Consider the following integral: INTEGRAL (1/x) dx Perform integration by parts: let u = 1/x , dv = dx du = -1/x2 dx...
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Successive Differences of Powers
List the squares: 0, 1, 4, 9, 16, 25, 36, 49, … Then take their successive differences: 1, 3, 5,...
Continue reading...Pick’s Theorem
A lattice point in the plane is any point that has integer coordinates. Let P be a polygon in the plane whose vertices have...
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The intersection of two spheres is generally a circle (but might also be a point or the empty set). That...
Continue reading...Difference of Squares
You have all learned that a2 – b2 = (a + b)(a – b) But perhaps you haven’t thought about how to...
Continue reading...Magic 1089
Here’s a cool mathematical magic trick. Write down a three-digit number whose digits are decreasing. Then reverse the digits to...
Continue reading...Math Limerick
Question: Why is this a mathematical limerick? ( (12 + 144 + 20 + 3 Sqrt[4]) / 7 ) +...
Continue reading...Birthday Problem
How many people do you need in a group to ensure at least a 50 percent probability that 2 people...
Continue reading...Are Coins Fair?
When you flip a coin, what are the chances that it comes up heads? If the coin is “fair” then we...
Continue reading...Largest Known Primes
Since there are infinitely many primes, what are the largest primes that we know of?The largest known primes are ones of...
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