Equations that changed the world - photo

[Altair]

Equations that changed the world.




Previously:

Einstein explaining his famous formula e=mc2 - GIF
1960s NASA before PowerPoint and using ladders to do math - photos
Hyperboloid of revolution
Chaos theory demonstration - GIF
Richard Feynman explains: What keeps a train on the track?

[mklotz]

Forgot a very important one, Euler's formula...

e^ix = cos x + i sin x

which, when evaluated for x = π, yields the amazing relation...

e^iπ + 1 = 0

An irrational number raised to an irrational, imaginary value yields an integer - astounding.

And here's one way to prove it...

[Toolmaker51]

Forgot a very important one, Euler's formula...

That's because Euler didn't have a good publicist or agent;
or
the convening board felt a third revolutionary concept per mathematician an excess.

[2wheelcharlie]

the chemists secrets are freely told to the carpenter ( emerson)

[Toolmaker51]

the chemists secrets are freely told to the carpenter (emerson)

Note those who needing an exclusive vocabulary to restrain such occurrence.

[mwmkravchenko]

Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )

[Toolmaker51]

Whew! Thought I was the one making all that noise.

[Jon]

Don't forget the critical mathematical contributions of the American woke movement in the past few years:

[mklotz]

Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )

Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

[mwmkravchenko]

Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

Yup, my spelling prowess is slipping little by little. Funny how language changes, is Old English they even used similar spelling to German. Roots of English being German and French for a great part, and a lot of Greek too. Pays to do a little appreciating of how things we use regularly come to be. It's called history. Some of it is even honest!