is defined as and if you don't know what is, its not the sweet treat, I can assure you.
is defined as the ratio of the circumference of a circle to its diameter. This means -
Visualized :)
Now, back to , it is . This means -
The first digits of (sometimes written as 'pi' and pronounced 'pie') go like this -
And the first digits of (sometimes written as 'tau' and pronounced 'tau') are twice that -
Since is an irrational number(), it is also irrational.
But here comes the big question, why waste another Greek Letter, to define it as times an already existing number?
We tried to be considerate towards the people who dislike pies?WRONG
It was because we being humans, wanted everything to be easier. Once we started doing Trigonometry, started to get annoying. Radians was only . But what's the point of trying to use something that's only half of the circles angle, when a full would be much easier. The point is, we needed a new number that made Trigonometry with unit circles, easy and we decided to use yet another greek letter for it -
Since Radians would be , it made all our calculations, graphs and Trigonometry as a whole, easier.
Fun Fact : Before in Radians was given the name Tau, it was called a Turn, until , when Micheal Hartl proposed to call it .
Let's talk some more about
is the th letter of the Greek Alphabeet and has a value of in Greek Numerals.
Hi, I'm Tau and this is Capital Tau. I am even though I look like half of . Capital Tau looks like T, but don't tell him that, he has very sensitive feelings :)
The Greek Letter is used in many aspects of Math and Science, some of which are listed below -
Used to represent the Golden ratio (1.618...), although (phi) is more common.
Represents Divisor function in number theory, also denoted or .
Tau is an elementary particle in particle physics.
Tau in astronomy is a measure of optical depth, or how much sunlight cannot penetrate the atmosphere.
It is the symbol for tortuosity in hydro-geology.
is found in many of the famous formula's and identity. But sometimes, is preceded by a , and we all know by now, that .
Here are the well known formula's where can be replaced with , making the formula simpler and more elegant -
Integral over space in polar coordinates -
Gaussian (normal) Distribution -
roots of unity -
A picture of Tau celebrating its many advantages
Cauchy's Integral Formula -
Fourier Transform -
Riemann Zeta Function -
The Kronecker limit formulas -
I have highlighted the 's in red. If replaced with , these formula's could be simpler. This is only one of the advantages of .
Another advantage that is very useful is in Trigonometry.
When dealing with Unit Circles in Trigonometry, we usually use Radians as our angle measure. As already stated, radians is a while radians is a full turn or . Due to this, using is much easier.
When we use , of the unit circle is actually Radians, as shown in the picture below. This is cause for major confusion.
But if we use all our problems vanish, and everything makes sense again. of the unit circle is radians, as shown in the picture below.
This really shows that might actually be better to use than . Yet, we all have our weaknesses, so let's look at the Disadvantages of next.
The Pi vs Tau Conflict is a very long conflict between people who love and people who love .
It is a battle to find which of the irrational numbers is better and makes our calculations easier.
An illustration of the epic battle :)
The basic arguments given by both teams were as follows -
while
A circle is usually defined by its radius and the radius is something that mathematicians are generally more interested in than the diameter.
The formula for a circle's circumference is also simplified with
Radians is equal to , while Radians is equal to . This value of Pi makes it a bit confusing in dealing with Trigonometry using Unit Circles, but Tau makes it look like easy as pie (pun intended)
Pi has been around since a long time. The number Tau also has its flaws. For example - The formula for the area of a circle is made even more complex by using
Also, redefining the circle constant differently and replacing it will destroy the beautiful Euler Identity -
This conflict is as long as the amount of digits in Pi and Tau. I will not take sides and either number isn't necessarily better. This is only a fragment of the conflict. This conflict has been around for a few years and hasn't officially ended yet.
These are the first digits of Tau, but if you want more, go here -
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Image Credits - Thanks to https://www.wikipedia.org/, for the 'Visualising Pi' image, the 'capital and small tau' image and the 'Pi vs Tau' image and to https://tauday.com/tau-manifesto for the Unit Circle images in 'Advantages of Tau'.
Cite as : Tau, Brilliant.org. Retrieved from https://brilliant.org/discussions/thread/tau/
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Comments
so tau is double the value of pi even though the symbol is half of pi interesting
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Yes, a fun fact @Nathan Soliman :)
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what do we use tau to calculate
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How? Please comment this in Latex Club @Páll Márton
Can you please update?
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I've completed Advantages of Tau. Only Disadvantages left. It'll be done by next week :)
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No offence, but when I first read your reply, it said you replied 3 weeks, 3 days ago.>:)
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Also, redefining the circle constant differently and replacing it will destroy the beautiful Euler Identity e^(pi * i) +1 = 0
Actually, with tau, it becomes even better, but yea
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its the argument the pi-ers make. they're stupid lol
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Agreed 🥂
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'Agreed 🥂'
😁
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What conclusion does that idea lead you to though?
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lawl
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Damn where does your mind go?
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@Frisk Dreemurr - I'm making a wiki for fun :)
How is it?
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@Frisk Dreemurr
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Nice @Percy Jackson, I never noticed any note on the debate of Tau and Pi until today :)
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@Frisk Dreemurr - I added a rating system LOL :)
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@Nathan Soliman
What?Log in to reply
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Thanks! I really need to take some time to complete this, but life isn't kind to you after 9th grade lol
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And to sum it all up
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It isn't good, but I am still laughing
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yeah, very sad
I feel bad for anyone who experienced a divorce, even though I'm still laughing.
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As once a (smartest mthfker in the universe) man said: " Love is just chemistry that couples animals into breeding, it reaches a peak then fades away ..."
I heard he beated Zeus singlehandedly. The man's a certified god.
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girlfriend: wait we dont have chemistry
Boyfriend: exactly
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Michael: this morning Meredith was ran over. I took her to the hospital and the doctors did everything they could and... she is going to be ok
Stanley: what is wrong with you
Another scene
Michael: during the weekend my father had a stroke
Of luck
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Erica : Why did you call me to the gym if we're just gonna sit like this?
Ryan : Because we're not working out.
'The Lazy Breakup'
--Ryan Higa 2015--
lmao
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Girlfriend: Why not
Boyfriend: Because I realised you are not right for me and that it’s time I left you
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What grade are you in now?
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what troubles me more is that a billion has different meanings in different countries.
@Páll Márton - I was looking at your formatting guide while making this, its really useful, thanks :)
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BTW go to my feed to see my latest note on buttons. You can add that to your guide @Páll Márton
@Yajat Shamji - Look at this :)
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I really like it. However, I am impartial to both π and τ so I am neutral in this war/conflict.
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I wrote that I'm neutral but I'm actually a Tauist LOL. Glad you like it :)
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@Yajat Shamji - There is an astronomy point in 'More About Tau' :)
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Thanks.
P.S. 5 stars!
P.S.S. I challenge you to find geometric sums and limits involving π that result in τ and geometric sums and limits involving τ that result in π.
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@Yajat Shamji
I'll try :)P.S Thanks you for 5 stars!
@Yajat Shamji, I added a few integral formula's that I could think of. I still don't have a limit though, I'll work on that :)
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π so you'll need to multiply the entire limit by 2):
I found some (but the result'sLog in to reply
Pi limits
I need something where I don't need to multiply actually. There are many Pi limits -@Yajat Shamji - I added a limit formula that doesn't need me to multiply the limit by 2 and do some crazy math, but I don't know its name.
no, the beautiful Euler identity would not disappear, since e^i tau - 1 = 0 (but I am a pie fan)
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Its what they argue, its the truth. It may not be correct, but its an arguement