Math Figures

A collection of mathematical figures. A figure is an illustration, graphic or image that represents a math concept. Each figure is linked to relevant pages and contains an explanation of how to construct the figure.

This figure illustrates the standardized angle that represents an twelfth turn.
1/12 τ Radians
This figure illustrates the angle of 1/24 τ (tau) radians.
1/24 τ Radians
This figure illustrates the standardized angle that represents an fourth turn.
1/4 τ Radians
This figure illustrates the standardized angle that represents an sixth turn.
1/6 τ Radians
This figure illustrates the standardized angle that represents an eighth turn.
1/8 τ Radians
This figure illustrates the measured angle of 135 degrees.
135 Degree Angle
The 30 60 90 special right triangle is defined by the angles: 30, 60 and 90 degrees.
30 60 90 Triangle
This figure illustrates the measured angle of 30 degrees.
30 Degree Angle
This figure illustrates the measured angle of 330 degrees.
330 Degree Angle
This figure illustrates the measured angle of 360 degrees.
360 Degree Angle
This figure illustrations a full rotation in degrees divided by 4.
360 Degrees divided by 4
This figure illustrations a full rotation in degrees divided by 4.
360 Degrees divided by 8
The 45 45 90 special right triangle is defined by the three angles: 45, 45 and 90 degrees. Its simple geometry makes it useful in applications.
45 45 90 Triangle
This figure illustrates the measured angle of 45 degrees.
45 Degree Angle
This figure illustrates the measured angle of 60 degrees.
60 Degree Angle
This figure illustrates the measured angle of 90 degrees.
90 Degree Angle
This figure illustrates the plot of the absolute value function.
Absolute Value Function
An angle is defined as the amount of rotation between two rays.
Angle
This figure illustrates an angle formed between three points.
Angle Between Points
This figure illustrates the angle formed between two tail-to-tail vectors in the 2D cartesian coordinate system.
Angle Between Two Vectors (2D)
This figure illustrates the formula for the angle formed between two tail-to-tail vectors in the 2D cartesian coordinate system.
Angle Between Two Vectors Formula (2D)
This figure illustrates the output of the arctangent function.
Arc Tangent Function
The ATAN2 function returns the angle corresponding to the (x,y) point on the circle.
Arc Tangent Function 2
Plot of the ArcCosine function.
ArcCosine Function
Plot of the ArcSine function.
ArcSine Function
Plot of the ArcTangent function.
ArcTangent Function
This figure illustrates the parallelogram area formed between two vectors.
Area Between Vectors
This figure illustrates how the area between two vectors is given by the magnitude of their cross product.
Area Between Vectors Formula
This figure illustrates the area of circle formula.
Area of Circle
This figure illustrates the area of circle formula using the constant π (pi).
Area of Circle π (pi) Formula
This figure illustrates the area of circle formula.
Area of Parallelogram
This figure illustrates the area of a rectangle formula.
Area of Rectangle Formula
This figure illustrates the area of a trapezoid formula.
Area of Trapezoid Formula
This figure illustrates the area of a triangle formula.
Area of Triangle Formula
This figure illustrates the percentage area under the normal distribution (σ = 1).
Area Under Normal Distribution
This figure illustrates the basis vectors i hat and j hat placed in the cartesian coordinate system.
Basis Vectors
This figure illustrates the Cartesian Coordinate System which is a system used to define the position of points in space relative to an origin.
Cartesian Coordinate System
This figure illustrates the circle as a center point and a radius.
Circle
Circle in Cartesian Coordinates
Circle Cartesian Coordinate System
This figure illustrates the geometry used to define the circle definitions of the trigonometric functions.
Circle Functions
Circle Polar Coordinate System
Circle Polar Coordinate System
This figure illustrates the trigonometric functions defined using the circle.
Circle Trigonometry
This figure illustrates the circumference of a circle formula.
Circumference of Circle Formula
This figure illustrates the circumference of a circle formula.
Circumference of Circle Formula
This figure illustrates a number the complex plane. The horizontal axis represents the real part of a complex number and the vertical axis represents the complex part of a complex number.
Complex Number
The visualization of complex number addition.
Complex Number Addition
This figure illustrates the complex plane. The horizontal axis represents the real part of a complex number and the vertical axis represents the complex part of a complex number.
Complex Plane
This figure illustrates visual representation of multiplying a complex number by the complex number i.
Complex Plane (Complex Property)
This figure illustrates visual representation multiplying 1 by a complex number
Complex Plane (Identity Property)
This figure illustrates visual representation of multiplying two complex numbers together.
Complex Plane Multiplication
A point on the unit circle in the complex plane.
Complex Unit Circle
A point on the unit circle in the complex plane corresponding to a negative angle.
Complex Unit Circle Negative Angle
This figure illustrates the relationship between compound interest and exponential growth.
Compound Interest and Exponential Growth
This figure depicts the graph of the compound interest formula given some example values.
Compound Interest Formula
This figure is a graph of a quarterly compound interest example.
Compound Interest Quarterly Example
Plot of the cosecant function from 0 to τ (tau) radians.
Cosecant Function
Plot of Cosine from 0 to τ (tau) radians.
Cosine Plot
Plot of Cosine Function from 0 to 360 degrees
Cosine Plot (Degrees)
Plot of the cotangent function from 0 to τ (tau) radians.
Cotangent Function
This figure illustrates how the cross product operator returns the normal vector to the two input vectors.
Cross Product Operator
This figure illustrates a cube defined by the length of its sides.
Cube
This figure illustrates the formula for the volume of a cube.
Cube
This figure illustrates a cylinder defined by the length of its radius and height.
Cylinder
This figure illustrates the degree angle system which represents a full rotation as 360 units called degrees.
Degree Angle System
Special angles measured using Degrees
Degrees Common Fractions
This figure illustrates the definition of the derivative operator in terms of a limit.
Derivative Limit Definition
This figure illustrates the "proof without words" of the difference of two angles identities
Difference of Two Angles Identities
This figure illustrates the formula for finding the distance between two points in one dimension.
Distance Between Two Points 1D Formula
This figure illustrates the formula for finding the distance between two points in two dimensions.
Distance Between Two Points 2D Formula
Euler's Formula in the Complex Plane
Euler's Formula
This figure shows the graph of the exponential function on the domain [0,1].
Exponential Function Graph
This figure illustrates an exponential tree.
Exponential Tree
An exponential tree demonstrated 2 raised to the third power.
Exponential Tree Properties
This figure illustrates the area under the curve represented by the integral between two points.
Integral
This figure illustrates the intermediate value theorem.
Intermediate Value Theorem
This figure illustrates the intermediate value theorem.
Mean Value Theorem
An illustration of the formula for finding the midpoint of a line defined by two points.
Midpoint Formula
This figure illustrates the bell-shape of a normal distribution.
Normal Distribution
This figure illustrates how the standard deviation corresponds to the distribution of data around the mean.
Normal Distribution Area
This figure illustrates the propperties that a point has in both the polar and cartesian coordinate system.
Point in Polar and Cartesian Coordinates
The polar coordinate system describes points in space relative to the origin using a combination of radius and angle.
Polar Coordinate System
This figure shows how growth rate influences the population using the formula for population growth.
Population Growth Rate coefficient Values
The Pythagorean Identity relates the radius of length one on the unit circle to the squares of the sine and cosine function.
Pythagorean Identity
This figure illustrates the geometric interpretation of the Pythagorean theorem.
Pythagorean Theorem
The quadratic formula returns the x-intercept points of a quadratic equation.
Quadratic Formula
This figure illustrates the radian angle system annotated using the circle constant τ (tau).
Radian Angle System
This figure illustrates the radian Angle System annotated with the constant π (pi).
Radian Angle System π (pi)
Radius Invariance Property
Radians (Radius Invariance Property)
This figure illustrates the geoemtric definiton of a radian angle.
Radians Definition
Radians Unit System Fractions τ (tau)
Radians Special Angles
The right triangle has three sides relative to the angle that defines its shape: the adjacent, opposite and hypotenuse.
Right Triangle
Plot of the secant function from 0 to τ (tau) radians.
Secant Function
This figure visualizes the set intersection operator using a venn diagram.
Set Intersection Diagram
Plot of Sine Function from 0 to 2π radians.
Sine Function Plot π (pi)
Plot of Sine Function from 0 to τ (tau) radians.
Sine Plot
Plot of Sine Function from 0 to 360 degrees
Sine Plot (Degrees)
This figure illustration that an angle by itself is measured from the positive rightwards direction on the circle with the positive in the counter-clockwise direction.
Standard Angle Convention
This figure illustrates the standard for measuring angles in the XY coordinate plane.
Standard XY Angle
This figure illustrates the "proof without words" of the sum of two angles identities
Sum of Two Angles Identities (Visual Proof)
This figure illustrates the output of the two functions tangent and cotangent on the unit circle
Tangent and Cotangent
Plot of the tangent function from 0 to τ (tau) radians.
Tangent Function
This figure plots the taylor series of sine.
Taylor Series of Sine
Trigonometry is about circles
Trigonometry (Circles)
This truth table illustrates the logical "xor" operator.
Truth Table Exclusive Or
This truth table illustrates the logical "and" operator.
Truth Table Logical And
This truth table illustrates the logical "if and only if" operator.
Truth Table Logical If and Only If
This truth table illustrates the logical "implies" operator.
Truth Table Logical Implies
This truth table illustrates the unary negation operator.
Truth Table Logical Negation
This truth table illustrates the logical "or" operator.
Truth Table Logical Or
A circle of radius one placed at the origin of the coordinate system.
Unit Circle
The unit circle chart shows the positions of the points along the unit circle that are formed by dividing the circle into eight and twelve parts respectively. This figure is measured using the radian angle system and annotated with the circle constant tau.
Unit Circle Chart
The Unit Circle Divided by 4 measured using the circle constant.
Unit Circle Chart 4
This figure illustrates the unit circle chart measured in degrees which shows the positions of the points along the unit circle that are formed by dividing the circle into eight and twelve parts respectively.
Unit Circle Chart Degrees
This figure illustrates the unit circle chart divided into eight equal parts measured in degrees.
Unit Circle Chart Degrees Eigths
This figure illustrates the unit circle chart divided into twelve equal parts measured in degrees.
Unit Circle Chart Degrees Twelfths
The Unit Circle Divided by 8 measured using the circle constant.
Unit Circle Chart Eighths τ (tau)
The unit circle chart shows the positions of the points along the unit circle that are formed by dividing the circle into eight and twelve parts respectively.
Unit Circle Chart Eights π (pi)
This figure illustrates the points where the unit circle chart intersects the x and y axis in the cartesian coordinate system.
Unit Circle Chart Start
The unit circle chart shows the positions of the points along the circle that are formed by dividing the circle into eight and twelve parts respectively.
Unit Circle Chart Twelfths π (pi)
The Unit Circle Divided by 12 measured using the circle constant.
Unit Circle Chart Twelfths τ (tau)
The unit circle chart shows the positions of the points along the unit circle that are formed by dividing the circle into eight and twelve parts respectively. This figure is measured using radians and degrees.
Unit Circle Chart π (pi)
Variables associated with the Unit Circle
Unit Circle Notation
The unit circle demonstrates the output of the trigonometric functions sine, cosine and tangent.
Unit Circle Trigonometry
This figure illustrates the trigonometry of the unit circle.
Unit Circle Trigonometry
This figure illustrates the shape of a vector in the 2D cartesian coordinate plane.
Vector
This figure illustrates the shape of a vector in the cartesian coordinate plane.
Vector
This figure illustrates the geometry formed by adding two vectors together
Vector Addition
This figure illustrates the volume of cylinder formula defined by the length of its radius and height.
Volume of Cylinder
This figure illustrates the volume of cylinder formula defined by the length of its radius and height.
Volume of Cylinder π (pi)
This figure illustrates the x-intercepts of a quadratic equation
x Intercepts
The definition of π (Pi) in terms of the circumference and diamater of the circle.
π (Pi) Definition
A half-rotation is π (pi) radians.
π (pi) Radians
Definition of the circle constant τ (tau)
τ (tau) Definition
An angle measured as τ (tau) radians.
τ (tau) Radians
This figure illustrations a full rotation in radians divided by 4.
τ (tau) Radians Divided by 4
This figure illustrations a full rotation in radians divided by 8.
τ (tau) Radians Divided by 8