Category Archives: Geometry

Circles in a Square – Part 3

Posted on November 23, 2019 by kevin

By adding one more quarter circle, we have the following figure. The question is: what is the area of the region bounded by arc $\stackrel \frown {AE}$, $\stackrel \frown {EF}$ and $\stackrel \frown {FA}$? In fact, based on the calculations … Continue reading →

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Circles in a Square – Part 2

Posted on November 22, 2019 by kevin

Continuing this topic, look at the following diagram, with two quarter circles in a unit square, the question is: what are the area of of each of the 4 regions inside the square? To answer the question, we need to draw … Continue reading →

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Solution to November 21, 2019’s Challenge

Posted on November 22, 2019 by kevin

Actually, you can not make such a shape in our 3-dimension world 🙂 You need to be living in a 4-dimension universe to construct $10$ equilateral triangles with only $10$ matchsticks. The 4-dimension object is called tetrahedral pyramid or 5-Cell. … Continue reading →

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Problem of the Day – November 21, 2019

Posted on November 21, 2019 by kevin

Make $10$ equilateral triangles, all of the same size, using $10$ matchsticks, where each side of every triangle consists of exactly one matchstick. Hint: Think outside the box 🙂

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Circles in a Square – Part 1

Posted on November 20, 2019 by kevin

Circles and squares are two common geometric shapes encountered very often in our daily life. In this series we present a class of fun problems involving circles in a square. Look at the following figure, a quarter circle is drawn inside a … Continue reading →

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