Category Archives: Equations

Q: What’s the chance of getting a run of K or more successes (heads) in a row in N Bernoulli trials (coin flips)? Why use approximations when the exact answer is known?

Posted on July 24, 2010 by The Physicist

The original question was: Recently I’ve come across a task to calculate the probability that a run of at least K successes occurs in a series of N (K≤N) Bernoulli trials (weighted coin flips), i.e. “what’s the probability that in … Continue reading →

Posted in -- By the Mathematician, -- By the Physicist, Combinatorics, Equations, Math, Probability | 54 Comments

Q: What are complex numbers used for?

Posted on March 24, 2010 by The Physicist

Physicist: If you’ve ever had to do square roots you’ve probably come up against the problem of taking the square root of a negative number.  If you restrict your attention only to real numbers (0,1, -17, , √2, …, any … Continue reading →

Posted in -- By the Physicist, Equations, Math, Quantum Theory | 23 Comments

Q: How did mathematicians calculate trig functions and numbers like pi before calculators?

Posted on February 27, 2010 by The Physicist

Physicist: Don’t know.  But if you’re ever stuck on a desert island, here are some tricks you can use.  The name of the game is “Taylor polynomials“. All the other trig function are just combinations of sine and cosine, so … Continue reading →

Posted in -- By the Physicist, Equations, Math | 11 Comments

Q: What’s so special about the Gaussian distribution (i.e. the normal distribution / bell curve)??

Posted on February 13, 2010 by The Physicist

Physicist: A big part of what makes physicists slothful and attractive is a theorem called the “central limit theorem”.  In a nutshell it says that, even if you can’t describe how a single random thing happens, a whole mess of … Continue reading →

Posted in -- By the Mathematician, -- By the Physicist, Entropy/Information, Equations, Math, Probability, Quantum Theory | 11 Comments

Q: What’s the relationship between entropy in the information-theory sense and the thermodynamics sense?

Posted on January 18, 2010 by The Physicist

Physicist: The term “Entropy” shows up both in thermodynamics and information theory, so (since thermodynamics called dibs), I’ll call thermodynamic entropy “entropy”, and information theoretic entropy “information”. I can’t think of a good way to demonstrate intuitively that entropy and … Continue reading →

Posted in -- By the Physicist, Entropy/Information, Equations, Math, Philosophical, Physics | 12 Comments

Q: Why is e to the i pi equal to -1?

Posted on October 29, 2009 by The Physicist

Physicist: This equation () was recently voted one of the most famous equations ever.  That isn’t part of the answer, it’s just interesting. First, you’ll find (by plugging them into a graphing calculator and graphing) that: 1) 2) 3) Where … Continue reading →

Posted in -- By the Physicist, Equations | 30 Comments