Remarkable pairing of items: a TLS signed "A. Einstein," one page, 8.5 x 11, Institute for Advanced Study, Princeton letterhead, March 4, 1943, responding to Harold Feldman's request to "Prove that ABC is an isosceles triangle if the lines bisecting the angles B and C and going to the opposite sides are equal," in full: "Your little problem has amused me indeed. I was not able to solve it in a purely geometrical way. On the enclosed sheet a proof is given in part algebraically."
On the included sheet, Einstein draws the triangle and marks the angles A, B, and C, the bisecting line m and b, and the bisected halves of the A-C side b´ and b″. He starts out the proof, "mb22 = c2 = b´2 - 2b´c cos α." He goes on to prove the problem presented algebraically, filling the whole sheet with formulas and calculations before concluding: "The fraction being essentially positive it follows c - b = 0." In fine condition. Accompanied by the original mailing envelope and Feldman's original handwritten problem on an index card. Originally sold by Robert F. Batchelder in 1991, and accompanied by a letter to Batchelder from a research assistant associated with the publication of the Collected Papers of Albert Einstein, requesting photocopies of the materials.
Handwritten mathematical manuscripts by Einstein are rare—particularly in so complete a form—and, paired with Einstein's playful letter responding to the challenge, this is a particularly excellent example.
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