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.

Line segment : A line segment AB is a one-dimensional shape consisting of the points A and B and all the points on the straight connection of A and B. A and B are both endpoints of the line segment AB.

Pyramid : A pyramid is a polyhedron that has a base equal to a polygon. In addition to the corners in the polygon the pyramid has exactly one additional corner, the so called apex of the pyramid. All the corners of the base shape are connected to the apex and all the faces besides the base face are triangles.

Quadrilateral : A quadrilateral or quadrangle is a polygon with four corners. Rectangles, trapezoids, kites, rhombuses, squares and parallelograms are all specific kinds of quadrilaterals. The sum of the interior angles in a quadrilateral is always $360^{\circ}.$

Shape : A shape is a set of points in space.

Three-dimensional shape : A three-dimensional shape is a shape that has a volume.

Volume : Volume refers to the size of a three-dimensional objects measured by how many unit cubes it would take to fill the shape.

Degree : For angles one degree is defined as the angle represented by a $\frac{1}{360}$ of the angle represented by a full circle. For measuring temperatures one can use either degrees Celsius or degrees Fahrenheit. In a polynomial the degree describes the highest exponent of $x$ that has a non-zero coefficient. For example the degree of $1+x+x^2$ is 2.

Degrees Celsius : The Celsius scale for measuring temperature is specified by saying that $0^{\circ}$ C is the temperature at which water freezes and $100^{\circ}$ C is the temperature at which water boils. To convert degrees Fahrenheit into degrees Celsius one can use the formula $C=\frac{5}{9}\cdot(F-32).$

Degrees Fahrenheit : The Fahrenheit scale for measuring temperature is specified by saying that $32^{\circ}$ F is the temperature at which water freezes and $212^{\circ}$ F is the temperature at which water boils. To convert degrees Fahrenheit into degrees Celsius one can use the formula $C=\frac{5}{9}\cdot(F-32).$

Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.

Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$

Real number : A real number is any number that can be represented by a possibly infinite decimal expansion. All rational and irrational numbers are real numbers.

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 $\sqrt{9}=3.$

Subtraction : Subtraction is the mathematical operation that describes decreasing a number by an amount equal to a second number. The mathematical symbol for subtraction is the minus sign $-.$ The term subtraction is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.