Tim Rohde
358 followers -
Instigator, Strategist, Beast
Instigator, Strategist, Beast

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Simple, elegant way of thinking about infinitesimals. Note how as the pie slices get thinner the amount of the curve that protrudes under the x axis diminishes until, when it get's near to the "width" of a point, it's no longer an issue.﻿
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The Brachistochrone
This animation is about one of the most significant problems in the history of mathematics: The Brachistochrone Challenge:

If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?

Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.

Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics,Calculus of Variations, had to be invented to deal with such problems. Today, calculus of variations is vital in Quantum Mechanics and other fields.

Reference:
http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Brachistochrone.html
http://www.hep.caltech.edu/~fcp/math/variationalCalculus/variationalCalculus.pdf

Animation via imgur

#math   #animation   #brachistochrone  ﻿
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the noblehuman project™

I am excited to announce the launch of my new clothing graphics line:

www.NobleHumans.com

We live in a world profoundly in need of human evolution. In need of a more noble reality.

How do we accomplish this? How do we rise above hate? How do we rise above differences? How do we become more Noble Humans?

The Noble Pursuits influenced some of the greatest philosophers humankind has ever known, as far back as Thales, Parmenides, Heraclitus, Socrates, Plato, Aristotle and Aspasia. And later, throughout the history of every culture on Earth. How do we ensure a future dedicated to the highest ethics humanity can attain? By becoming noblehumans and re-embracing millennia-held virtues and ideals: Truth. Courage. Compassion. Perseverance. Wisdom. Trust. Gratitude. Respect. Harmony. Imagination. Peace. Joy. Love.

Noblehumans.com™ and the noblehuman project™ comprise a global campaign to spark evolutionary growth for humanity. By supporting, practicing and living these noble virtues and ideals, we will evolve toward a higher power of being. Through a variety of social media/educational platforms and web/television programming, we are launching this effort to inform, to engage… to inspire a movement. To create a more evolved humanity. noblehumans.com and the noblehuman project will help build the best of all possible futures.

One of our goals is to support, and donate to, worthy causes that reflect and promote these noble virtues and ideals.

NobleHumans… Humanity to a Higher Power.﻿
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Is insurance about to get Amazonned?﻿
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I can't wait to read more of these!!﻿
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Just beautiful.﻿
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Cool periodic table animation!﻿