# Geometric Explorations

Last Updated on 2021-05-04 by Michael Horvath

Here you can find a series of tutorials and worksheets I created using The Geometer’s Sketchpad and GeoGebra. You can view all of the GeoGebra resources I have created, here.

## Music

##### Graphical chord and scale calculator:
An interactive diagram depicting musical intervals, chords and scales and component elements.
##### Frequency doubling:
A description of how the frequency of musical tones double as the number of octaves increases.

## Art

##### Color cube:
A demonstration of how the different color components combine to create colors on your computer monitor.
##### Sri Yantra:
A Hindu mystical diagram.

## Conic sections

##### Bezier / parabola:
A demonstration showing that a Bezier curve is also a parabolic segment.
##### Parabola construction:
A demonstration showing how to trace a parabola.
##### Ellipse & hyperbola construction:
A demonstration showing two methods of constructing the ellipse and hyperbola geometrically.
##### Conic section tools:
Five GeoGebra tools for creating conic sections.

## Other curves

##### Beta distributions:
A great class of curves for generating smooth random distributions with known limits.
A demonstration showing how to construct a quadratic Bezier curve geometrically.
##### Cubic Bezier curve construction:
A demonstration showing how to construct a cubic Bezier curve geometrically.
##### Lissajous curves:
A demonstration of how to trace Lissajous curves.
##### Spirals:
Some examples of different types of spirals.
##### Peano-Gosper curve:
Six GeoGebra tools for creating the Peano-Gosper curve.

## Surfaces

##### Parametric sphere with Euler rotations:
A demonstration showing how to plot three-dimensional curves in GeoGebra and apply Euler rotation matrices to them. Curves are not drawn in perspective however.
##### Metaballs: sticky, gooey blobs:
A description of different techniques used to create the class of surfaces known as metaballs or “blobs”.

## Trigonometry:

##### Trigonometric functions:
A worksheet showing the relationship between the trigonometric functions and the unit circle.
##### Triangle components:
A worksheet showing the various components of a triangle.
Screenshot
##### Vectors:
A demonstration of the different components of a vector, as well as vector operations.

## Miscellaneous

##### Geodetic latitude:
A description of geodetic latitude and its relationship to the Earth’s surface. Also a discussion of “circles of latitude”.
##### Solar system model:
An animation showing the eight major planets of the solar system orbiting the sun.

## Utility

##### JavaScript/XML demo:
GeoGebra demo showing JavaScript evaluation and XML modification from inside an HTML page.