Category Archives: Math

Q: If you suddenly replaced all the water drops in a rainbow with same-sized spheres of polished diamond, what would happen to the rainbow? How do you calculate the size of a rainbow?

Physicist: A normal rainbow is created when light enters a water droplet, bounces once off of the far side, and comes back out. Diamond “droplets” however don’t make rainbows.  In order to get a rainbow that exists, and isn’t in … Continue reading

Posted in -- By the Physicist, Equations, Geometry, Physics | 4 Comments

Q: Is 0.9999… repeating really equal to 1?

Mathematician: Usually, in math, there are lots of ways of writing the same thing. For instance: = = = =   As it so happens, 0.9999… repeating is just another way of writing one. A slick way to see this … Continue reading

Posted in -- By the Mathematician, Equations, Math | 117 Comments

Q: How do I estimate the probability that God exists?

Mathematician: Before jumping into this question, it is important to realize that probabilities are not objective, observer independent quantities. We can think of the claim that a particular outcome will happen with a probability of 0.30 as meaning (loosely speaking) … Continue reading

Posted in -- By the Mathematician, Philosophical, Probability, Skepticism | 36 Comments

Q: How do you calculate 6/2(1+2) or 48/2(9+3)? What’s the deal with this orders of operation business?

Mathematician: Now that the Physicist and I have answered questions like these ones at least 9 times via email, I figure we should get this horrible topic out of the way once and for all with a short post. The … Continue reading

Posted in -- By the Mathematician, Conventions, Math | 342 Comments

Q: Is the edge of a circle with an infinite radius curved or straight?

Physicist: Straight. In fact, in mathematics the “curvature” of a curve is usually defined as the “reciprocal of the radius of the osculating circle”.  This is fancy talk for: fit a circle into the curve as best you can, then … Continue reading

Posted in -- By the Physicist, Geometry, Math | 26 Comments

Q: Is there a formula to find the Nth term in the Fibonacci sequence?

Physicist: Hells yes!  It’s , where the “≈” is close enough that you can round to the nearest integer.  Astute readers will notice that is the golden ratio, and may wonder if this is a coincidence.  Yes. Everything after this … Continue reading

Posted in -- By the Physicist, Equations, Math | 22 Comments