Mathematical proof shows logical guarantee of mathematical statements using axioms. Proofs derive from Latin "probare" meaning "to test". Ancient Greek mathematicians like Thales and Hippocrates pioneered proofs. Euclid revolutionized proofs with axiomatic method still used today
Quadratic formula describes solutions of quadratic equations. Formula uses discriminant to find roots of equation. Two roots exist when equation has two distinct real roots. One repeated real root when discriminant is positive. Two complex roots when discriminant is negative
Babylonians used base 60 system with counting to 12 and 60. Pythagoras introduced triplets and right-angled triangle theorem. Ancient Greeks discovered irrational numbers like sqrt(2)
Geometry studies shapes, spatial relationships, and properties of space. Euclidean geometry codified in Elements by Euclid around 300 BCE. Analytic geometry introduced by Descartes with rectangular coordinates. Projective geometry developed by Desargues for non-projecting figures. Differential geometry initiated by Gauss for surveying problems
Denial of P is ¬P. De Morgan's laws relate negation of logical operators and quantifiers. First law states P∨Q must fail only if both P and Q fail. Second law shows "x is not between 2 and 3" is equivalent to (x≤2)∨(3≤x). Laws can be used to simplify negations of P⇒Q
Pi Day is celebrated on March 14th, denoted as 3.14 in the US. Pi represents the ratio of a circle's circumference to its diameter. Pi is irrational and continues infinitely without a repetitive pattern