# 2009 Top Ten of Polemic for Mathematics

Distributive property
In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the
Volume
Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface. For example, the space that a substance or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes
Definition
A definition is a statement of the meaning of a term. Definitions can be classified into two large categories, intensional definitions and extensional definitions. Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions
Rhombus
In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a 'diamond', after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge (shape), though the former sometimes refers specifically to a rhombus with a 60° angle, and the latter sometimes refers specifically to a rhombus
Table of prime factors
The tables contain the prime factorization of the natural numbers from 1 to 1000
Number sentence
In mathematics education, a number sentence is an equation or inequality expressed using numbers and mathematical symbols. The term is used in primary level mathematics teaching in the US, Canada, UK, Australia, New Zealand and South Africa
Train track (mathematics)
In the mathematical area of topology, a train track is a family of curves embedded on a surface, meeting the following conditions:The curves meet at a finite set of vertices called switches. Away from the switches, the curves are smooth and do not touch each other. At each switch, three curves meet with the same tangent line, with two curves entering from one direction and one from the other
Composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other
Tits group
In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order 211 · 33 · 52 · 13 = 17,971,200