In the Morning

How to be Amazing

onlinecounsellingcollege:

- Give more than is required
- Learn as much as you can
- Be strong and courageous
- Speak and live your truth
- Be true to your values
- Resist mediocrity
- Seek to inspire others
- Love wholeheartedly.


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.

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.

(Source: saulofortz, via visualizingmath)

For me, it’s been liberating to put myself in the mind of a fictitious six year-old each day, and rediscover my own curiosity. I’ve been amazed at how one ideas leads to others if I allow my mind to play and wander. I know a lot about dinosaurs now, and the information has helped me out of quite a few deadlines.
A playful mind is inquisitive, and learning is fun. If you indulge your natural curiosity and retain a sense of fun in new experience, I think you’ll find it functions as a sort of shock absorber for the bumpy road ahead.

- Bill Watterson, excerpt from his commencement speech at Kenyon College, class of 1990.