## The man who conned a mathematician

Mathematicians are definitely among the most logical and analytical of persons. But sometimes, passion can blind anyone, even them. This was what happened to Michael Chasles (1793-1880), an accomplished French mathematician during his time. Chasles was a professor of Mathematics and Ecole Polytechnique and a winner of the Copey Medal of the Royal Society of London. A chair of geometry was also established for him at Sorbonne University in 1846.

One day Chasles met a Denis Vrain-Lucas, con man extraordinaire. Lucas knowing the former’s patriotism and passion for mathematical history, he convinced Chasles that he was in possession of letters from Blaise Pascal to Isaac Newton implying that gravity was discovered by the former. If proven true, a French would have discovered gravity and not an English.  Chasles paid Lucas and asked for more letters. From 1861 to 1870, Lucas had forged 27,000 letters which Chasles paid for a staggering amount of 140 000 francs!

Lucas’ career ended when the supposed letter of Pascal to Newton was shown to the French Academy of Science.  It was discovered that Pascal’s handwriting in that letter was very different from his writing in the academy’s archives.  Lucas was proven guilty and was sentenced for two years imprisonment, but Chasles credibility was tarnished.

Had Chasles read all the letters, he would have realized that all the historical letters from different continents including the letters of Alexander the Great to Aristotle, Cleopatra to Julius Caesar, Mary Magdalene to Lazarus — yes, he forged all of it — were all written in French!

Source: Mathematical Scandals

## Milkshakes, Beads, and Pascal’s Triangle

Note: This is the first part of the Binomial Theorem Series

Binomial Theorem I: Milkshakes, Beads, and Pascal’s Triangle

Binomial Theorem II: The Binomial Expansion

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The Milk Shake Problem

Problem 1: Issa went to a shake kiosk and want to buy a milkshake. The shake vendor told her that she can choose plain milk, or she can choose to combine any number of flavors in any way she want. There are four flavors to choose from: Apple, Banana, Chico, and Durian.

How many possible combinations can Issa create?

It is clear that Issa can choose her milk shake to have no flavor (pure milk shake), one flavor, two flavors, three flavors, or four flavors. The possible combinations are shown below.

Table 1