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 $\triangle ABC$?

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 $\triangle ABC$?

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: $$e^{\pi}\ -\ \pi\ -\ 20 \approx 0$$ $$\pi^4\ +\ \pi^5\ -\ e^6 \approx 0$$ $$e^{\pi\sqrt{163}}\ -\ 262537412640768744 \approx 0 $$
Did you know that 0.999… = 1? Or that the first 3 digits of π viewed backwards spells “pie” or “ριε”? Have you ever wanted something fun and challenge with math? If yes, then this website is perfect for you!