Category: Math Puzzles
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What Fraction Of The Decagon Is Shaded?
What fraction of this regular decagon is shaded? Give this problem a try before jumping in for the solution! Solution: Brute Force The first solution is done with trigonometric functions. We first let each side length of the decagon equal 1. We then add two straight lines as shown below. The size of the angles can…
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So How Far Has The Ant Walked?
This is a question on the application of complex numbers. The standard solution requires us to formulate a function to represent the action of moving forward one unit and turning to the right by 2π/9, and compute the sum using the sum of geometric series formula. But there’s a more elegant way to do this, which lets us…
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Apparently There’s A Math Problem In America
If I were to tell you that your go-to meal at the local steakhouse has a price reduction of 600%, what would you do? Well of course, you’d drop everything that you are doing and order as many fatty ribeye steaks served the finest fries and salads as you possibly can. Why? Because not only…
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Calculus Challenge: A Slanted Revolution
In this entry, we will solve the above problem using a rotational matrix. Give this problem a try before jumping into the solution! Solution By rotating the curve C and the line y = x by π/4 radians anticlockwise about the origin, the rotated volume will be given by the rotated curve about the y axis between the points at which…
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Math Genius Mary Adler’s Calculus Problem
The real Math Girl Mary Adler is a fictional character from the movie ‘Gifted’. In the Gifted universe, she is a seven year-old math prodigy. I must say I was also considered a ‘Gifted’ child by many. Gifted not because I was good at mathematics, but because I wielded the exceptional prowess of ‘舉一反三’, which…
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University Has Become A Wealth Extraction Machine And Taught Me Absolutely Nothing Useful
An Absurd Price Hike When I did my mathematics degree, I was charged around £28,000 each year for a 3-year undergraduate course. 3 years later, the exact same course, teaching the exact same timeless mathematics is now priced at £35,530 per year at the university I went to. Needless to say, there has been similar price…
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Here’s How Archimedes Measured a Curve Without Calculus
Archimedes tackled the long-standing problem of finding the area of a parabolic segment (the region between a parabola and a chord). In Quadrature of the Parabola, a 3rd-century BC treatise addressed to his friend Dositheus, he proves that the area of any parabolic segment is 4/3 times the area of the inscribed triangle on the same…
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An Oxford MAT Exam Question
This is a fairly standard exercise in integral calculus. I guess the standards for getting into Oxford to read mathematics is dropping. Oh well. Anyway, can you figure out the right answer? If so, perhaps you too, deserve a place at Oxford. Solution There’s a bit to unpack here. We have sketched the equation y…
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Oxford University Mathematics Challenge
A simple cubic equation sort of looks like a snake meandering through the origin. Adding other terms changes the way it meanders, which often results in different intersections it makes with the axes. Our challenge today is to analyze the above equation find out exactly how many solutions it has. Now are you ready? Let’s…