## Monthly Archives: November 2015

### Sophie Germain

Sophie Germain was a French mathematician who did important work in number theory and differential equations. She is best known for her work on Fermat’s Last Theorem, where she gave a simple criterion that suffices to show that the equation a^{p}+b^{p}=c^{p} has no solutions with abc not divisible by p. She also did work on acoustics and elasticity, especially the theory of vibrating plates. As a mathematics student, she was forced to take correspondence courses from the Ecore Polytechnique in Paris, since they did not accept women as students. For a similar reason, she began her extensive correspondence with Gauss using the pseudonym Monsieur Le Blanc, but when she eventually revealed her identity, Gauss was delighted and sufficiently impressed with her work to recommend her for an honorary degree at University of Gottingen.

Nalin Pithwa

### The stolen Car Puzzle

The stolen car.

Nigel Fenderbender bought a secondhand car for USD 900 and advertised it in the local paper for USD 2900. A respectable looking elderly gentleman dressed as a clergyman turned up at the doorstep and enquired about the car, and bought it at the asking price. However, he mistakenly made his cheque out for USD 3000, and it was the last cheque in his cheque-book..

Now, Fenderbender had no cash in the house, so he nipped nextdoor to the local newsagent, Maggie Zine, who was a friend of his, and got her to change the cheque. He paid the clergyman USD 100 change. However, when Maggie tried to pay the cheque in at the bank, it bounced. In order to pay back the newsagent, she was forced to borrow USD 3000 from another friend, Honest Harry.

After Fenderbender had repaid this debt as well, he complained vociferously. “I lost USD 2000 profit on the car, USD 100 in change, USD 3000 repaying the newsagent and another USD3000 repaying Honest Harry. That’s USD 8100 altogether!

How much money had he actually lost?

More detective math puzzles later ! (for example, do you know that math can be used to detect art forgeries also?)

Nalin Pithwa

### Hexagonal honey comb magic puzzle

more fun with math promised !

Nalin Pithwa

### Fun with Number Theory — Pre-RMO

Here is an elementary number theory problem which can be looked upon as practice problem for pre-RMO or even RMO or just plain fun with math.

Problem:

Find the least number whose last digit is 7 and which becomes 5 times larger when this last digit is carried to the beginning of the number.

Solution:

This is fun way to learn number theory or some Math. So, go ahead and try it. Your suggestions, answers, comments are welcome 🙂

More later,

Nalin Pithwa

### Duplicating the Cube

Duplicating the Cube:

The problem of duplicating the cube is nowhere near as well known as the other two — trisecting the angle and squaring the circle. The traditional story is that an altar in the shape of a perfect cube must be doubled in volume. This is equivalent to constructing a length of $\sqrt{2}$ starting from the rational points of the plane. The desired length satisfies another cubic equation, this time the obvious one, $x^{3}-2=0$. For the same reason that trisecting the angle is impossible, so is duplicating the cube, as Pierre Wantzel pointed out in his 1837. Cube -duplications are so rare you hardly-ever come across one. Trisectors are ten a penny.

More later,

Nalin Pithwa