secrets-of-mental-math-malestrom

20
Secrets of Mental Math
Carl Friedrich Gauss: Mathematical Prodigy
Aprodigy is a highly talented child, usually called precocious or
gifted, and almost always ahead of his peers.The German mathematician
Carl Friedrich Gauss (1777–1855) was one such child. He
often boasted that he could calculate before he could speak. By the
ripe old age of three, before he had been taught any arithmetic, he
corrected his father’s payroll by declaring “the reckoning is wrong.” A
further check of the numbers proved young Carl correct.
As a ten-year-old student, Gauss was presented the following mathematical
problem:What is the sum of numbers from 1 to 100? While
his fellow students were frantically calculating with paper and pencil,
Gauss immediately envisioned that if he spread out the numbers 1
through 50 from left to right, and the numbers 51 to 100 from right to
left directly below the 1–50 numbers,each combination would add up
to 101 (1 100, 2 99, 3 98, . . .). Since there were fifty sums, the
answer would be 101 50 5050.To the astonishment of everyone,
including the teacher, young Carl got the answer not only ahead of
everyone else, but computed it entirely in his mind. He wrote out the
answer on his slate, and flung it on the teacher’s desk with a defiant
“There it lies.” The teacher was so impressed that he invested his own
money to purchase the best available textbook on arithmetic and gave
it to Gauss, stating, “He is beyond me, I can teach him nothing more.”
Indeed, Gauss became the mathematics teacher of others, and
eventually went on to become one of the greatest mathematicians in
history, his theories still used today in the service of science. Gauss’s
desire to better understand Nature through the language of mathematics
was summed up in his motto, taken from Shakespeare’s King
Lear (substituting “laws” for “law”):“Thou, nature, art my goddess; to
thy laws/My services are bound.”
EXERCISE: THREE-DIGIT ADDITION
242
137
312
256
635
814
457
241
1. 2. 3. 4. 5. 912
475