Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Integral : The integral of a function $f$ between $a$ and $b$ is defined as $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n}).$ For example $\int\limits_{a}^{b}xdx=\frac{b^2}{2}-\frac{a^2}{2}.$ The fundamental theorem of calculus provides a simple way to calculate integrals using antiderivatives.

Interval : An interval is a part of the number line between two numbers $a$ and $b.$ $a$ and $b$ can but do not have to be part of the interval. If $a$ and $b$ are part of the interval the interval is a closed interval. If $a$ and $b$ are not part fo the interval the interval is an open interval. If either $a$ or $b$ but not both are part of the interval the interval is called half-open or half-closed. $a$ can be equal to $-\infty$ and $b$ can be equal to $\infty$.

Midpoint : The midpoint of a line segment is the point on the line segment that cuts the line segment into two equal length pieces.

Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$

Random variable : A random variable $X$ describes all the possible outcomes of a random experiment. The probability distribution of $X$ describes how likely all these outcomes are.

Uniformly distributed : A random variable $X$ is uniformly distributed on the interval $[a,b]$ if it only takes values in $[a,b]$ and any value within the interval is equally likely in the sense of $P[X\lt x]=\frac{x-a}{b-a}.$ for $a\leq x\leq b.$ A uniformly distributed random variable has a mean $E[X]=\frac{a+b}{2}$ and a variance of $var[X]=\frac{(b-a)^2}{12}.$

Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.

Geometric series : A geometric series is a sequence $x_1, x_2, x_3,\ldots$ of numbers where $x_n$ is the sum of the first $n$ numbers in a geometric progression. For example the n-th element of the geometric series related to the geometric progression $1, q, q^2, \ldots$ is $1+q+q^2+q^{n-1}$ $=\frac{q^n-1}{q-1}.$

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Number : A number $x$ is a mathematical symbol representing a quantity.

Quarter : One quarter is the number $\frac{1}{4}=0.25.$

Ratio : A ratio is a comparison of two numbers using a division.

Sum : A sum is the result of an addition.

Boundary : The boundary of a 2-dimensional shape is the 1-dimensional shape that separates the 2-dimensional shape from the rest of the 2-dimensional space.

Center : The center of a circle is the unique point in the circle, such that all points on the boundary of the circle have a constant distance equal to the radius from that point. The center of a regular polygon is the point that has equal distance from all its corners.

Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.

Constant : Constant is another word for a fixed number that is mainly used in the context of expressions or functions like $f(x)=c$ that are equal to the same number irrespective of any variable.

Ellipse : An ellipse is a two-dimensional shape with a boundary that is a set of points for which the combined distance from two points is constant. Circles are special cases of ellipses. The boundary of an ellipse can also written as the set of points $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$

Point : A point is an element in a space. Shapes are made of sets of points.

Set : A set is a collection of objects.