Perimeter: The total distance around the outside of a polygon. A kind of proof in which the statements 38 ÷ 12 = 3 remainder 2, and 26 ÷ 12 = 2 remainder 2, therefore 38 and 26 are congruent modulo 12, or (38 ≡ 26) mod 12, monomial: an algebraic expression consisting of a single term (although that term could be an exponent), e.g. Mathematicians have several phrases to describe proofs or proof techniques. Use up and down arrows to review and enter to select. —The proof that there are infinitely many prime numbers. Tree Diagram: Used in probability to show all possible outcomes or combinations of an event. Rectangles, squares, and pentagons are just a few examples of polygons. Centimeter: A metric unit of measurement for length, abbreviated as cm. Rectangle: A parallelogram with four right angles. x2 + 3x – 4, algebraic equation: a combination of numbers and letters equivalent to a sentence in language, e.g. subsets of {a, b} could include: {a}, {b}, {a, b} and {}, surd: the n-th root a number, such as √5, the cube root of 7, etc, symmetry: the correspondence in size, form or arrangement of parts on a plane or line (line symmetry is where each point on one side of a line has a corresponding point on the opposite side, e.g. a picture a butterfly with wings that are identical on either side; plane symmetry refers to similar figures being repeated at different but regular locations on the plane), tensor: a collection of numbers at every point in space which describe how much the space is curved, e.g. There are two major types of proofs: direct proofs and I have heard Professor Eddington, for example, maintain that proof, as pure … Addition Property of Equality. Proper Fraction: A fraction whose denominator is greater than its numerator. Multiplicand: A quantity multiplied by another. Protractor: A semi-circle device used for measuring angles. Like Fractions: Fractions with the same denominator. Rhombus: A parallelogram with four sides of equal length and no right angles. Line of Symmetry: A line that divides a figure into two equal shapes. "0, 1, 1, 2, 3, 5, 8, 13, 21, 34..." is a Fibonacci sequence. At higher levels, you should always use an informal proof. Midpoint: A point that is exactly halfway between two locations. Although ultimately every mathematical argument must meet a high standard of precision, mathematicians use descriptive but informal statements to discuss recurring themes or concepts with unwieldy formal statements. a(b + c) = ab + ac, element: a member of, or an object in, a set, ellipse: a plane curve resulting from the intersection of a cone by a plane, that looks like a slightly flattened circle (a circle is a special case of an ellipse), elliptic geometry: a non-Euclidean geometry based (at its simplest) on a spherical plane, in which there are no parallel lines and the angles of a triangle sum to more than 180°, empty (null) set: a set that has no members, and therefore has zero size, usually represented by {} or ø, Euclidean geometry: “normal” geometry based on a flat plane, in which there are parallel lines and the angles of a triangle sum to 180°, expected value: the amount predicted to be gained, using the calculation for average expected payoff, which can be calculated as the integral of a random variable with respect to its probability measure (the expected value may not actually be the most probable value and may not even exist, e.g. Tangent: A straight line touching a curve from only one point. Integers: All whole numbers, positive or negative, including zero. Slope: Slope shows the steepness or incline of a line and is determined by comparing the positions of two points on the line (usually on a graph). Perpendicular: Two lines or line segments intersecting to form a right angle. A proof in which a statement is shown to be true because the assumption that its Histogram: A graph that uses bars that equal ranges of values. The edge of a protractor is subdivided into degrees. Regular pentagons have five equal sides and five equal angles. for multiplication, the identity is one; for addition, the identity is zero, imaginary numbers: numbers in the form bi, where b is a real number and i is the “imaginary unit”, equal to √-1 (i.e. the factors of 10 are 1, 2 and 5, factorial: the product of all the consecutive integers up to a given number (used to give the number of permutations of a set of objects), denoted by n!, e.g. Take the StudyWell Proof Test. Diameter: A line that passes through the center of a circle and divides it in half. the highest power is 4), of the form ax4 + bx3 + cx2 + dx + e = 0, the highest order polynomial equation that can be solved by factorization into radicals by a general formula, quaternions: a number system that extends complex numbers to four dimensions (so that an object is described by a real number and three complex numbers, all mutually perpendicular to each other), which can be used to represent a three-dimensional rotation by just an angle and a vector, quintic equation: a polynomial having a degree of 5 (i.e. They are very commonly used in geometry. Proof of the angle sum theorem A crystal clear proof of the angle sum theorem. Pi: Pi is used to represent the ratio of a circumference of a circle to its diameter, denoted with the Greek symbol π. Cone: A three-dimensional shape with only one vertex and a circular base. Radius: A distance found by measuring a line segment extending from the center of a circle to any point on the circle; the line extending from the center of a sphere to any point on the outside edge of the sphere. factor: a number that will divide into another number exactly, e.g. Division Property of Equality. Mode: The mode in a list of numbers are the values that occur most frequently. Isosceles: A polygon with two sides of equal length. negation is true leads to a Many square roots are also irrational numbers. Odd Number: A whole number that is not divisible by 2. Natural Numbers: Regular counting numbers. contradiction signifies that there has been a mistake in reasoning, and can be Modular Arithmetic: A system of arithmetic for integers where numbers "wrap around" upon reaching a certain value of the modulus.
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