It's Pi day today and everyone is preoccupied with problems about circles and circumference length. A circle, while appearing to be the simplest geometric shape, is also both fascinating and important. Let’s take a closer look at the incredible properties of a circle. What makes it so special? Is it, say, “better” than a square, and while we are on the subject - what is “better”, a cube or a sphere?
Let’s start our dive into the world of circles with some food for thought.
Solution. Here are a few arguments in favor of the circle shape. A round cover is easier to close, as one does not need to match the corners; One does not run the risk of having the square cover fall through the vent if it is not properly positioned. (A square cover poses this risk because the diagonal of a square is longer than its side. Hence, a vertically positioned square cover can fall through.) A round cover is easier to move: one can roll it on the ground like a wheel; A round cover takes up less area than a square of the same diameter, hence fewer materials are used in the manufacturing;
A space probe has landed on an asteroid. The only information we know is that the asteroid is both a sphere and a cube. The probe has moved along the surface to reach a point that is symmetrical to its starting point with respect to the center of the asteroid. During all of this time, the probe was continuously transmitting its coordinates to the space station where a 3D model of the probe’s movement trajectory was created. Is it possible that this information is insufficient to determine whether the probe was moving along a cube or a sphere?
