Lesson1

Galois, Évariste (1811-1832)

French mathematician who developed new techniques to study the solubility of equations .  Simultaneously with Abel, he showed that the general quintic equation  and polynomial equations of higher degree are not soluble in terms of a finite number of rational operations and root extractions.  Galois's life was a tragic one. His father committed suicide. In his examination to the Preparatory School in 1830, the physics teacher Péclet wrote of the young genius "He knows absolutely nothing. I have been told that this student has mathematical ability; this certainly astonishes me. Judging by his examination, he seems of little intelligence, or has hidden his intelligence so well that I found it impossible to detect it" (Infeld 1948, pp. 101-102). Galois also failed to gain admittance to the École Polytechnique not once, but two times. During the first of these examinations, in 1829, Galois was so frustrated by the inane questions that he vented his anger by throwing an eraser at his examiner M. Dinet (Infeld 1948, pp. 99-100).  Galois suffered the additional misfortune of having his work not only ignored, but completely misplaced by its caretakers on several occasions. When Galois gave Cauchy a paper containing his most important results to present (without keeping a copy himself), Cauchy proceeded to lose it (Infeld 1948, pp. 89-90). When Galois submitted a paper for the Académie's prize in math, Fourier took the paper home to peruse, but died shortly thereafter and this paper was also lost. Poisson returned a second paper which contained important results in group theory  as incomprehensible.  Galois, always a radical, joined the National Guard, but was subsequently imprisoned in 1831 after proposing a toast interpreted as a threat to the King. On the night before his death in 1832, Galois wrote a letter to his friend Auguste Chevalier, setting forth his discovery of the connection between group theory  and the solutions of polynomial equations by radicals (Galois 1959). After writing the letter, Galois was shot to death in his intestine in a gun fight. The exact circumstances of his death are not well established, and various accounts hold that he was shot by a rival in a feud over a woman, that he was challenged by a royalist who objected to his political views, or that he was killed by an agent of the police.

 

Problem of the week

A triangle has sides 10, 17, and 21.  A square is inscribed in the triangle.  One side of the square lies on the longest side of the triangle.  The other two vertices of the square touch the two shorter sides of the triangle.  What is the length of the side of the square?

 

Special Quadrilaterals Worksheet