Tag: Geometry
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An American President’s Proof of The Pythagorean Theorem
US President: James A Garfield As the 20th President of the United States in 1881, James Garfield came up with an elegant proof of the Pythagorean Theorem in 1876 while being a Congressman. His proof of this well-known theorem was later published in the New England Journal of Education Without further ado, let’s dive in! a²…
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How Would YOU Find The Total Shaded Area?
This is another geometry puzzle by Catriona Agg on X. Both the regular hexagons have area 6. What’s the total shaded area? Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the solution. And if you come up with your…
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What Is The Area Of The Square?
The circle has a radius 1. The diagonal of the square extends to be a tangent of the circle. The circle touches the black lines at three points as shown. Find the area of the square. Once again, this is a good moment to pause the article and give the problem a go yourself. When…
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How Would You Tether Your Goat?
A goat is tethered to the edge of a circular paddock, with a lead adjusted so that the goat can eat just half of the field. So can you tell us how long the tether must be? Here’s a smoother paraphrased version that preserves the meaning while reading more naturally: At first glance, it seems…
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Can You Solve This Classic Geometry Puzzle?
I was browsing through Twitter and came across this very interesting problem by @Pratik Matematik. There are two ways to solve it, one using geometry, the other relying on trigonometric formulas! Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the…
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So How Does The Koch Snowflake Have Finite Area?
Following part one of the series, we will now look at the area of a Koch snowflake starting with an equilateral triangle with a side length of 1. Give the problem a try before jumping in for the solution! Area Let’s look at what happens in the first iteration We are adding one new triangle for each…
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Even A 6 Year-Old Kid Can Solve This In 7 Seconds. But Can You?
The area of a triangle is 1/2(b)(h), where b is the base and h is the height. What that means is that a triangle can have the same area with many different shapes. This simple but insightful puzzle can be solved in under 7 seconds if only you know well enough about triangles ⏳ Personally…
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How Does The Koch Snowflake Have Infinite Perimeter?
What is the perimeter of the above Koch snowflake starting from an equilateral triangle with side length 1? This is part one of a two-part series on Koch snowflake. Stay tuned for the next post on finding the area! Give this problem a try before jumping in for the solution! Introduction The Koch snowflake is…
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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…