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.

Follow from : A second equation or inequality follows from an initial equation or inequality if all solutions of the initial equation are also solutions from the second equation or inequality. It does not necessarily have to be the case that all solutions of the second equation or inequality have to by solutions of the first inequality. For example $x^2=1$ follows from $x=1$, but $x^2=1$ is not equivalent to $x=1$ as -1 is a solution of $x^2=1$ but not a solution of $x=1.$

Fractional exponent : The definition of a power with a fractional exponent is $x^\frac{a}{b}:=\sqrt[b]{{x}^a}.$ For example $8^{\frac{2}{3}}=\sqrt[3]{{8}^2}=4.$

N-th root : The n-th root of a number $x\gt 0$ or $\sqrt[n]{x}$ is defined as the positive solution of the equation $(\sqrt[n]{x})^n=x.$ For example $\sqrt[4]{16}=2$ as $2^4=2 \cdot 2 \cdot 2 \cdot 2=16.$

One seventh : One seventh is the number $\frac{1}{7}=0.\overline{142857}.$

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 $b.$

Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$

Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Corner : A corner of a shape is a point in the shape such that this point does not lie on the line segment between any two other points in the shape. Every triangle has 3 corners and every quadrilateral has 4 corners.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Cosine law : The cosine law states that in any triangle we have $c^2=a^2+b^2-2ab\cos \gamma.$ In can be used to calculate the length of the third side if the lengths of two sides and the angle in between those two sides is given. It can also be used to calculate angles if all three side lengths are given. The Pythagorean theorem is the special case of the cosine law with $\gamma=90^{\circ}.$

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

Inch : An inch or $in$ is a unit of measurement for length. 12 inches are one foot and 1 inch is about 2.54 $cm.$

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Square inch : Square inch is a unit of measurement for measuring area. 1 square inch is the area of a square with side length 1 inch. 144 square inches are 1 square foot.

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$

Odd function : A function $f$ is called odd if and only if we have $f(x)=-f(-x)$ for all $x.$ The graph of an odd function is symmetric with respect to the point (0,0).

Pi : Pi or $\pi$ is an irrational number approximately equal to 3.14 that is defined as the quotient of the circumference and the diameter of a circle.

Tan : The tangent of an angle $0\leq\alpha\leq 180^{\circ}$ or $\tan \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the leg adjacent to $\alpha.$ For arbitrary angles the tangent function can be extended in a periodic way by inscribing the right triangle in a circle. The tangent function can be used to calculate unknown side lengths and angles in right triangles via its definition. We have $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$