Monthly Archives: November 2019

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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Problem of the Day – November 19, 2019

Posted on November 19, 2019 by kevin

In $\triangle ABC$, $D$ is on line $\overline{BC}$ and $\overline{BD}=\overline{CD}$, $E$ is on line $\overline{AC}$ and $\overline{AE}=2\overline{CE}$. Find the value of $\dfrac{\overline{DF}}{\overline{AF}}$.

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Problem of the Day – November 18, 2019

Posted on November 18, 2019 by kevin

In the following figure, point $C$, $D$ and $E$ are the middle points of line segment $AB$, $AC$ and $BC$, with the length of line segment $AB$ as $4$. Additionally, 6 semi-circles are drawn with diameters as $AD$, $AC$, $AE$, $DB$, $CD$ and $EB$. Find … Continue reading →

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Problem of the Day – November 17, 2019

Posted on November 17, 2019 by kevin

In the figure below, $D$ is the middle point of line $\overline{AB}$, $E$ is the middle point of $\overline{BC}$. $\overline{AE}$ and $\overline{CD}$ intersect at $F$. What is the area ratio $\triangle DEF$ and $\triangle ABC$?

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Fun Math Facts

Posted on November 1, 2019 by kevin

Euler’s Identity\(\ e^{i\pi} + 1 = 0\) is the most well-known relationship between \(e\) and \(\pi\). The following are a few less-known facts or coincidences between them: $$e^{\pi}\ -\ \pi\ -\ 20 \approx 0$$ $$\pi^4\ +\ \pi^5\ -\ e^6 \approx 0$$ $$e^{\pi\sqrt{163}}\ … Continue reading →

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