The Mind-Bending Challenge of Estimating Distance Between Spheres🤓💯📚 #shorts #math #mathstricks
17Suppose you have two identical spheres, A and B. Sphere A has a radius of 1 unit, and sphere B has a radius of 2 units. Now, imagine that sphere A is nested inside of sphere B, so that they share the same center point.
Here's the challenge: Without using any tools to measure or calculate distances, estimate the distance between the surface of sphere A and the surface of sphere B at the point where they intersect.
At first glance, it might seem like the answer is 1 unit (the radius of sphere A) plus 2 units (the radius of sphere B), which would give a total of 3 units. However, due to an optical illusion called the Ebbinghaus illusion, the actual distance between the two surfaces might appear to be greater or smaller than this estimate.
Give it a try and see what you come up with!
The Ebbinghaus illusion is a visual illusion that can make it difficult to accurately judge distances between objects. In this case, it might make the distance between the surface of sphere A and the surface of sphere B at their point of intersection appear to be either greater or smaller than the sum of their radii.
The actual distance between the surfaces of the spheres at their point of intersection can be calculated as follows:
Let d be the distance between the centers of the spheres. Then, by the Pythagorean theorem, we have:
d^2 = (2r)^2 - (r)^2
d^2 = 4r^2 - r^2
d^2 = 3r^2
d = sqrt(3)*r
Substituting r=1, we get d=sqrt(3) units.
Therefore, the distance between the surfaces of the spheres at their point of intersection is approximately 0.732 units (which is equal to sqrt(3)-1). However, due to the Ebbinghaus illusion, this distance might appear to be greater or smaller than this estimate.