Hi! Can You Tell Some Uni Or Colleges Math Resources?

the mathematics students

crisp, grey mornings

the scratch of pencil on graph paper

working through complex problems just for the joy of it

baroque era piano music playing in the background

a love of patterns and puzzles

writing out your favorite proofs again and again

advanced math courses, sitting with the upperclassmen

the dusty green of an empty chalkboard

formulas scribbled on your hand in pen

going through a problem again and again until you understand it fully

carefully sketched graphs

short, bitten nails

ice cold water

hands marked with graphite

using math to take apart the world around you

doodling fractals on scratch paper

memorizing digits of pi just to show off to your friends

the moment of clarity when a problem fits together

hair clipped back out of your face

looking for fibonacci sequences in nature

watching a long and complicated equation simplify down to something short and compact

An Oxford student looking through a book on sale England, 1950

Incorrect AOT quotes

Saint Veronica with the Veil (Original piece by Mattia Preti c.1655-1660) Touched by Clayshaper

Vampire amoeba

Potential energy is energy debt borrowed from vacuum energy bank

Potential energy is defined as the energy difference between the energy of an object at a current position and the energy of the object at a reference position (generally, infinitely distant position) in a force field.

The gravitational potential energy of a combination of an object with mass M and another object with mass m separated by distance R is expressed by the following formula using the gravitational constant G.

The potential energy is zero when the distance between objects is infinite, and the negative energy increases as the distance decreases by gravity.

Because there can be no negative energy in the real space, potential energy should be considered as fictitious energy. Regarding potential energy as “energy debt” is easy to understand. Then what do objects borrow energy from? The answer is the vacuum space. Potential energy is the energy debt borrowed from “the vacuum energy bank”. An increase in the negative energy means an increase in the energy given by the vacuum space.

Therefore, the law of conservation of energy is established only when the vacuum energy is counted.

When an object is attracted to another object by gravity, a certain amount of energy is given to it from the vacuum space. Hence its energy debt increases by the amount given from the vacuum space, and its momentum energy increases then it accelerates.

On the contrary, when applying a force to an object and moving it against gravity, it returns a certain amount of energy to the vacuum space. Hence the energy debt decreases by the amount returned to the vacuum space, and its momentum energy decreases then it decelerates from the initial speed.

We say “potential energy increases” when the energy debt decreases, but we should say “potential energy decreases”.

Pan (moon of Saturn) - March 07 2017

NASA/JPL-Caltech/SSI/Kevin M. Gill

Beautiful proofs (#4) - When Gauss was a young child...

The legend goes something like this:

Gauss’s teacher wanted to occupy his students by making them add large sets of numbers and told everyone in class to find the sum of 1+2+3+ …. + 100.

And Gauss, who was a young child (age ~ 10) quickly found the sum by just pairing up numbers:

Using this ingenious method used by Gauss allows us to write a generic formula for the sum of first n positive integers as follows: