a slightly different proof, together with the "Behold!" exclamation, to Bhaskara, and refers to the present proof simply as the Arya Bhata proof without words.
If you can throw further light on the origin of this proof, send me a note.