Blog Posts on high school mathematics
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Counting the Number of Squares on a Chess Board by Mathematics and Multimedia on May 26, 2012Chess is one good source of puzzles and mathematical problems. In this post, we discuss one of the most basic problems in chess: Counting the number of squares on the chessboard. How many squares are there in a standard chessboard … Continu...
Proof of the Sum of Square Numbers by Mathematics and Multimedia on May 26, 2012Yesterday, we have counted the number of squares on a chessboard, and we have discovered that it is equal to the sum of the squares of the first 8 positive integers. We call these numbers square numbers. So, the first 4 … Continue reading &#...
A Simple Proof of the Arithmetic Mean Geometric Mean Inequality by Mathematics and Multimedia on May 16, 2012Last February, we have used area to prove the Arithmetic Mean – Geometric Mean Inequality (AM-GM Inequality). In this post, we show a simpler proof. Recall that the AM-GM Inequality states that given two numbers, their geometric mean is...
The Proof of the Tangent Half-Angle Formula by Mathematics and Multimedia on May 2, 2012In this post, we prove the following trigonometric identity: . Proof Consider a semi-circle with “center” and diameter and radius equal to 1 unit as shown below. If we let , then by the Inscribed Angle Theorem, . Draw perpendicular R...
Another Proof of the Sum of the First n Positive Integers by Mathematics and Multimedia on Apr 29, 2012We have discussed how Gauss was able to devise a clever way to add the first positive integers at a very young age in a few minutes. We generalized his method and have also seen the link between the sum and the … Continue reading →...
Wedding Guests and Circular Permutations by Mathematics and Multimedia on Apr 22, 2012In a wedding banquet, guests are seated in circular table for four. In how many ways can the guests be seated? We have learned that the number of permutations of objects on a straight line is . That is, if … Continue reading →...
Divisibility by 9 by Mathematics and Multimedia on Apr 19, 2012This is the 8th part of the Divisibility Rules Series. In this post, we discuss divisibility by 9. When 10 is divided by 9, it gives a remainder of 1 since 10 = 9 + 1. Also, 100 divided by … Continue reading →...
Guest Post – Mega Millions Lottery Jackpot Winners Beat the Odds by Mathematics and Multimedia on Apr 9, 2012Three Mega Millions lottery tickets successfully matched all 5 number draws and the Mega Ball pick in the March 30 draw, earning them each one third of the $656 million jackpot. It is reported that over 1.5 billion Mega Million … Continue readi...
Counting the Number of Subsets in a Set by Mathematics and Multimedia on Apr 5, 2012Problem: How many groups can be formed from 5 persons? First, we represent the persons by small letters a, b, c, d, and e, and we denote a group whose members are c and d as {c, d}. We can … Continue reading →...
A US President’s Proof of the Pythagorean Theorem by Mathematics and Multimedia on Mar 25, 2012James Garfield, the 20th president of the United States, came up with an original proof of the Pythagorean Theorem in 1876 when he was still a Congressman. His proof was published in New England Journal of Education. Recall that the … Continue...
