### Rob Laney

Discussion -That's the life

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Also, Happy = Sad. I tend to agree with +Simos Xenitellis

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That's the life

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Also, Happy = Sad. I tend to agree with +Simos Xenitellis

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So, how'd you find it?

Analytically, or by making a spreadsheet?

Analytically, or by making a spreadsheet?

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just a share without any thought going in the process of sharing i think.

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Omar Crosby

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That's an interesting way of looking at it I guess

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When we want to divide a fraction by a fraction such as (a/b) : (c/d) we usually multiply a with d and then we divide by b multiplied with c, (a*d): (b*c). I thought we can just do the following (a:c)/ (b:d).

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As a side note, it's generally considered tacky to like your own comments.

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Equations tell us of all the things that are fundamentally equal.

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Math is everywhere)))

Most high school students are afraid of math lessons wondering whether they can ever use the acquired knowledge in the real life. Today, when so many calculations are carried out by computers, algebra and geometry find good realization in 3D graphics industry. And if you still don't know how why math is so useful for 3D graphics, this article is for you. In the 21st century, 3D graphics is frequently used in the movies, cartoons, games, etc. If p...

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LevKozlodoev

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it might be wiser to ask how math isn't used in 3D graphics... I couldn't think of one thing in 3D graphics that can be done without math.

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«Of course, the Common Core lists only academic standards, and leaves the curriculum to individual districts — some of which are indeed incorporating recreational mathematics.»

‘Fun’ problems can lead to striking, unexpected discoveries.

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+Rohan Patel So is the 6 beside it. No, really, that upside down 8 really does make that 6 next to it look upside down.

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Paul Hartzer

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+Alexandre Leite Here's a quick way to generate triples (but it doesn't generate all of them): Square an odd number greater than 1. Divide it in half and take the integers to either side. The odd number and these two other numbers will form a triple.

E.g.: 7^2 = 49; 49/2 = 24.5. (7, 24, 25) is a triple. 13^2 = 169; 169/2 = 84.5. (13, 84, 85) is a triple.

It works because:

(a, (a^2 - 1)/2, (a^2 +1)/2) implies a^2 + (a^2 -1)^2/4 = (a^2 + 1)^2/4

Implies 4a^2 + a^4 - 2a^2 + 1 = a^4 + 2a^2 + 1

Implies 2a^2 + 1 = 2a^2 + 1

which is always true, so (a, (a^2 - 1)/2, (a^2 + 1)/2) always generates three numbers that satisfy the Pythagorean Theorem. However, to be a triple, you need (a^2 - 1)/2 and (a^2 + 1)/2 to be integers, which is true when a^2 is odd and hence a is odd.

E.g.: 7^2 = 49; 49/2 = 24.5. (7, 24, 25) is a triple. 13^2 = 169; 169/2 = 84.5. (13, 84, 85) is a triple.

It works because:

(a, (a^2 - 1)/2, (a^2 +1)/2) implies a^2 + (a^2 -1)^2/4 = (a^2 + 1)^2/4

Implies 4a^2 + a^4 - 2a^2 + 1 = a^4 + 2a^2 + 1

Implies 2a^2 + 1 = 2a^2 + 1

which is always true, so (a, (a^2 - 1)/2, (a^2 + 1)/2) always generates three numbers that satisfy the Pythagorean Theorem. However, to be a triple, you need (a^2 - 1)/2 and (a^2 + 1)/2 to be integers, which is true when a^2 is odd and hence a is odd.

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Riemann zeta function

Realization of sieve of Eratosthenes of Euler product can correspond to Riemann zeta function, Li(x) correspond to x*Euler product, zero of zeta function(Po=1/2+14=1/2+21......) equal to mod(X,Pm)/Pm for prime number equal and less than x^1/2, every time add one prime number on Euler product can calculate exactly total of prime number up to p^2, for number not equal to p^2 can take biggest prime number <x^(1/2) for upper limit, in this way for x^((1/2)+e) can take off e be x^(1/2) exactly for Euler product.(Pm for combination of prime number equal and less than X^(1/2))

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Reflecting on Week 7 - $600 bouncy balls, building robots, and figuring out how to teach dividing decimals

http://wp.me/p3LdGY-eU

http://wp.me/p3LdGY-eU

It's been a fairly good lucky number week 7. Had our first auction and started to build robots. Content has been going well for the most part, with exception to some pretty dull 6th grade math le...

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Illarion Bykov

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Value? One million dollars!

But I'll take 64 from any of you guys!

And the X is sneaky, trying to camouflage himself as a Y. Must be a Y day on Sesame Street.

BTW, the question, as posed, is ambiguous to those who haven't encountered one like this before. It doesn't specify if X is an angle, and it's right on top of a curve so that you have to look close to even see it's an X. And is it referring to the angle between the side of the triangle and then line? Something else?

This is as much of a test of mainstream modern mathematics cultural knowledge as it is a test of geometrical thinking. The College Board and the Educational Testing Service would not allow something this ambiguous on any of their SAT/AP/GRE tests.

But I'll take 64 from any of you guys!

And the X is sneaky, trying to camouflage himself as a Y. Must be a Y day on Sesame Street.

BTW, the question, as posed, is ambiguous to those who haven't encountered one like this before. It doesn't specify if X is an angle, and it's right on top of a curve so that you have to look close to even see it's an X. And is it referring to the angle between the side of the triangle and then line? Something else?

This is as much of a test of mainstream modern mathematics cultural knowledge as it is a test of geometrical thinking. The College Board and the Educational Testing Service would not allow something this ambiguous on any of their SAT/AP/GRE tests.

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If Shinichi Mochizuki's proof was correct, it would be one of the most astounding achievements of mathematics this century and would completely revolutionize the study of equations with whole numbers.

http://www.scientificamerican.com/article/math-mystery-shinichi-mochizuki-and-the-impenetrable-proof/

http://www.scientificamerican.com/article/math-mystery-shinichi-mochizuki-and-the-impenetrable-proof/

A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right

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Challenge accepted!

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Some math from outerspace ?

A Japanese mathematician claims to have solved one of the most important problems in his field.

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They still haven't figured it out! It's been three years!!! **sigh**...

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sin20sin40sin60sin80=√3/4 sin202sin80sin40=√3/4sin20(cos40-cos120) this follows the result

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Is it possible that Quantum Mechanics and General Relativity are merely different manifestations of Discrete Mathematics?

The central problem of modern physics is that we have two very successful theories that don’t seem to be able to talk to each other. On the one hand we have General Relativity, a theory of the very large and the very fast, and on the other we have Quantum Mechanics, a theory of the very small. These two great pillars of modern physics are, at their core, fundamentally incompatible; moreover, neither seem to be able to explain black-holes. In this paper we will consider the possibility that maybe we live in a “discrete space-time” universe and that both great theories are merely different physical manifestations of the “discretization” of Euler’s Formula, and a black-hole is simply the physical manifestation of Euler’s Identity (e^iπ = -1).

http://www.kierandkelly.com/quantum-theory/

#mathematics #physics #STEM #QuantumMechanics

The central problem of modern physics is that we have two very successful theories that don’t seem to be able to talk to each other. On the one hand we have General Relativity, a theory of the very large and the very fast, and on the other we have Quantum Mechanics, a theory of the very small. These two great pillars of modern physics are, at their core, fundamentally incompatible; moreover, neither seem to be able to explain black-holes. In this paper we will consider the possibility that maybe we live in a “discrete space-time” universe and that both great theories are merely different physical manifestations of the “discretization” of Euler’s Formula, and a black-hole is simply the physical manifestation of Euler’s Identity (e^iπ = -1).

http://www.kierandkelly.com/quantum-theory/

#mathematics #physics #STEM #QuantumMechanics

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Ryan Dupée

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No. I believe that the reason for the prevalence of both of those theories are due to the mathematics. Quantum mechanics relies heavily on use of statistics and the theory of relativity gained traction because of the use of vector calculus and publicized popular support with confirmed accuracy.

There are other theories that work as well as relativity or quantum mechanics. Relativity has a huge following which makes a difference. The same goes for quantum mechanics. The uses were expanded far beyond the scope of the originator's written principle papers. Scientifically, both have failed in some ways significant to satisfy underlying priori and are patched without a thorough reevaluation. While successful, they fail at valid explanations and require constant adjustments and additions to stay successful.

A problem could be the wrong mathematics were used; there's a possibility that errors in Kirchoff's work and the effect on Planck's work has cascaded into complex theories that attempt to explain imaginary/false phenomena.

There is a possibility then that black holes are not as they are described and are as they were first described as dark stars. Reality may not be quantized. No dark matter; no big bang. Right now, observations do not match theory by orders of magnitude.

It may not be the mathematics that is the problem but the failure in the application of the prevalent scientific methodology and lack of understanding of the underlying philosophies.

As Newton wrote about the absurdity of innate gravity "no man who has in philosophical matters any competent faculty of thinking can ever fall into it." Yet the theory of gravity is ascribed to him as is work credited to Planck, Hubble, Einstein, etc. with which they had no papers, letters or writings.

This paper may be yet another bandaid on something that just would not continue to work, with no fault of the mathematics but that if its application.

There are other theories that work as well as relativity or quantum mechanics. Relativity has a huge following which makes a difference. The same goes for quantum mechanics. The uses were expanded far beyond the scope of the originator's written principle papers. Scientifically, both have failed in some ways significant to satisfy underlying priori and are patched without a thorough reevaluation. While successful, they fail at valid explanations and require constant adjustments and additions to stay successful.

A problem could be the wrong mathematics were used; there's a possibility that errors in Kirchoff's work and the effect on Planck's work has cascaded into complex theories that attempt to explain imaginary/false phenomena.

There is a possibility then that black holes are not as they are described and are as they were first described as dark stars. Reality may not be quantized. No dark matter; no big bang. Right now, observations do not match theory by orders of magnitude.

It may not be the mathematics that is the problem but the failure in the application of the prevalent scientific methodology and lack of understanding of the underlying philosophies.

As Newton wrote about the absurdity of innate gravity "no man who has in philosophical matters any competent faculty of thinking can ever fall into it." Yet the theory of gravity is ascribed to him as is work credited to Planck, Hubble, Einstein, etc. with which they had no papers, letters or writings.

This paper may be yet another bandaid on something that just would not continue to work, with no fault of the mathematics but that if its application.

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