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...

# Category - Physics, Math

Interesting Physics and Math Stuff

Imagine you are in a spaceship moving away from the earth at a velocity v. Imagine that a TV broadcast is sent to your spaceship from Earth. How would you see the broadcast? The Approach to the solution We imagine that observers...

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...

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 problems for fun (I...

Imagine a long distance runner who runs 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, there should...

Light has no mass – yet it can push solar sails. How? It is true that photons do not have “rest” mass. They do have energy – and hence an associated mass given by m = E/c2. Light has momentum given by p...

If you threw an egg at your bedsheet or blanket (held from all 4 ends), would it break? The answer is no. Newton said that the force that the egg would experience, would depend on the ‘rapidity’ with which it came to a...

One of the most formidable hurdles in getting into a top 10 MBA school is the application essay. I know this because several people close to me have applied and gone on to get degrees from these coveted institutions – including...

## The complex exponential

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