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Old January 11th, 2017, 08:36 AM   #41

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Excellent. Now for those who have ignored math can you say something about why all that is important to us?

If we were to create an exhibit for a children's science center, what picture would represent each one of these, and what the explanation be?

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Originally Posted by GogLais View Post
Off the top of my head

Newton's Laws and equations - that's three already
Picture: any object whose movements we need to predict: cars, planes, rockets, etc.

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Boyle's Laws of Gases and Pressures
Click the image to open in full size.

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Clerk-Maxwell Electro-Magnetic stuff
Something that converts mechanical energy into electrical energy:

Click the image to open in full size.

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E = Mc2 of course
The satellite because we need to account for relativity to have clear communications with something that is moving 14,000 km/hr. The power plant because it converts mass into energy. The other two have to do with radioactivity, and I'm more of a math guy than a physics guy, so you'd have to ask them.
Click the image to open in full size.

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Laws of Thermodynamics
That's a tougher one for me to visualize, but again I'm more math and not so much physics.

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The basic electrical volts, amps, ohms stuff
Anything electronic!
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Old January 11th, 2017, 08:49 AM   #42

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Actually, one idea I have for encapsulating math history is something like "The history of mathematics in 10 (or some number)" problems. Problems as in exercises, or fundamental questions. That would be way cooler than equations. (yawn)
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Old January 11th, 2017, 09:15 AM   #43
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Actually, one idea I have for encapsulating math history is something like "The history of mathematics in 10 (or some number)" problems. Problems as in exercises, or fundamental questions. That would be way cooler than equations. (yawn)
Like something along these lines?

The Top 100 Theorems

It strikes me as a pretty good list, I might fiddle with the rankings a bit, I think it gives a bit too much weight to the proofs of the ancient Greeks, but, overall, it lists all the significant advancements in Mathematics. But, yes, looking at the most significant mathematical theorems gives a better picture of the important achievements in mathematics than looking at equations; most the great accomplishments in the history of Mathematics don't have an equation to go along with them, just a theorem and a proof.
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Old January 11th, 2017, 10:20 AM   #44

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Like something along these lines?

The Top 100 Theorems

It strikes me as a pretty good list, I might fiddle with the rankings a bit, I think it gives a bit too much weight to the proofs of the ancient Greeks, but, overall, it lists all the significant advancements in Mathematics. But, yes, looking at the most significant mathematical theorems gives a better picture of the important achievements in mathematics than looking at equations; most the great accomplishments in the history of Mathematics don't have an equation to go along with them, just a theorem and a proof.
This is nice. A couple of things I find odd are that many of these are not theorems. We did not have this type of thinking (definition - theorem - proof) until the Greeks. That would usually rule out the Egyptian and Babylonian contributions but they are present in this list.

In my own list I would like to add Indian contributions.

Edit:
I think having them as "problems" or "questions" instead of theorems would be more enlightening. Sometimes the answer to a math question is a number. But sometimes the answer is an equation. Sometimes it's "yes" or "no." Sometimes the answer is a theorem (with it's accompanying proof).

-Dave K

Last edited by DaveK; January 11th, 2017 at 10:24 AM.
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Old January 11th, 2017, 05:09 PM   #45

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most the great accomplishments in the history of Mathematics don't have an equation to go along with them, just a theorem and a proof.
Yes, better said than I originally submitted. The really important math contributions to civilization are rarely described by a single equation but are a system of related logical theorems that solve some problem which is reduced to a single proof.
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Old January 11th, 2017, 07:53 PM   #46
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Originally Posted by GogLais View Post
Off the top of my head

Newton's Laws and equations - that's three already
Boyle's Laws of Gases and Pressures
Clerk-Maxwell Electro-Magnetic stuff
E = Mc2 of course
Laws of Thermodynamics
The basic electrical volts, amps, ohms stuff
good list.
add to that elementary optics equations, which was the origin of everything from optical telescopes and microscopes, to perspective geometry and modern map projection.

more importantly, tho, than specific equations, was the development of whole branches of mathematics, from geometry and algebra, to tensor calculus, without which Einstein could not have come up with relativity.

Newton's contribution of the laws of motion and gravity were not nearly as impactful as his development of calculus.... because with calculus eventually someone would have figured out gravity....because gravity is apparent and only in need of description. But Calculus is NOT apparent. It has to derived from first principles.

Newton gets credit for his laws of gravity and motion... but his calculus enabled hundreds of other scientists and mathematicians to work out vastly more equations in a wide variety of fields.


It is really the formulation of new branches of mathematics that enables the useful equations we derive thru them.
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Old January 12th, 2017, 09:23 AM   #47

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Newton gets credit for his laws of gravity and motion... but his calculus enabled hundreds of other scientists and mathematicians to work out vastly more equations in a wide variety of fields.
I prefer to think of it as Leibniz's calculus.

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Old January 12th, 2017, 10:04 AM   #48
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I prefer to think of it as Leibniz's calculus.

-Dave K
If we're going to play that game, I'm going to play the contrarian and argue that Isaac Barrow invented calculus.
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Old January 12th, 2017, 10:16 AM   #49

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If we're going to play that game, I'm going to play the contrarian and argue that Isaac Barrow invented calculus.
Then I'll go out full whackadoodle and claim Archimedes ALMOST had it.

I *love* this game.

The reason I usually say it though is my bias towards pure mathematicians and the fact that Leibniz notation is the one we use today. Even more unreasonably I am biased against Newton purely on grounds of character. He was, as far as I can tell, "not very nice." Probably a greater mind than even the iconic Einstein, but still, not nice!

-Dave K
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Old January 12th, 2017, 10:40 AM   #50

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Originally Posted by DaveK View Post
Then I'll go out full whackadoodle and claim Archimedes ALMOST had it.

I *love* this game.

The reason I usually say it though is my bias towards pure mathematicians and the fact that Leibniz notation is the one we use today. Even more unreasonably I am biased against Newton purely on grounds of character. He was, as far as I can tell, "not very nice." Probably a greater mind than even the iconic Einstein, but still, not nice!

-Dave K
Pfft with regards to math it is Euclid and Archimedes, the rest follows at a huge distance. You can only stand on the shoulders of giants when the lowest giants are gigantic.
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