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.

1 over 4 Rotation Radians
1 over 4 Rotation Radians
1 over 6 Rotation Radians
1 over 6 Rotation Radians
Angle measured as 1 radians.
1 Radian
This figures illustrates the standardized angle that represents an twelfth turn.
1/12 τ (tau) Radians
This figures illustrates the standardized angle that represents an fourth turn.
1/4 τ (tau) Radians
This figures illustrates the standardized angle that represents an sixth turn.
1/6 τ (tau) Radians
This figures illustrates the standardized angle that represents an eighth turn.
1/8 τ (tau) Radians
This figure illustrates the measured angle of 135 degrees.
135 Degree Angle
An angle measured as 2 radians.
2 Radians
An angle measured as 3 radians.
3 Radians
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
An angle measured as 4 radians.
4 Radians
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
An angle measured as 5 radians.
5 Radians
An angle measured as 6 radians.
6 Radians
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
This figure illustrates an angle as it would appear in applications.
Angle
An angle is defined as the amount of rotation between two rays.
Angle
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 two vectors and the angle formed between them.
Angle Between Two Vectors (2d) Example
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
This figure illustrates the output of the arctangent function.
Arc Tangent Function (1,1)
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 percentage area under the normal distribution (σ = 1).
Area Under Normal Distribution
This figure illustrates the percentage area under the normal distribution associated with the standarad deviation of the distribution.
Area Under Normal Distribution
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 trigonometric functions defined using the circle.
Circle Functions
Circle Polar Coordinate System
Circle Polar Coordinate System
This figure illustrates the trigonometric functions defined using the circle.
Circle Trigonometry
Color intensity shown as a gradient from black to white.
Color Intensity
Placing a neutral color in different environments changes its appearance.
Color Intensity Optical Illusion
The spectrum of possible hues of color.
Color Spectrum
This figure illustrates the additive color model as a color spectrum circle.
Color Spectrum Circle
The color wheel visualizes the circular nature of the possible hues of color.
Color Wheel
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
A point on the unit circle in the complex plane.
Complex Unit Circle
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
Yearly Compound Interest Example
Compound Interest Yearly Example
Plot of the cosecant function from 0 to τ (tau) radians.
Cosecant Function
Plot of Cosine from 0 to τ (tau) radians.
Cosine Function
Plot of Cosine Function from 0 to 360 degrees
Cosine Function (Degrees)
Graph of Cosine from 0 to τ (tau) radians.
Cosine Function Plot
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 a cylinder with a radius of 2 and a height of 2.
Cylinder Example
This figure illustrates a cylinder with a radius of 3 and a height of 2.
Cylinder Example
This figure depicts how the degrees system measures angles where one full rotation is 360 degrees.
Degree Angle System
Special angles measured using Degrees
Degrees Common Fractions
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 Example
An exponential tree growth rate 2 levels 4 leaves 16.
Exponential Tree Example
An exponential tree with a base of 3 a height of 2 and 9 leaves.
Exponential Tree Example
An exponential tree demonstrated 2 raised to the third power.
Exponential Tree Properties
Test
Grid Test
This figure illustrates the area under the curve represented by the integral between two points.
Integral Definition
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 how the standard deviation corresponds to the distribution of data around the mean.
Normal Deviation Area
This figure plots the tangent function from 0 to τ (tau) radians.
Plot of Tangent Function
The polar coordinate system describes points in space relative to the origin using a combination of radius and angle.
Polar Coordinate System
This figure illustrates the polar coordinates point (3, 0.2 τ)
Polar Coordinates Point
Population Growth Formula Example
Population Growth Constant
This figure shows how growth rate influences the population using the formula for population growth.
Population Growth Rate Coeffecient 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
The quadratic formula returns the x-intercept points of the quadratic equation it is applied to.
Quadratic Formula
This figures illustrates the radian angle system.
Radian Angle System
Radian Angle System
Radian Angle System
Radian Angle System π (pi)
Radian Angle System π (pi)
Radius Invariance Property
Radians (Radius Invariance Property)
The geometric Definition of Radian System.
Radians Definition
Radians Unit System Fractions τ (tau)
Radians Special Angles
This figure illustrates the right triangle.
Right Triangle
Plot of the secant function from 0 to τ (tau) radians.
Secant Function
Plot of Sine Function from 0 to τ (tau) radians.
Sine Function
Plot of Sine Function from 0 to 360 degrees
Sine Function (Degrees)
Plot of Sine Function from 0 to 2π radians.
Sine Function Plot π (pi)
Visualization of the return value of sine on the unit circle.
Sine of One Third Tau
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 "proof without words" of the sum of two angles identities
Sum of Two Angles Identities
Plot of the tangent function from 0 to τ (tau) radians.
Tangent Function
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
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 Intersections
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)
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 π (pi) Test
Variables associated with the Unit Circle
Unit Circle Notation
The unit circle demonstrates the output of the trigonometric functions sine, cosine and tangent through the shared geometry of the right-triangle defined by a point on the perimeter of the circle.
Unit Circle Trigonometry
Inverse Property of Exponential Function
Verify Inverse Property of Exponential Function
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)
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