Two friends decide to meet at a definite place between 9 AM and 10 AM. The first to arrive waits for his friend for 15 minutes and then leaves. If each of them arrives at an arbitrary moment between 9 … Continue reading →

Traffic flow is not that different from the flow of anything else. Imagine heat flow along an iron rod or water flowing down a pipe. If you observe the traffic (on a highway) from a far enough distance, the mass … Continue reading →

The real logarithmic function has two interesting properties:

The Flattening property:  – a product is flattened into a sum

The Linearizing property: –> Linearized an exponential (growth) function

These properties show the general ‘tone it down’ nature of the logarithmic function. It’s … Continue reading →

Problem Statement
Consider n points lying on the Unit Sphere (the image shows a unit circle instead of a sphere). Show that the sum of the squares of the lengths of all segments determined by the n points is less than … Continue reading →

Even if you do not consider math to be a hobby, this article may provide an understanding of why a lot of people do. Not being a math-aficionado, my wife thought it a bit strange that I enjoyed solving math … Continue reading →

Imagine a long distance runner who runs a 10 miles in 50 minutes (averages 1 mile every 5 minutes).  Is it true that he has to have one stretch of 2 miles which is completed in EXACTLY 10 minutes?

Intuitively, … Continue reading →

The complex exponential – reduces to Euler’s identity if -i.e. is purely imaginary.