Waste less time on Facebook — follow Brilliant.
×

Mathematical Equation of the Week (MEoW)

Basically, post the weirdest, most beautiful or just the coolest mathematical equation you have ever come across. Here is an example:

\[e^{ix} = \cos{x} + i \sin{x}\]

Only one entry per person is allowed and the winner is determined by the number of up votes. Any down votes will be added on as up votes. Good luck, have fun and do math.

P.S.

Who understands the abbreviation? Why is it significant?

Note by Sharky Kesa
2 years, 1 month ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

This number amazed me:

\[1741725= 1^7+7^7+4^7+1^7+7^7+2^7+5^7\] Hasan Kassim · 2 years ago

Log in to reply

@Hasan Kassim Check out Narcissistic Number. There're even more than that! Samuraiwarm Tsunayoshi · 2 years ago

Log in to reply

@Samuraiwarm Tsunayoshi Wow they are much!! Thanks for sharing that :) Hasan Kassim · 2 years ago

Log in to reply

Megh Choksi · 2 years ago

Log in to reply

@Megh Choksi Why is it fascinating? Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay It seemed to me fascinating because

\(Oa = Ob , OA=OB \)

\(\frac{AB}{ab} =\frac{OA}{Oa}\)

\(\frac{Perimeter of the outer polygon}{Perimeter of the inner polygon} = \frac{n.AB}{n.ab} = \frac{AB}{ab}=\frac{OA}{Oa}\)

\(\frac{Circumference of outer circle}{Circumference of inner circle} = \frac{OA}{Oa} = \frac{Radius of outercircle}{radius of inner circle}\)

Thus

\( \frac{Circumference of outer circle}{radius of outercircle} = \frac{Circumference of inner circle}{radiusof inner circle}\)

You know \(\frac{Circumferenceofanycircle}{Diameter} =\) the constant\( \pi\)

The approximate values were given as \( \pi = \frac{22}{7}\) , more accurate was \(\frac{355}{113}\)

You can see now why it is fascinating@Agnishom Chattopadhyay Megh Choksi · 2 years ago

Log in to reply

@Megh Choksi Hahahaha. I was asking why Ramanujan's formula for pi is interesting to you. Isn't the one than comes from arctan more simple and beautiful? Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay Many great mathematicians could'nt give its accurate value , and Ramanujan gave an interesting formula.

Which one is that which comes from arctan that is more simple and beautiful? Megh Choksi · 2 years ago

Log in to reply

@Megh Choksi \(\pi = 4(1- \frac{1}{3} + \frac{1}{5}-\frac{1}{7}+\cdots )\)

To get this, you should realise arctan(1)=pi/4 and the. Just substitute arctan(1) with its taylor series.

However, your formula is better because it has faster convergence) Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay Gathered some information about Pi

Pi, written as π, equals 3.1415926… and its digits goes on forever, without any repeating pattern. Numbers with this property are called irrational numbers. Many ancient mathematicians – including the famous Pythagoras – were horrified when they discovered that such bizarre and ‘impure’ numbers exist.

Today many mathematicians believe that Pi has an even more curious property: that it is a normal number. This would mean that the digits from 0 to 9 appear completely at random, as if nature had rolled a 10-sided dice, again and again, to find the next digit. It also means that if you think of any string of digits, like 123456789, it has to appear somewhere in the digits of Pi – but you might have to calculate millions of digits.

We could even convert an entire book, like the works of Shakespeare, into a very long string of digits (a = 01, b = 02, and so on). If Pi is normal, this string must also appear somewhere in its digits. But even if we used all computers on Earth to calculate more and more digits of Pi, we would probably have to look for longer than the age of the universe… The First few Digits of Pi

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628

0348253421170679821480865132823066470938446095505822317253594081284811174502841027019

3852110555964462294895493038196442881097566593344612847564823378678316527120190914564

8566923460348610454326648213393607260249141273724587006606315588174881520920962829254

0917153643678925903600113305305488204665213841469519415116094330572703657595919530921

8611738193261179310511854807446237996274956735188575272489122793818301194912983367336

2440656643086021394946395224737190702179860943702770539217176293176752384674818467669

4051320005681271452635608277857713427577896091736371787214684409012249534301465495853

7105079227968925892354201995611212902196086403441815981362977477130996051870721134999

9998372978049951059731732816096318595024459455346908302642522308253344685035261931188

1710100031378387528865875332083814206171776691473035982534904287554687311595628638823

53

There are many different ways to calculate Pi, some of which use sequences or series of numbers. One example is the following series discovered by Gottfried Wilhelm Leibniz (1646 – 1716). As you add more and more terms, following the same pattern, the result will get closer to Pi:

\(π = \frac{4}{1} – \frac{4}{3} + \frac{4}{5} – \frac{4}{7} + \frac{4}{9} – \frac{4}{11} + …\)

Another sequence, published by Nilakantha Somayaji (1444 – 1544), is even better since it gets closer to Pi with fewer terms:

\(π = 3 + \frac{4}{2 × 3 × 4} – \frac{4}{4 × 5 × 6} + \frac{4}{6 × 7 × 8} – \frac{4}{8 × 9 × 10} + …\)

This formula was published by John Wallis in 1655:

\(π = 2 × \frac{2}{1} × \frac{2}{3} × \frac{4}{3} × \frac{4}{5} × \frac{6}{5} × \frac{6}{7} × \frac{8}{7} × \frac{8}{9} × …\)

Using powerful computers, Pi has been calculated up to 10 trillion digits (that’s a 1 with 13 zeros)! Because Pi is so easy to understand, yet important in many areas of mathematics, it enjoys an unusual popularity in our culture (unusual, at least, for areas of mathematics). There even is a Pi Day on 14 March or 22 July, since \(\frac{22}{7}\) is a close approximation to pi. @Agnishom Chattopadhyay Megh Choksi · 2 years ago

Log in to reply

@Megh Choksi Hm, I remember wishing 'Happy Pi Day' to my beloved ones Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay Prove it! :P Does anyone has a proof of it? Kartik Sharma · 2 years ago

Log in to reply

@Kartik Sharma Prove what? The faster convergence rate? Or the arctan formula for pi? Or Ramanujan's formula?

I have a proof for my formula Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay Ramanujan's formula! Kartik Sharma · 2 years ago

Log in to reply

@Kartik Sharma I have not Agnishom Chattopadhyay · 2 years ago

Log in to reply

For \[n = 1,2,3,4,5,6\] is true that:

\[14^n+16^n+45^n+54^n+73^n+83^n = 3^n+ 5^n + 28^n + 34^n+ 65^n + 66^n + 84^n\] Jordi Bosch · 2 years, 1 month ago

Log in to reply

@Jordi Bosch Can you tell me why is this happening? Kartik Sharma · 2 years ago

Log in to reply

@Kartik Sharma Probably magic. You can check here to see more than that. Samuraiwarm Tsunayoshi · 2 years ago

Log in to reply

@Samuraiwarm Tsunayoshi Nice! Thanks for sharing! Kartik Sharma · 2 years ago

Log in to reply

A number which rearrange itself upto multiplication by 6

142857 \(\times\) 1 = 142857

142857 \(\times\) 2 = 285714

142857 \(\times\) 3 = 428571

142857 \(\times\) 4 = 571428

142857 \(\times\) 5 = 714285

142857 \(\times\) 6 = 857142

Here is the interesting part

142857 \(\times\) 7 = 999999 Krishna Sharma · 2 years ago

Log in to reply

@Krishna Sharma \(\frac{1}{7}=0.142857...\) Christopher Boo · 2 years ago

Log in to reply

@Krishna Sharma Cyclic number. Sharky Kesa · 2 years ago

Log in to reply

\(\displaystyle e^{\pi \sqrt(163)} \approx 262537412640768743.99999999999925007 \approx 640320^3+744-0.00000000000075\)

Coincidence

Coincidence

What do you think?

Credits : Tumblr (& The Incredibles), Ramanujan, Wikipedia. B.S.Bharath Sai Guhan · 2 years ago

Log in to reply

@B.S.Bharath Sai Guhan What's so special about this equation? Christopher Boo · 2 years ago

Log in to reply

@Christopher Boo This equation's speciality is that it uses irrational numbers to get very, very, very, very close to an integer. Check this one out: \(\displaystyle e^\pi -\pi = 19.999099979189 \approx 20\)

Is that a coincidence or what?!

P.S: You might wanna check out 163 and Ramanujan's constant. B.S.Bharath Sai Guhan · 2 years ago

Log in to reply

@B.S.Bharath Sai Guhan What does that even mean? Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay That means that with irrational numbers, we can get as close as we want, at least for practicality's sake, to an integer. That just blows my mind!

P.S: You might want to check out Almost Integer for more such 'coincidences'. B.S.Bharath Sai Guhan · 2 years ago

Log in to reply

From http://math.stackexchange.com/questions/8814/funny-identities?rq=1

\[ \frac{\pi}{2} = \frac{2}{1}\cdot\frac{2}{3}\cdot\frac{4}{3}\cdot\frac{4}{5}\cdot\frac{6}{5}\cdot\frac{6}{7}\cdot\frac{8}{7}\cdot\ldots\\ \frac{\pi}{4} = 1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}+\ldots\\ \frac{\pi^2}{6} = 1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\ldots\\ \frac{\pi^3}{32} = 1-\frac{1}{3^3}+\frac{1}{5^3}-\frac{1}{7^3}+\frac{1}{9^3}+\ldots\\ \frac{\pi^4}{90} = 1+\frac{1}{2^4}+\frac{1}{3^4}+\frac{1}{4^4}+\frac{1}{5^4}+\ldots\\ \frac{2}{\pi} = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{2+\sqrt{2}}}{2}\cdot\frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}\cdot\ldots\\ \pi = \cfrac{4}{1+\cfrac{1^2}{3+\cfrac{2^2}{5+\cfrac{3^2}{7+\cfrac{4^2}{9+\ldots}}}}}\\ \] Agnishom Chattopadhyay · 2 years ago

Log in to reply

I loved this one as well.

\[\dfrac {d}{dx} (e^x) = e^x\] Sharky Kesa · 2 years ago

Log in to reply

Honestly, the equation that comes into my mind was

\[x^2-x-1=0\]

which is related to the golden ratio and the Fibonacci Sequence. Christopher Boo · 2 years ago

Log in to reply

Fermat's last theorem.. \(a^{n}+b^{n}=c^{n}\) for all a,b,c,n being integers gives real integral solutions only if n<=2 . The proof of the solution took 7 years of hard solitary work!!! Ankit Chatterjee · 2 years ago

Log in to reply

\(a^2 + b^2 = c^2\) (Pythagoras Theorem)

Edit-These positive integers \(a,b,c\) form the sides of a right triangle necessarily. Anuj Shikarkhane · 2 years ago

Log in to reply

Inclusion-Exclusion: Either you like something, or you don't.

If you like this, then upvote it, or else, if you don't like it, then downvote it. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha For the first time, there is not a single downvote(see!) in such an open discussion. Kartik Sharma · 2 years ago

Log in to reply

@Kartik Sharma -- You haven't read the note carefully. Despite me bolding the text, your despicable eyes have failed to read it -- Krishna Ar · 2 years ago

Log in to reply

@Krishna Ar They might be added but I still have downvoted comments I do not like. Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay So it was you who did that -_- Krishna Ar · 2 years ago

Log in to reply

@Krishna Ar Yes, I downvoted -1/12 because I can't stand these Kaboobly Doo ideas. Agnishom Chattopadhyay · 2 years ago

Log in to reply

@Agnishom Chattopadhyay It's not a; kaboobly; idea - there is proof of the outcome. It just seems counter-intuitive because it would seem to equal infinity. However, that is only because you are imagining what happens if you stop it at the 10th terms, 100th term, 1000th term etc. Curtis Clement · 1 year, 10 months ago

Log in to reply

@Agnishom Chattopadhyay What Irony -_- (says master of KD) Krishna Ar · 2 years ago

Log in to reply

@Agnishom Chattopadhyay But that is actually true. In certain maths... That kind of "weird" calculation is commonly seen in physics.

See this Julian Poon · 2 years ago

Log in to reply

@Julian Poon The issue I have with it, is that it is not made explicit where the calculation is done, which is why we would default to working in the "usual" arithmetic, and say that the sum is infinite.

It is similar to saying " 11 + 2 = 1 " (where the arithmetic is performed on the clock)

It is similar to saying "1 + 1 = 0 ". (Where the arithmetic is performed in the field of order 2)

Neither of these would be "acceptable", and are only technically right by omission. I value clarity of expression much more than showing off. Calvin Lin Staff · 2 years ago

Log in to reply

@Krishna Ar So it was you who did that. Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa So who was it who did WHAT?! Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha Bolded that sentence. Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa Yes, an' I edited this comment of yours too :P Krishna Ar · 2 years ago

Log in to reply

@Kartik Sharma Yeah there is. Check out Samuraiwarm's comment below. 1 downvote. Sharky Kesa · 2 years ago

Log in to reply

@Satvik Golechha I neither like it nor dislike it :3 Krishna Ar · 2 years ago

Log in to reply

@Krishna Ar Expected from you. You can still upvote it. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha @Sharky Kesa I just trolled your meow... Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha EDIT OF SATVIK GOLECHHA'S COMMENT:

@Sharky Kesa I just trolled your (meow)


I just trolled your what? Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa Depends. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha And, at the end of your edited comment, why did you say 'meow'?

Read this slowly:

MATHISNOWHERE

What does it say? Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa MATH IS NOWHERE OR MATH IS NOW HERE. :D Anuj Shikarkhane · 2 years ago

Log in to reply

@Anuj Shikarkhane Which one do you prefer? Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa I prefer "MATH IS NOW HERE" Anuj Shikarkhane · 2 years ago

Log in to reply

@Sharky Kesa MAT HIS NOW HER E

read like "matt, his now - hurry" Justin Wong · 2 years ago

Log in to reply

@Sharky Kesa I've got to note that one... Julian Poon · 2 years ago

Log in to reply

@Sharky Kesa Depends. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha Which one do you prefer? Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa Depends. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha How so? Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa That too depends. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha List why it depends. Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa It actually doesn't depend. I was just replying "Depends" for fun. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha So then, answer my question. Sharky Kesa · 2 years ago

Log in to reply

@Sharky Kesa Which question? You've asked more than one. Satvik Golechha · 2 years ago

Log in to reply

@Satvik Golechha All of them. Sharky Kesa · 2 years ago

Log in to reply

@Satvik Golechha That is a very good idea, Agnishom Chattopadhyay · 2 years ago

Log in to reply

\[\sin{(2°\times{10}^{-n})}-\sin{(2°\times{10}^{-(n+1)})}\approx\pi\times{10}^{-(n+2)}\]

Try to derive it and you'll see the magic. Julian Poon · 2 years ago

Log in to reply

@Julian Poon Oh, nice. LOL Calvin Lin Staff · 2 years ago

Log in to reply

\({ G }_{ \mu v }=8\pi G\left( { T }_{ \mu v }+{ \rho }_{ \Lambda }{ g}_{ \mu v } \right) \)

Einstein field equation Shivamani Patil · 2 years ago

Log in to reply

1+(e^(i*pi))=0

five fundamental numbers in one equation... almost all you guys are already familiar with this Rohan Asif · 2 years ago

Log in to reply

Taylor Series -

\(f(x) = \sum _{ n\quad =\quad }^{ \infty }{ \frac { { f }^{ (n) }(0) }{ n! } { x }^{ n } } \)

I have one more(if it is allowed):

https://qph.is.quoracdn.net/main-qimg-7beca9cf6c835bdfeabac3541a778973?converttowebp=true

And one more:

http://en.wikipedia.org/wiki/Tupper%27sself-referentialformula

*The last 2 are just for sharing Kartik Sharma · 2 years ago

Log in to reply

\[\zeta(-1) = 1+2+3+\dots = -\frac{1}{12}\]

where \(\zeta(s)\) is the Riemann zeta function. Samuraiwarm Tsunayoshi · 2 years ago

Log in to reply

@Samuraiwarm Tsunayoshi Please state the system of arithmetic in which this statement is true.

Otherwise, it is similar to saying " 1 + 1 is equal to 10 "

\( \vdots \)

(where I am working in binary) Calvin Lin Staff · 2 years ago

Log in to reply

@Samuraiwarm Tsunayoshi The Riemann Zeta function also links with quantum mechanics and is said to encode a 'formula' for the distribution of primes. Whether it does is the million dollar question! Curtis Clement · 2 years ago

Log in to reply

@Samuraiwarm Tsunayoshi wait waa? Julian Poon · 2 years ago

Log in to reply

it is...........................

.

.

.

.

.

.

.

.

.

1 = 1 Math Man · 2 years ago

Log in to reply

@Math Man what is so great in that?@math man Anuj Shikarkhane · 2 years ago

Log in to reply

@Anuj Shikarkhane idk lol Math Man · 2 years ago

Log in to reply

@Math Man :D Anuj Shikarkhane · 2 years ago

Log in to reply

This is not for competition. However this is what I remember since I was of teen age.\(\color{blue}{152207 * 73= 11111111.(Eight~ '1's)\\~ It~ is ~ clear~ that ~if ~we~use~N*73, N=1,2,...9,~~\\we~ get~ EIGHT~ Ns.~\\152207~is ~divisible ~by ~11. ~(11|152207)} \) Niranjan Khanderia · 1 year, 10 months ago

Log in to reply

\(V-E+F=2\) Danny Kills · 2 years ago

Log in to reply

@Danny Kills Euler's formulae Parth Lohomi · 2 years ago

Log in to reply

@Danny Kills And what is that about? Hasan Kassim · 2 years ago

Log in to reply

substitute x=pi. then eqution becomes e^(i pi)+1=0. this relation connects 5 most important numbers of mathematics, which makes this most beautiful relation. :) Thushar Mn · 1 year, 10 months ago

Log in to reply

\[\Im(i^{i})=0\] Pranjal Jain · 2 years ago

Log in to reply

You all have really good entries. I don't know I only have one equation that may seem not as good as yours. Still have a look. e^{i(pi)}= -1 This equation is derived from De Moivre's Theorem(Sorry Sharky Kesa) But I loved it more than the original theorem since it is of the form An irrational number raised to the product of an imaginary and irrational number which gives us a real number. P S I don't know how to write 'pi' in Greek. Usama Khidir · 2 years ago

Log in to reply

Haha...The abbreviation is Meow :) Tan Li Xuan · 2 years ago

Log in to reply

The sequence 1-1+1-1+1-1... an Oscillatory series equals 1/2 even though all are integers . Keshav Tiwari · 2 years ago

Log in to reply

@Keshav Tiwari Interesting! But can you explain why that happens? Ninad Akolekar · 2 years ago

Log in to reply

@Ninad Akolekar Refer to this note https://brilliant.org/discussions/thread/interesting-sums/ . Hope it helps ! :) Keshav Tiwari · 2 years ago

Log in to reply

@Keshav Tiwari Thanks! Ninad Akolekar · 2 years ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...