How did the mathmeticians of past and present go from point A:1+1=2 to point B: pi=3.14(as a sidenote, what fucntion does pi have in something like multiplication or anything? Why is 3.14 different from 3.15 or 3.13?) to point C: prime numbers are(something to do with being able to multiply itself)?
I also can’t understand how you can say e=MC^2 means that energy times matter explains amount of matter in the universe, or how you’d even come up for a equation for something.
I don’t understand your question. Do you want a brief history of mathematics?
It’s a bit easier if I work backwards. The “2” in e=mc^2 came directly from 1+1=2. Originally it was e=mc^(1+1). Then Einstein made the big discovery that 1+1=2 and solved that equation. As for 3.14 being different from 3.13 and 3.15, it is actually the average of the last two: 3.14=(3.13+3.15)/2. The primes are everything inbetween. Does that clear things up?
Buy a book like this. Read it.
Even the ancient Egyptians knew the approximate value of Pi. It’s how they built the pyramids at the scale they did with such accuracy: they measured out the space using a wheel and could make computations from there.
Pi can actually be computed (although very very slowly) like this:
(1-1/3+1/5-1/7+1/9-1/11+…) *4
Moderator’s Note: This isn’t so much a debate as it is a General Question which would take a book to answer. I’ll move it over there and those who want to chip away at it can do so.
Pi is the ratio of the circumferance of a circle to its diameter. The diameter * pi = the circumferance. Pi is approxiamently 3.14159265…, usually rounded to 3.14 - the actual value is trandencental, and the the digits go on infinity.
Pi is a ratio; the circumference of a circle (the distance around the edge) is pi times greater than the diameter of the circle (the distance from one side of the circle to the other in a straight line through the center). If for some reason you know the diamter of the circle but not the circumference, you can multiply the diameter by pi and compute the circumference; and vice versa, you can divide the measured or known circumference by pi to compute the diameter: 2[symbol]p[/symbol]r. ([symbol]p[/symbol] is the form of the Greek letter “pi” from which the ratio gets its name.) The formula is actually usually given in terms of the radius of the circle, the distance from the center to the edge, or half the diameter. This is because pi is actually found in many ratios, not just that of the circumference to the diameter (or radius); for example, the area of a circle is equal to pit multiplied by the radius squared (the radius multiplied by itself). Pi shows up not just in the formulas for the circumference or area of circles, but for example in the formulas for the surface area or volume of a sphere, and in various other mathematical formulas.
Pi is an irrational number. It isn’t equal to 3.14 or 3.15 or 3.13; it starts out as 3.14159… and keeps on going, forever. If you multiply the diameter of your circle by some number other than exactly pi, your result for the circumference will be off a bit. You could multiply just by 3, for example, but you’ll have about a four and a half percent error in your result if you do. Since pi goes on forever, you can’t ever really calculate by the exact value of pi–even 3.14159 is just another approximation, it goes on from there: 3.1415926535897932384626433832795…–but if you use enough digits of pi you can get a result that’s exact enough for just about any conceivable purpose. Even a relatively few digits would be sufficient for specifying the circumference of a circle that’s miles in diameter with an error of no more than an inch.
Prime numbers are numbers that cannot be wholly divided except by itself and 1.
Also, sometimes you find pi referred as a transcendental number (a number which is not the root of any polynomial equation with integer coefficients, if that helps any).
e=mc^2 Energy equals mass times the speed of light squared.
The equation means that the destruction of matter releases energy equivalent to the mass destroyed times the speed of light squared. We’re talking about destruction at the atomic level, actually removing an atom of matter from existence, not changing the chemical composition of something - like burning a piece of paper.
I’m not sure how Einstein came up with the equation, but I think it’s been verified many times in cyclotrons (atom splitters).
This question is a bit broader than can be answered without writing a book.
If you want a brief history of mathematics, look up the following individuals: Pythagoras, Euclid, Archimedes, Newton, Gauss, Dedekind, Weierstrass, Cantor, Riemann, Russell, Lebesgue, Hilbert, Gödel, and Turing. That’ll give you a rough history up to the early 20th century, which is probably all that a layman can understand.
btw, E = mc[sup]2[/sup] is a result from physics, not mathematics.
E = mc[sup]2[/sup] has nothing to do with explaining the amount of matter in the universe. It explains how two seemingly different things - matter and energy - are actually equivalent to one another. You derive explanations from observations about how the real world works.
But there is nothing special about Einstein’s formula. In fact, in freshmen physics, we learned that you can derive E = mc[sup]2[/sup] from Newton’s F = ma.
Unfortunately, this question is an illustration of my pet theory of how the Internet is wonderful for quick facts and virtually useless for true knowledge and understanding. You really do need to read some books to get the background, context, and basic comprehension even to ask a more coherent question, let alone appreciate the answers. I hope you take the advice of the posters here, go to the library (510 is the math section in most public libraries), and start reading.
The history of math is utterly fascinating and there are books you can start with that use a minimum of equations and mathematical jargon.
You can even go to the children’s room to start. I’m not kidding. I’m a professional writer and I often start with a good children’s or young adult book just to get a fast overall take on a subject because so many adult books are too specialized to be the first thing to read.
Yes… Like how you start out with 1+1 and go to prime numbers… The question I have is: How do they logically leap from one aspect of math to the other that would make sense.
The rough outline is this:[ol][]People start studying something.[]They notice certain patterns that recur frequently.[]They start studying those patterns.[]Go back to 2.[/ol]For any more detail than that, you will have to go to a book.
Actually, it wasn’t proved that 1+1=2 until the early 20th century when Russel and Whitehead did it in Principia Mathematica, using the Peano Axioms.
I know other people have suggested books, but I just read this one:
A little while back… it’s informative and actually a pretty fun read. It’s part math, part history. I liked it quite a bit.
I’m a philosophical dilettante, but I was under the impression that despite their best efforts, Russel and Whitehead were unable to prove that 1+1=2 without making certain other assumptions. Can someone elaborate please?
You can’t prove anything without making assumptions. Russell and Whitehead took the Peano axioms as givens.