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The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1]
∇ AREA ← DEGREES SEGMENTAREA RADIUS; FRACTION; CA; SIGN FRACTION ← DEGREES ÷ 360 CA ← CIRCLEAREA RADIUS SIGN ← (× DEGREES) ≠× RADIUS AREA ← FRACTION × CA ×~ SIGN ⍝ this APL statement is more complex, as a one-liner - but it solves vectorized arguments: a tradeoff - complexity vs. branching ∇ 90 180 270 ¯90 ∘.
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as (−n) 3 = −(n 3). The volume of a geometric cube is the cube of its side length, giving rise to the
There are no self-descriptive numbers in bases 2, 3 or 6. In bases 7 and greater, there is exactly one self-descriptive number: () + + +, which has b−4 instances of the digit 0, two instances of the digit 1, one instance of the digit 2, one instance of digit b – 4, and no instances of any other digits.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right ...