## Follow Your Passion in Math

April 18, 2018 Leave a comment

Grow your passion by motivating practice like the 11-year-old Math Marvel

“Chess is a mathematical poem” – *Aarushi Maheshwari *

Math and Logic Puzzles

April 18, 2018 Leave a comment

Grow your passion by motivating practice like the 11-year-old Math Marvel

“Chess is a mathematical poem” – *Aarushi Maheshwari *

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October 1, 2017 Leave a comment

The largest known prime number was discovered in 2016 by a computer laboratory of the University of Central Missouri .

**2 ^{57,885,161} – 1 **

is one of the Mersenne primes that can be written in form 2^{n} – 1, where n is an integer. They are named after 17-century French mathematician Marin Mersenne.

The number written in the decimal form contains 17 million digits.

September 3, 2017 Leave a comment

The Babylonian clay tablet from the collection of Columbia University dating from 1,000 years before Pythagoras’s theorem is a trigonometric table which has 15 pairs of numbers forming Pythagorean triples: three whole numbers a, b and c:

a^{2} + b^{2} = c^{2}

The tabet is known as the world’s oldest trig table. Babylonians used the base-60 numbers, which permitted many more accurate fractions than the contemporary base 10. For example, 2/3 = 0.6666… (or 40 minutes) was a finite number. The base-60 system were inspired from such shapes as a circle and the regular hexagon (see an example).

June 4, 2017 Leave a comment

“Love is like **π** – natural, irrational, and very important.” – Lisa Hoffman

Certain scientists think that love is a chemical state of mind and the formula for love is as follows:

dopamine + seratonin + oxytocin

C_{8}H_{11}NO_{2} + C_{10}H_{12}N_{2}O + C_{43}H_{66}N_{12}O_{12}S_{2}

How many atoms are there in the formula of love?

April 15, 2017 Leave a comment

Terry Moore explains that the inventors of algebra were Arabic scientists. Their definition:

X = something, some undefined unknown thing = the unknown thing.

When the books were translated from Arabic to Spanish the Arabic unknown was “* SH*” that did not exist inSpanish. They replaced it by “

X is “* X*” because Spanish language does not have “

March 4, 2017 Leave a comment

*Mary has a cat, and a rat, and a hat, and a mat.*

**If the cat is on the mat, and rat is in the hat, but the hat is on the mat, where is the rat?**

This is a simple puzzle asked by Leslie Green, who collects dozens challenging puzzles. The collection of Leslie Logic and Math Puzzles is presented at the website Aplusclick. It’s worth to try the challenging questions.

November 9, 2016 1 Comment

Math and Logic are full of paradoxes.

**1. Achilles and the Tortoise** The Paradox of Achilles and the Tortoise was described by the Greek philosopher **Zeno of Elea** in the 5th century BC. The great hero Achilles challenges a tortoise to a footrace. He agrees to give the tortoise a head start of 100m. When the race begins, Achilles starts running, so that by the time he has reached the 100m mark, the tortoise has only walked 10m. But by the time Achilles has reached the 110m mark, the tortoise has walked another 1m. By the time he has reached the 111m mark, the tortoise has walked another 0.1m, then 0.01m, then 0.001m, and so on. The tortoise always moves forwards while Achilles always plays catch up. Why is Achilles always behind the tortoise?

**2. Bermuda Triangle Paradox. **Why the sum of the interior angles of the Bermuda triangle is not 180 degrees?

**3. Simpson Paradox. **The average score for dance of boys and girls in class A are 16 and 21, respectively. The average score of boys and girls in class B are 15 and 20, respectively. Twenty percent of class A students are girls. Forty percent of class B students are girls. Which class has a higher average score?

**4. Braess paradox.** The diagram shows a road network. All cars drive in one direction from A to F. The numbers represent the maximum flow rate in vehicles per hour. Engineers want to construct a new road with a flow rate of 100 vehicles per hour. Drivers randomly choose the road at crossroads. What new road decreases the capacity of the network (the number of vehicles at point F)?

**5. Barber Paradox **In a city, the barber is the ‘one who shaves all those, and those only, who do not shave themselves.’

Who shaves the barber?

**6. The Two Envelope Paradox.** One envelope has twice as much money as the second one. Gerry does not know which envelope contains the larger amount. He takes one of the envelopes, counts the money, and is offered the chance to switch the envelope. He thinks “If the amount of money in the chosen envelope is X dollars, then the other envelope contains either 2X of 0.5X dollars, with equal probability of 0.5. The expected value of switching is 0.5 (2X) + 0.5 (0.5X) = 1.25X. This is greater than the value in the initially chosen envelope. It is better to switch.” What is your advice?

**7. Potato Paradox.** I have 100kg of potatoes, which are 99 percent water. I dry them until they are 98 percent water. How much do they weigh now?

**8. Leonard Euler’s Paradox. **Why the average of all of the numbers is not a zero?

1, -1, 2, -2, 3, -3, . . .

9. **Friendship Paradox. **Your friends have more friends than you. Why?

**10. Uninteresting Number Paradox. **How many uninteresting numbers exist?

**11. Gabriel’ Horn Paradox.** The shape obtained from rotating the equation about x-axis resembles a trumpet. If we need an infinite volume of paint to paint the infinite horn, how much paint does the horn can contain inside itself?

**12. Pop Quiz Paradox.** A teacher announces that there will be a quiz one day during the next week. The teacher gives the definition that they would not when they come in to the class that the quiz was going to be given that day. The brightest student says that the quiz cannot be on Friday because they will know the day. With the same technique, she eliminates Thursday, Wednesday, Tuesday, and Monday. “You cannot give us a pop quiz next week” she says. When does the teacher give the pop quiz? I know the paradox from Charles Carter Wald. Probably, Martin Gardner described it for the first time in The Colossal Book of Mathematics.

10. Uninteresting Number Paradox