The unit circle is probably the most over-memorized diagram in mathematics.

Look for the pattern, not the values.

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When the Nazis occupied Denmark, Niels Bohr had to hide two gold Nobel Prize medals.

Instead of burying them, he dissolved them in aqua regia, leaving an ordinary-looking jar of orange liquid on a laboratory shelf.

The Nazis walked right past it.

After the war, the gold was recovered and the medals were recast.

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"My life has consisted in learning and forgetting and learning and forgetting and learning and forgetting statistical mechanics".

- Leonard Susskind

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All formulas for circle

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Percentage Trick

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There is so little use for them that they are generally unfamiliar to most of us.

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Jastrow Illusion. A pretty interesting optical illusion. The two figures are the same size.

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Maurits Cornelis Escher.

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Walk along the Fibonacci numbers as far as you like and you will never again land on a perfect square once you pass 144.

Beyond the trivial 1, it is the only large Fibonacci number that is also a square - a fact proven by John H. E. Cohn in 1964.

Fittingly, 144 sits at position twelve and equals twelve squared.

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In the early nineteenth century, Carl Friedrich Gauss and Wilhelm Weber helped turn magnetism into a quantitatively precise science through careful measurements of Earth’s magnetic field.

Michael Faraday then introduced the physical idea of magnetic field lines, treating magnetism not merely as a force between objects, but as a field distributed through space.

James Clerk Maxwell gave these ideas their mathematical unity.

In his electromagnetic theory, magnetic fields were described as having no isolated sources or sinks. In modern language, the divergence of the magnetic field is zero.

This means that magnetic field lines do not begin or end at a single magnetic charge. Instead, they form continuous loops. Even when a bar magnet is divided, each piece still possesses both a north and a south pole.

The equation commonly written today was not presented in this compact vector form by Gauss or Maxwell. The modern notation emerged later, especially through the work of Oliver Heaviside and others who reformulated Maxwell’s theory using vector calculus.

So this single equation contains several stages in the development of physics:

Gauss helped make magnetism measurable.

Faraday gave us the field picture.
Maxwell unified electricity, magnetism, and light.
Heaviside helped express the theory in the mathematical language students use today.

That is why is more than a formula.

It is a compressed statement about both the structure of magnetic fields and the historical development of electromagnetic theory.

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Take a number made only of ones — a repunit — and square it. Out tumbles a perfect palindrome that climbs up to the count of ones and then walks right back down.

The staircase holds beautifully up to nine ones; beyond that the digits begin to carry and the mirror finally cracks.

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Can you believe?

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Math family

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This is how cinema looked like before electricity

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