Types of Numbers
The definition of numbers has evolved with time and the set of all numbers now includes the Real Numbers (natural numbers, integers, rational numbers, irrational numbers and transcendental numbers) and Complex Numbers. The branch of mathematics that studies structure and patterns in number systems is called abstract algebra and uses concepts such as groups, rings and fields.
Arithmetic as we know it is concerned with the study of performing operations on numbers. Unitary operations take a single input number X and produce a single output number Y like the successor operation Y=X+1 or exponentiation Y=exp(X). Binary operations take two input numbers X and Y and produce a single output number Z like addition Z=X+Y, subtraction Z=X-Y, multiplication Z=XY, division Z=X/Y.
Important Numbers
Pythagorus’ constant √2 ≈ 1.41421 35623 73095 04880 16887 24209 69807
Theodorus’ constant √3 ≈ 1.73205 08075 68877 29352 74463 41505 87236
Imaginary number i=√(-1)
Archimedes’ constant π ≈ 3.14159 26535 89793 23846 26433 83279 50288
Naperian constant e ≈ 2.71828 18284 59045 23536 02874 71352 66249
Common logarithm log102 ≈ 0.693147180559945309417232121458
Feigenbaum constant δ ≈ 4.66920 16091 02990 67185 32038 20466 20161
Golden ratio φ ≈ 1.61803 39887 49894 84820 45868 34365 63811
googol = 10100
prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97…
Number Patterns
Pascal’s triangle
Fibonacci sequence
Mandlebrot set
Roots of unity
