# Tag: geometry

## alculus – Area covered by a constant length segment rotating around the center of a square.

The Question : 63 people think this question is useful This is an idea I have had in my head for years and years and I would like to know the answer, and also I would like to know if it’s somehow relevant to anything or useless. I describe my thoughts with the following image:

## alculus – Why is the derivative of a circle’s area its perimeter (and similarly for spheres)?

The Question : 109 people think this question is useful When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle. Similarly, when the formula for a sphere’s volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$, we get $4 \pi r^2$. Is

## alculus – What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?

The Question : 127 people think this question is useful My friend gave me this puzzle: What is the probability that a point chosen at random from the interior of an equilateral triangle is closer to the center than any of its edges? I tried to draw the picture and I drew a smaller (concentric)

## eometry – How do CSS triangles work?

The Question : 1888 people think this question is useful There’re plenty of different CSS shapes over at CSS Tricks – Shapes of CSS and I’m particularly puzzled with a triangle: How and why does it work? The Question Comments : You can: jsfiddle.net/wbZet How about the square that’s not there? jsfiddle.net/minitech/sZgaa @mskfisher The size