Torus

Torus Facts Notice these interesting things:   It can be made by revolving a small circle along a line made by another circle.   It has no edges or vertices   It is not a polyhedron   And for reference:   Surface Area = 4 × π2 × R × r   Volume = 2 × π2 × R × r2   Note: Area and volume formulas only work when the torus has a hole!
And did you know that Torus was the Latin word for a cushion? (This is not a real roman cushion, just an illustration I made)	Torus in the Sky. The Torus is such a beautiful solid, this one would be fun at the beach !

Transedental Number

An irrational number which cannot be represented by an algebraic structure or an equation is called transedental irrational number. Best example of these numbers are pai and exponential number i.e. 'π' and 'e'.  

pai

π, The symbol, called as pai, has value either 22/7 or 3.1416, which ratio of circumference of a circle and its diameter. π is an irrational trancendental number.

Fibonacci Sequence

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it.

• The 2 is found by adding the two numbers before it (1+1)

• Similarly, the 3 is found by adding the two numbers before it (1+2),

• And the 5 is (2+3),

• and so on!

Example: the next number in the sequence above would be 21+34 = 55

It is that simple!

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 

4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...



Fibonacci Spiral

The Rule

The Fibonacci Sequence can be written as a "Rule" 

(see Sequences and Series).

First, the terms are numbered from 0 onwards like 

this:

n =	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	...
xn =	0	1	1	2	3	5	8	13	21	34	55	89	144	233	377	...

So term number 6 is called x₆ (which equals 8).

Example: the 8th term is   the 7th term plus the 6th term: x8 = x7 + x6

So we can write the rule:

The Rule is x_n = x_n-1 + x_n-2

RAMANUJAN, The great Mathematician , Born in Erode Tamilnadu , India.