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EsX_Raptor
United States2802 Posts
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ComaDose
Canada10357 Posts
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EsX_Raptor
United States2802 Posts
![[image loading]](http://i56.tinypic.com/wc0rno.png) Whoever solves that differential equation can ask the next question. Edit: This rooms needs some abstract decoration, too: ![[image loading]](http://i52.tinypic.com/10pua6f.png) | ||
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Iranon
United States983 Posts
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ComaDose
Canada10357 Posts
y(t) = (const)/t^2 + 1/12(3*t^2 - 4t + 6) next question: to what extent was Albert Einstein involved in the creation of the atomic bomb. | ||
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NeoLearner
Belgium1847 Posts
On August 17 2011 22:55 ComaDose wrote: Ans: y(t) = (const)/t^2 + 1/12(3*t^2 - 4t + 6) next question: to what extent was Albert Einstein involved in the creation of the atomic bomb. Well, E=mc2 shows the huge amount of energy that could be released from the small mass that disappears during nuclear fission. Also, he wrote a letter urging the government to develop an A-bomb before the Germans. Was that the answer you were looking for? If so, prove that e^(pi i) = -1 | ||
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ComaDose
Canada10357 Posts
On August 17 2011 23:01 NeoLearner wrote: Well, E=mc2 shows the huge amount of energy that could be released from the small mass that disappears during nuclear fission. Also, he wrote a letter urging the government to develop an A-bomb before the Germans. Was that the answer you were looking for? If so, prove that e^(pi i) = -1 I will accept that answer. I was looking more toward pointing out the lack of desire to physically take part in the construction and testing leading up to it despite being pressured to by the American physicists/government. He spent that time sailing and contemplating other theories. Should I let someone else write out Euler's theorem? EDIT: made me think of + Show Spoiler + ![[image loading]](http://www.smbc-comics.com/comics/20110518.gif) | ||
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EsX_Raptor
United States2802 Posts
e^(pi * i) = -1, it is necessary to understand what raising a number to an imaginary power means. However, according to de Moivre's formula, we four out e^(i * x) = cos(x) + i * sin(x) for all x. This illustrates how closely related the exponential function is to the trigonometric functions. It thus follows that e^(pi * i) = cos(pi) + i * sin(pi) = -1 + i * 0 = -1. Do write out the Euler theorem! | ||
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ComaDose
Canada10357 Posts
And you didn't ask another question ;p | ||
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EsX_Raptor
United States2802 Posts
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Iranon
United States983 Posts
On August 17 2011 23:15 EsX_Raptor wrote: To understand the equation e^(pi * i) = -1, it is necessary to understand what raising a number to an imaginary power means. However, according to de Moivre's formula, we four out e^(i * x) = cos(x) + i * sin(x) for all x. This illustrates how closely related the exponential function is to the trigonometric functions. It thus follows that e^(pi * i) = cos(pi) + i * sin(pi) = -1 + i * 0 = -1. Do write out the Euler theorem! For a neat bit of insight, look at the Taylor series for e^x. Replace x with iz in the e^z series. Now look at the Taylor series for cos x and sin x... On August 17 2011 23:24 EsX_Raptor wrote: In laymen terms, what is the Riemann hypothesis all about? Not hard, but not that helpful either. There's this function on the complex numbers called the Riemann zeta function. It's easy to see that the function is zero at the negative integers, but there are other zeros too. We think they all lie on the vertical line which hits the real axis at 1/2, but nobody knows how to prove it. If it turned out that this were true (Riemann's hypothesis), it would imply all sorts of useful results, most notably in number theory. | ||
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ComaDose
Canada10357 Posts
On August 17 2011 23:24 EsX_Raptor wrote: In laymen terms, what is the Riemann hypothesis all about? can you put that in laymens terms lol. should we start by describing what a 0 is ;p EDIT: i guess he^ did *the negative even integers* -correction i would have added that its somehow related to the location of prime numbers too. but you didn't ask another question. | ||
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EsX_Raptor
United States2802 Posts
Iranon, you forgot to ask your question! | ||
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Nemesis
Canada2568 Posts
fun^10 x int^40 = Ir2 | ||
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Archas
United States6531 Posts
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EsX_Raptor
United States2802 Posts
![[image loading]](http://i54.tinypic.com/2rojbco.png) http://www.youtube.com/watch?v=ATbMw6X3T40 | ||
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Iranon
United States983 Posts
On August 17 2011 23:38 EsX_Raptor wrote: It is also believed that a proof to the Riemann hypothesis would compromise internet security. Iranon, you forgot to ask your question! Oh, right! And it sure would -- for number theoretic reasons. It would allow for a fast factoring algorithm, which compromises RSA. I'll keep on the topic of fun math that a lot of people know about but relatively few actually follow. Can you turn a sphere inside out without poking holes in it or making any sharp creases? The sphere's surface can pass through itself, and you can stretch and rotate parts of it as much as you like, but you can't break it and glue it back together. If you know what the terms mean, I'm asking for a diffeomorphism between two spheres that reverses the orientation. | ||
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ComaDose
Canada10357 Posts
On August 17 2011 23:49 Iranon wrote: Oh, right! And it sure would -- for number theoretic reasons. It would allow for a fast factoring algorithm, which compromises RSA. I'll keep on the topic of fun math that a lot of people know about but relatively few actually follow. Can you turn a sphere inside out without poking holes in it or making any sharp creases? The sphere's surface can pass through itself, and you can stretch and rotate parts of it as much as you like, but you can't break it and glue it back together. If you know what the terms mean, I'm asking for a diffeomorphism between two spheres that reverses the orientation. This is a good one. I have no idea. I'm reading about Riemann and internet security and I'm getting very motivated to become involved in pure math ;p | ||
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EsX_Raptor
United States2802 Posts
On August 17 2011 23:49 Iranon wrote: Oh, right! And it sure would -- for number theoretic reasons. It would allow for a fast factoring algorithm, which compromises RSA. I'll keep on the topic of fun math that a lot of people know about but relatively few actually follow. Can you turn a sphere inside out without poking holes in it or making any sharp creases? The sphere's surface can pass through itself, and you can stretch and rotate parts of it as much as you like, but you can't break it and glue it back together. If you know what the terms mean, I'm asking for a diffeomorphism between two spheres that reverses the orientation. You can! I found a rather amazing animation of this possibility (min. 1:24): http://www.youtube.com/watch?v=R_w4HYXuo9M&t=1m25s | ||
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ComaDose
Canada10357 Posts
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