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Sinusoidal Functions

In a unit circle, the cosine of an angle is equal to the x-coordinate of the point on the circle that corresponds to that angle. Similar to the sine function, as the angle increases from 0 to 360 degrees (or 0 to 2π radians), the value of the cosine function oscillates between -1 and 1. In trigonometry, the tangent relates the ratio of two sides of a right triangle, specifically the side opposite an angle and the side adjacent to that angle.

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• The Unit Circle
• The sinusoidal functions family

Circles, Hypocycloids, Epicycloids

Hypocycloids and epicycloids are 2 types of curves that are formed by tracing a point on a circle as it rolls around the inside or outside of another circle, respectively. They can be used to model the motion of gears in mechanical systems or the movement of planets in orbit around a star

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• Hypocycloids
• Epicycloids

Epitrochoids

An epicycloid is actually a type of epitrochoid. An epicycloid is a specific type of epitrochoid in which the point attached to the rolling circle is on its circumference.

Hypotrochoids

Rose Curves

Rose Curves have symmetrical shapes that have inspired mathematicians for centuries.

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• Counting rose petals
• Description and propoerties

Rose Curve and stroboscopic effect

The stroboscopic effect or the wagon-wheel effect occurs because of the way our brain processes visual information. When we see a fast-moving object like a rolling wheel, our brain processes the individual images it receives in a sequence, and if the object's motion is fast enough, our brain can't keep up with the individual images and instead creates an illusion of motion that is not entirely accurate. This illusion can sometimes cause us to perceive the wheel as turning backwards or slowing down.

Rotating Spiral

By defining a set of angles and a set of phases, you can iterate over each phase and adjust the angles by adding the current phase. This process allows you to create a series of spirals that gradually rotate over time, resulting in an animation.

Tetrahedron

A tetrahedron is type of pyramid with a triangular base. A regular tetrahedron can be formed using six of the face diagonals of a regular cube.

The spacial configuration of methane consists of a tetrahedral molecule with carbon at its center and four hydrogen atoms at its vertices.

Square Pyramid

Great Circles

A great circle has the same center and radius as the sphere. It divides the sphere into two equal hemispheres and is the largest possible circle that can be drawn on a sphere. The equator is a great circle.