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Equations that changed the world.
https://diqn32j8nouaz.cloudfront.net...d_fullsize.jpg
Previously:
https://www.homemadetools.net/forum/...644#post159273
https://www.homemadetools.net/forum/...304#post131095
https://www.homemadetools.net/forum/...913#post133628
https://www.homemadetools.net/forum/...698#post209675
https://www.homemadetools.net/forum/...2811#post97204
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...
Attachment 44242
That's because Euler didn't have a good publicist or agent;Quote:
Originally Posted by mklotz
or
the convening board felt a third revolutionary concept per mathematician an excess.
the chemists secrets are freely told to the carpenter ( emerson)
Note those who needing an exclusive vocabulary to restrain such occurrence.Quote:
Originally Posted by 2wheelcharlie
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 )
Whew! Thought I was the one making all that noise.
Don't forget the critical mathematical contributions of the American woke movement in the past few years:
https://diqn32j8nouaz.cloudfront.net...e_equation.jpg
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.Quote:
Originally Posted by mwmkravchenko
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.
Attachment 44280
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!Quote:
Originally Posted by mklotz
I have an eidetic memory; once I've seen a word written, its spelling is locked in my memory. Surprisingly, it works for languages I do not speak. It's a blessing and a curse. When young, I won a lot of spelling bees and my wife says she's never seen me misspell a word (although that may be based on a small sample population of grocery lists). On the curse side, whenever I read something the spelling errors stand out like neon and really slow down my usually fast scanning.Quote:
Originally Posted by mwmkravchenko
English can be a pitfall for the unsure speller. It has the largest vocabulary in the world...
https://www.lexilab.it/en/profession...all-languages/
and prefers single word adjectives rather than descriptive phrases as used in German and the Romance languages. Furthermore, its many contributors lead to a huge collection of homophones, those nasty words that no spell checker can detect when the wrong one is selected. Most homophones are doublets but there are exceptions...
Rose (flower)
Rose (past tense of Rise)
Rows (plural of row (as in of chairs))
Row's (possessive of row)
Rows (third person present tense of to row (as in a boat))
Roes (collections of fish eggs)
Rhos (plural of the Greek letter rho)
Yep I talk about the craziness of English regularly.Quote:
Originally Posted by mklotz
I have similar memory for some things. Music being one of them. I was a championship speller way back. But not as much anymore. And it is truly sad because I correspond daily with friends and clients and use a spell checker. Oh well. My Dad told me don't get old. It sucks! To bad he told me in my late 40's :)
Mark
