How many apples did each automattician eat?

Four friends Matt, James, Ian and Barry, who all knew each other from being members of the Automattic, called Automatticians, sat around a table that had a dish with 11 apples in it. The chat was intense, and they ended up eating all the apples. Everybody had at least one apple, and everyone know that fact, and each automattician knew the number of apples he ate. They didn't know how many apples each of the others ate, though. They agreed…

Fox – Rabbit Chase Problems

Part I: A fox chases a rabbit. Both run at the same speed $ v$ . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs at an angle $ \alpha $ relative to the direction directly away from the fox. The initial separation between the fox and the rabbit is $ l$ . When and where does the fox catch the rabbit (if it does)? If it never does, what…

Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $ x$ but do not possess a derivative for any value. We now consider the celebrated function given by Weierstrass to show this fact. It will be shown that if $ f(x)= \displaystyle{\sum_{n=0}^{\infty} } b^n \cos (a^n \pi x) \ \ldots (1) \\ = \cos \pi x +b \cos a \pi x + b^2 \cos a^2 \pi x+ \ldots $ where $…

Bhaskara – Bhaskar II – Bhaskaracharya

Memory Methods

Memory, in human reference, is the ability to store retain and recall information when needed. Without hammering the mind in the definitions, let we look into the ten methods of boosting our memory:  1. Simple Repetition Method The classical method, very popular as in committing poems to memory by reading them over and over. 2. Full Concentration Method Concentrate on the topic content while learning. Do not allow your mind to wander. Focus on names and numbers. Try deliberately to…