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.
Tag: geometry
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.
Similar Triangles
Scatterplot graphs enable us to build shapes using spreadsheets and to practice transformational geometry. They are surprisingly flexible tools. And since they depend upon a table of value and that table can have both fixed numbers and rules, we can not only build shapes but change them and watch the graph immediately reflect those changes. In this lab we use that capability to get students to explore scaling, reflection, and transposition of a triangle. This is only the beginning and we hope students will take this further exploring symmetries for example.
Sierpinski Fractals
Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based on the odd numbers in Pascal’s triangle. We learn to create it easily by using Conditional Formatting which enables us to color cells or text based on a quantitative relationship. To turn Pascal’s triangle into a Sierpinski fractal all we have to do is color cells that are odd numbers. Here again is an amazing pattern involving odds and evens. There are a wide number of other Sierpinski fractal patterns.