Category: Geometry

Solar System

When I was young I loved to play with planetary data, to explore their patterns, to learn more about astronomy, and to deal with large numbers. Spreadsheets make it much easier to study the solar system and to find relationships between the planets that are fascinating and unexpected. In the process you will not only learn more science, you will gain spreadsheet skills working with data and functions.

String Diagrams

The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow much exploration. Mary Boole meant them as exercises in visualization. Building these diagrams using spreadsheets not only shows their versatility and capability for artistic expression, it helps students get used to using ordered pairs and axes of different sorts and thus builds their graphic sense. There are so many possibilities that you might think of having contests for the most interesting and thought provoking diagrams.

Drawing Triangles

Though spreadsheets lets you put geometric shapes on the screen, those shapes are not connected with the cells and cannot be changed by using different values. We wanted to make geometric shapes that we could control and change by changing parameters. This is our first try. You can learn to use linear functions to create and change a triangle. It is pretty cool. This Lab involves many different aspects of mathematics from geometric shapes to graphing, from slope to linear functions, from perpendicular lines to the definition of function.

Exploring Triangles

Create, manipulate, and explore triangles in this live interactive spreadsheet. On the surface, a triangle is being drawn on a graph, but the real magic lies in the formulas used to make this spreadsheet work.

String Challenge

Strings need not begin and end on axes that are at right angles to each other which we call Cartesian. It is quite interesting that Descartes himself did not use axes at right angles. We consider this a challenge because students have to figure out how to move both the axes and the lines. Once you understand the process there is no end to the beauty of the string diagrams you can make. We suggest you check out the Web and Wikipedia for more ideas.