## Excel in math and science

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestLet the length of one leg be \(\sqrt{2}\). Then we can calculate the semiperimeter as \(1+\sqrt{2}\), and thus the radius of the inscribed circle as \(\frac{1}{1+\sqrt{2}}\). The area is then \(\pi(\sqrt{2}-1)\). The next two figures are quite simple, we see that in the upper-right figure, the square is half of the area of the triangle, and in the last figure, the side length of the square is \(\frac{1}{3}\) of the hypotenuse, thus the area is \(4/9\). Computing, we find that the circle contains the largest area.

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