
02 Apr The most beautiful formulae/theorems/identities in mathematics
This is my personal collection of formulae/theorems which I consider lovely. By “lovely”, I mean objects which possess a certain degree of Elegance and Simplicity. The formulae/theorems are listed in no particular order.
Pythagoras’ theorem
The most popular and fascinating theorem in Euclidean geometry takes the first place in the list.
If AB, BC and AC are three sides of a right angled triangle ABC, where AC is the hypotenuse, then
Euler’s formula
, where
is the Euler’s number.
Heron’s formula
. where
is the area of a triangle whose sides are of length
and perimeter is
.
Bayes theorem
Or
Sine rule
If A,B,C are vertices of a triangle, and sides a,b,c are a = BC, b = CA, c = AB then
Cayley – Hamilton theorem
every square matrix over a commutative ring (such as the real or complex field) satisfies its own characteristic equation.
Euclid’s algorithm
If a and b are integers and a > b, then gcd(a, b) = gcd(a (mod b), b)
Trigonometric gem 1
sin(x – y) sin(x + y) = (sin(x) – sin(y)) (sin(x) + sin(y))
Trigonometric gem 2
X+Y+Z = XYZ if
X = tan(A)
Y = tan(B)
Z = tan(C)
and
Of course, this list is undeniably incomplete. There will be more entries, as I discover more gems.
Download this post as PDF (will not include images and mathematical symbols).
Taha
Posted at 08:34h, 19 AugustI know you could have added more, but you have to mention the quadratic formula, it has unbelievable impact on the world of maths and it shouldn’t go unnoticed.
Gonit Sora
Posted at 22:30h, 27 AugustWe agree with you, but it was the choice of the author. Thanks for the comment.