Is this a hate thread? If it is, stop it. Deadmau is very good at making music. I would rather listen to a dieING mouse, than justin bieber though.
It's a hate thread in the same way any other thread saying "Is A better than B or is B better than A?" It's comparing two things, not hating on either. It's also ironic and hypocritical that you are telling me to stop hating, when you clearly are hating on Justin Bieber.
Name: daasiangeek Age: 14 Time Zone: EST IGN: daasiangeek Skype Username: zhwyxj UHC Experience: About 10 or so battles; won 3 Can your record?: Yes, but I probably won't and if I do, I won't upload to Youtube.
Just becayse Pi is too mainstream. It works. Why wouldnt we use it? One could say that Tau is more efficient and useful than Pi but it doesnt shorten the equations significantly.
And it would take alot of time to start using other ways. Its like starting to use 12s instead of 10s. It would be better but transition from the old to new would take just too long.
It wouldn't take too long to switch, it would take too long to convince everyone that it's better.
Is it really that odd that it is left irrational? It is an infinite sum of fractions, so it makes since that it would be irrational. I'd say that the proof behind the area of a circle is far more interesting. I went through it today in calculus. It requires advanced integration techniques (well, at least advanced in a first semester calculus course).
1/2+1/4+1/8+1/16...=exactly 2.
Maybe he is capitalizing it since the date could be capitilized, like Presidents Day.
Alright, looks like a couple things need to be cleared up here.
Big deal, Champernowne's constant, by definition, contains every possible finite sequence of digits. Pi is more interesting in this regard because it's not normal by construction. In fact, we don't even know if it's normal. It probably is, but that's not been proven.
Champerone's constant was just a number I thought up; I don't consider it magical or anything the way billions see pi as magical.
Strictly speaking e is defined as the limit of (1 + 1/n)n as n tends to infinity. It turns out that the sum you gave also converges to e, but that's not its definition. That sum actually arises from the Taylor series expansion of ex around x = 0. The reason that sum takes such an apparently simple form is due to the fact that ex happens to be its own derivative (which is only true of functions of the form A ex for some constant A, since this is the family of solutions to y' = y).
My definition is not the official one, but it does give the right answer; most dictionaries have different definitions for words, but all the definitions can be correct.
I'm not sure why this formula is a selling point for e, pi has a similarly simple sum:
π = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ...
The alternating makes it a bit inferior in my opinion; most people don't think of that equation when they think pi.
Pi also participates in one of my favorite equations:
π2 / 6 = 1 + 1/4 + 1/9 + 1/16 + ... + 1/n2 + ...
What makes this one particularly interesting is that the following is also true:
Where p(n) denotes the n'th prime number. This is actually because of how the Riemann zeta function works.
That one's pretty interesting. A bit more advanced, of course, but is beautiful nonetheless.
First of all that definition is incomplete. The golden ratio is defined as the ratio a / b such that (a + / a = a / b = φ (the golden ratio). Dividing the top and bottom by b in (a + / a gets us:
(a/b + 1) / (a/b) = a/b = φ
So we can get rid of a and b, and just get this in terms of φ:
(φ + 1) / φ = φ
This equation is quadratic, we can put it into a more standard form:
φ2 - φ - 1 = 0
Since this is quadratic, it's got 2 solutions:
φ = (1 ± sqrt(5)) / 2
This work out to about 1.618033... and -0.618033. The golden ratio is taken to be the positive one.
I actually find the golden ratio to be slightly less special than either e or pi for one big reason: the golden ratio is an algebraic number. Both e and pi are not algebraic, they're transcendental. That means that they are not the roots of a polynomial with integer coefficients (and before anyone points out that algebraic numbers are typically defined as numbers that are roots of polynomials with rational coefficients, I will say that that's equivalent to integer coefficients because you can just multiply the polynomial by a sufficiently large integer to clear out the denominators without changing the roots of the polynomial).
The golden ratio is clearly algebraic, however, because φ2 - φ - 1 is clearly a polynomial with integer coefficients.
Alright...
It shouldn't leave you in awe. Every real number can be expressed as an infinite sum of rational numbers. And such sums are not unique. There's an infinite number of ways to express any real number as an infinite sum of rational numbers. This should not be a surprise and here's why:
It leaves me in awe not because that it works, but because of the simplicity. Factorial is a simple function, as are addition and division.
Consider any sequence of rational numbers that converges to a real number (this means it gets arbitrarily close). This is not hard to do, since the rational numbers are infinitely divisible, so we can get as close as we want to any real number. Now take the difference of each consecutive pair in our sequence. Since each number in our sequence is rational, the differences between them will also be rational. If we add up all those differences, we simply recover our original sequence. So in that way we can construct just about any infinite series of rational numbers that sums to whatever we want.
Again, it's the simplicity and not that it works that I find amazing.
You have still not given any crucial reason that pi should be considered nautical miles above other numbers; pi is useful, cool and incredible, I have never disputed that; but it is not the only number that is useful, cool and incredible. I do not dislike pi for any reason; I just think it eclipses other numbers' fame.
Here's your benchmark for simplicity:
Pi is the rate at which a circle's circumference is proportional to its diameter.
What about limits? I have never taken a calculus course and I understand the limit e=1/1!+1/2!+1/3!... That is simple and precise, and the fact that the result is irrational leaves me in awe.
I suggest the OP goes and Google "Maddox geeks aren't sexy".
Because that article tells the truth about how superficial the whole trend of "nerdy" stuff really is.
I did, and I can't quite tell who's side you're on. Anyways, I am not bringing it up because I think "nerdy" stuff is cool. In fact, I despise people who like things just because they're "nerdy". I am bringing it up because it interests me, and I want to hear opinions from the community.
Pi is easy to understand is is probably the first weird constant learned in mathematics. It is a constant that is very useful in many levels of mathematics from low levels of geometry to high levels of calculus. I admit that e is very useful in calculus but that is a subject that not very people understand or even want to try to understand. There are plenty of mathematical constants and I personally find c (speed of light in a vacuum) the most interesting due to its profound implications and usefulness in theoretical quantum physics.
People are inherently nostalgic and since Pi is one of the first few constants learned it makes complete sense that it is the most remembered. If a show or a person even brought up say R (ideal gas constant) for example, it would lose most of their audience since most people do not know it. However since Pi is taught early most people remember it and when using it you portray mathematics without losing much of your audience.
Pi is best for its simplicity not its intricacy or implications like other constants previously mentioned.
Pi is like bacon; it is good, but so many people go crazy for it that it becomes ridiculous.
Both are irrational numbers. Never end and never have a pattern. Finding a phone number in Champernowne's constant is just as easy as finding them in pi.
That is where you fail miserably. Irrational means unable to show as a ratio; they can have a pattern. Champerone's constant is 0.123456789101112131415161718192021222324... I hope you have the mental capacity to see that there is a pattern, and that it is child's play to find anyone's phone number in the digits.
It's popular because it's more accessible than other numbers. Its meaning can be easily conveyed to someone with very limited mathematical understanding. No, I don't see anyone writing songs about the Planck constant any time soon, but who cares?
Champerone's constant's meaning is easier to explain than pi, as is any whole number.
Justin Bieber, One Direction, Alicia Keys, Rihanna... (I could go on) are by no means dull, however deserve no where near the attention they get.
Pi, on the other hand, is actually useful and contributes to the world.
Indeed it does, and I addressed that, but everyone loves pi over other numbers. It contributes, no doubt about that, but so do so many underspoken numbers. Who memorizes thousands of digits of the Euler–Mascheroni constant? Who makes a movie about a math prodigy named "The First Feigenbaum Constant"? Admit it, pi is the first irrational number that pops in your head when you think irrational.
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It's a hate thread in the same way any other thread saying "Is A better than B or is B better than A?" It's comparing two things, not hating on either. It's also ironic and hypocritical that you are telling me to stop hating, when you clearly are hating on Justin Bieber.
I came up with it independently, not sure if I'm the first.
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Age: 14
Time Zone: EST
IGN: daasiangeek
Skype Username: zhwyxj
UHC Experience: About 10 or so battles; won 3
Can your record?: Yes, but I probably won't and if I do, I won't upload to Youtube.
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I predict tons of Mindcrack fanboys under the age of 12, consisting mainly of Etho fans. Good luck on the server, I guess.
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It wouldn't take too long to switch, it would take too long to convince everyone that it's better.
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There is a movie called Pi; the movie has nothing to do with pi, and the opening even gets the digits of pi wrong.
Pi results on Google: 842,000,000
Euler's constant: 949,000
Phi: 210,000,000
Nine: 584,000,000
Pi results easily outnumber the rest.
Also, pi Google Calulator only calculates pi, not e or phi or nine(but nine is a bad example).
You must be crazy to think pi is equally popular as other numbers.
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You have still not given any crucial reason that pi should be considered nautical miles above other numbers; pi is useful, cool and incredible, I have never disputed that; but it is not the only number that is useful, cool and incredible. I do not dislike pi for any reason; I just think it eclipses other numbers' fame.
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What about limits? I have never taken a calculus course and I understand the limit e=1/1!+1/2!+1/3!... That is simple and precise, and the fact that the result is irrational leaves me in awe.
I did, and I can't quite tell who's side you're on. Anyways, I am not bringing it up because I think "nerdy" stuff is cool. In fact, I despise people who like things just because they're "nerdy". I am bringing it up because it interests me, and I want to hear opinions from the community.
It's funny how you capitalize pi as if it's a proper noun. It is, in fact, a Greek letter.
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Pi is easy to understand is is probably the first weird constant learned in mathematics. It is a constant that is very useful in many levels of mathematics from low levels of geometry to high levels of calculus. I admit that e is very useful in calculus but that is a subject that not very people understand or even want to try to understand. There are plenty of mathematical constants and I personally find c (speed of light in a vacuum) the most interesting due to its profound implications and usefulness in theoretical quantum physics.
People are inherently nostalgic and since Pi is one of the first few constants learned it makes complete sense that it is the most remembered. If a show or a person even brought up say R (ideal gas constant) for example, it would lose most of their audience since most people do not know it. However since Pi is taught early most people remember it and when using it you portray mathematics without losing much of your audience.
Pi is best for its simplicity not its intricacy or implications like other constants previously mentioned.
Pi is like bacon; it is good, but so many people go crazy for it that it becomes ridiculous.
That is where you fail miserably. Irrational means unable to show as a ratio; they can have a pattern. Champerone's constant is 0.123456789101112131415161718192021222324... I hope you have the mental capacity to see that there is a pattern, and that it is child's play to find anyone's phone number in the digits.
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That is exactly what I hate.
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Champerone's constant's meaning is easier to explain than pi, as is any whole number.
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Indeed it does, and I addressed that, but everyone loves pi over other numbers. It contributes, no doubt about that, but so do so many underspoken numbers. Who memorizes thousands of digits of the Euler–Mascheroni constant? Who makes a movie about a math prodigy named "The First Feigenbaum Constant"? Admit it, pi is the first irrational number that pops in your head when you think irrational.