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Mathematics

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knightmare
1074027.  Wed May 14, 2014 2:42 am Reply with quote

Did Benoit Mandelbrot discover the Mandelbrot set? No:

Wikipedia wrote:
The Mandelbrot set has its place in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The first pictures of this fractal were drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBM's Thomas J. Watson Research Center in Yorktown, Heights, New York, Benoit Mandelbrot first saw a visualization of the set.

Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematical study of the Mandelbrot set really began with work by the mathematicians Adrien Douady and John H. Hubbard, who established many of its fundamental properties and named the set in honor of Mandelbrot.

The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books, and an internationally touring exhibit of the German Goethe-Institut.

The cover article of the August 1985 Scientific American introduced the algorithm for computing the Mandelbrot set to a wide audience. The cover featured an image created by Peitgen, et al


The concept is even older. For example, it isn't possible to know what the length of a coast is. Zoom in or zoom out, and the length will change.


Last edited by knightmare on Thu May 29, 2014 2:03 pm; edited 1 time in total

 
ali
1074088.  Wed May 14, 2014 6:37 am Reply with quote

Alfred North Whitehead wrote:
‘‘To come very near true theory and to grasp its precise application are two very different things as the history of science teaches us.
Everything of importance has been said before by somebody who did not discover it.’’


How Long is the Coast of Britain? by B.B. Mandelbrot (1967)

 
ConorOberstIsGo
1074377.  Thu May 15, 2014 8:20 am Reply with quote

Who was that teacher - the greatest of all perhaps - who was born on December 25th? Walked on water and rose from the dead?

That's right, Pythagoras!

It was said that a burglar broke into his home but fled without taking a thing because of the confusing things he saw.

He was one of several famous ancient Greeks who called Samos home which was - at the time - I believe under the control of the Ionian League..... anyway, Pythag you are a badass.

 
ConorOberstIsGo
1075471.  Wed May 21, 2014 10:27 am Reply with quote

A mantissa is the decimal part of a logarithm.

 
simacha
1075660.  Thu May 22, 2014 1:38 pm Reply with quote

I suppose that this would fall under a General Ignorance category (at least it did for me), but if you were to ask most people to state 'Einstein's equation,' the expected response would be E=mc^2.

While E=mc^2 is his most famous equation, used to describe special relativity, 'Einstein's equation' describes general relativity, and consists of the following:

 
ConorOberstIsGo
1075683.  Thu May 22, 2014 2:56 pm Reply with quote

Gosh. Yes, I remember this equation/formula. I believe it describes the mass of the universe. Einstein famously added in another number to allow for what was observed through telescopes. This was later withdrawn and described as Einstein's biggest blunder.

I remember folks saying "you are missing the Riccian tensor!" when asked folks about this online so it's clearly for physics legends only :)

 
knightmare
1076931.  Thu May 29, 2014 10:37 am Reply with quote

The number 70'ish can be used to quickly convert a reasonable triple-digit profit of 100% to a profit percentage per year:
Code:

 0.5%, 140 years: 2.01
 1.0%,  70 years: 2.01
 2.0%,  35 years: 2.00
 3.5%,  20 years: 1.99
 7.0%,  10 years: 1.97
 7.8%,   9 years: 1.97
 8.0%,   9 years: 2.00 (72)
 9.0%,   8 years: 1.99 (72)
10.0%,   7 years: 1.95
14.0%,   5 years: 1.93
35.0%,   2 years: 1.82
70.0%,   1 year:  1.70

If the way it is calculated remained unchanged, then an historical inflation rate of 2.25% means that prices doubled in about 70 : 2.25 = 31.11'ish years.

 
djgordy
1076962.  Thu May 29, 2014 12:49 pm Reply with quote

I think you'll find it's "maths", not "math".

 
knightmare
1076970.  Thu May 29, 2014 1:53 pm Reply with quote

Quote:
I think you'll find it's "maths", not "math".

http://en.wikipedia.org/wiki/Math
http://en.wikipedia.org/wiki/Maths
http://en.wikipedia.org/wiki/Mathematics

Betrand Russell wrote:
It is a misfortune for Anglo-American friendship that the two countries are supposed to have a common language


I've adjusted the subject, pretending to be neutral.

 
simacha
1077509.  Sun Jun 01, 2014 1:04 pm Reply with quote

I am about halfway through a 1951 edition of the late-scientist Lancelot Hogben's (1895-1975) fantastic book 'Mathematics for the Million'. While I had picked it up to get better with numbers, I keep finding myself laughing at Hogben's social observations, which are pretty ballsy for a book first published in 1936. He was a committed early socialist, and tosses in casual social body blows as he charts the rise of numbers through history.

Some quotes:

[context: after describing important discoveries in geometry and astronomy by ancient priests]

"The priestly caste soon acquired a position of dominance, because the first naive impulse to bribe and propitiate the august and puissant dwellers of the skies is highly profitable to those who act as their liaison officers. The shepherd cultivators bring presents for the gods and the priests wax fat on the presents."

[context: comparing the language of mathematics to other languages]

"The French language is especially suitable for the exercise of ironical wit. The English language is especially suitable to convey scientific truths concisely. The tortuous prolixity of German diction can be used to befuddle sensible and decent people till they believe that Hegel's dialectic makes sense, and Jew-baiting makes a nation prosperous."

"Mathematicians call marks like 'x' and '-' operators, just as Americans call workmen operatives. This means that they are not simply there for ornament, like dukes or beefeaters. They do real work."

"of course there are no interjections in mathematics because interjections have no place in the language of work. They are survivals of the noises our monkey ancestors made before they learned the social use of noises."

I'd love to see the book placed on the high school curriculum in Texas, just to hear the war of monkey-noises that would come about as a result. Looking forward to the rest of the book.

 
Morbius
1079546.  Wed Jun 11, 2014 3:52 pm Reply with quote

Who invented calculus?

Well, it certainly wasn't Isaac Newton. Although the man was a genius, the most it can be said he did was to have formalised it. The first documented case of someone using infinitesimals was by Archimedes in the third century BC. This can be seen in the recently rediscovered Archimedes Palimpsest, which was lost when Christian monks used the parchment for religious texts in the thirteenth century. Between 1999 and 2008, the palimpsest was digitally processed to recover the original text. This revealed a work of Archimedes called The Method of Mechanical Theorems where he calculates such things as the area of a parabola and the volume of a sphere.

 
suze
1079549.  Wed Jun 11, 2014 3:59 pm Reply with quote

Didn't Aristotle allude to the methods of calculus a century earlier even than Archimedes?

I don't know all that much about math, and neither do I know any Ancient Greek. But it was my understanding that - at a conceptual level, and without knowing quite what he had done - Aristotle used integral calculus to refute Zeno's paradox of Achilles and the tortoise.

 
Spud McLaren
1079551.  Wed Jun 11, 2014 4:09 pm Reply with quote

What do you get if you cut a paper loop along its length?
A: 2 paper loops.

What do you get if you cut a Möbius strip along its length?
A: Cutting a Möbius strip along the centre line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip. This happens because the original strip only has one edge that is twice as long as the original strip. Cutting creates a second independent edge, half of which was on each side of the scissors.

Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists.

Further mirthful variations can be found here.


Could be good as a practical for the panel.

 
Morbius
1079552.  Wed Jun 11, 2014 4:11 pm Reply with quote

suze wrote:
Didn't Aristotle allude to the methods of calculus a century earlier even than Archimedes?

I don't know all that much about math, and neither do I know any Ancient Greek. But it was my understanding that - at a conceptual level, and without knowing quite what he had done - Aristotle used integral calculus to refute Zeno's paradox of Achilles and the tortoise.


He certainly seems to be using ideas rooted in calculus. You can go even further back. Before Aristotle, Eudoxus of Cnidus formalised the Method of Exhaustion, which is a precursor to calculus. Even then, he only formalised it - the idea itself can be traced back to Antiphon in the fifth century BC.

 
ConorOberstIsGo
1079558.  Wed Jun 11, 2014 4:44 pm Reply with quote

Spud McLaren wrote:

What do you get if you cut a Möbius strip along its length?
A: Cutting a Möbius strip along the centre line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip. This happens because the original strip only has one edge that is twice as long as the original strip. Cutting creates a second independent edge, half of which was on each side of the scissors.


I really like this but it'd be nice to have a mathsmith's explanation of this and also things like:

When an ant crawls along a suspended string, it effectively gains an extra dimension:
http://physics.stackexchange.com/questions/99943/what-does-it-mean-for-an-extra-dimension-to-have-size

What is the biggest number there is?

It's not infinity because infinity is not a number but an idea. It is not even one idea; there are about a dozen different infinities.

Aleph null is a number in its own way. What alphabet is Aleph from?


Hebrew (apparently mathematicians got a bit carried away and ran out of Greek and Roman letters....).

 

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