Download spirograph.xls

This is an Excel spreadsheet that will generate the curve drawn by a
Spirograph kit, once you have specified the dimensions of the wheel etc that you
are using. No macros are used.

- System requirements
- Microsoft Excel
- The Analysis ToolPak will need to be enabled

- Enabling the Analysis ToolPak
- The Analysis ToolPak is enabled by going to Tools > Add-ins and ticking
Analysis ToolPak.
- Click OK

- Using the file
- Download the file to your hard drive and open it (making sure that the
Analysis ToolPak is already enabled)
- Enter the measurements of the wheels you are using in the three text
boxes. Do not include the units but make sure that all measurements are of the
same units.
- If you are unsure what the boxes mean, here is a diagram showing the
measurements of a standard spirograph wheel. The red spot is the hole where
you put your pen.

- The curve generated will be shown below. If there is no curve, you
probably forgot to enable the Analysis ToolPak.
- Click Print to the right of the textboxes to show a printable version of
the Spirograph curve generated

## Troubleshooting

- The Spirograph disappears, or does not appear
- Make sure you have enabled Analysis ToolPak

- The Spirograph looks too tall/wide
- Sorry, it is not possible to get the dimensions of the graph used to be
exactly correct. Try adjusting its size yourself until the curve looks
correct.

## The Maths

The locus of the tip of a pen fixed to a wheel rotating in the hole from
from a Spirograph set is called a Hypotrochoid. I generate it with the
following steps:

- In the 'Input' sheet, reference the variables inputted into the
interface
- Using the GCD function (from the Analysis ToolPak), calculate the number
of revolutions of the wheel that will be required to complete the drawing in
cell B12
- 1000 points will be plotted on the graph. The angle covered by each
point is calculated in cell B16. Generally, the higher this number, the
lower the accuracy of the curve generated.
- The 'Intermediate Calculations' sheet calculates the position of each
point on the graph, using trigonometry.
- The numbers generated may be very high. To keep the same scale on the
graph, the numbers are changed so that they are all between -1 and 1.
- The 'Output' sheet contains the actual values that will be plotted on
the graph
- Several graphs use this data. The main one is the graph shown on the
interface, but there is also a graph on the printable version of the
Spirograph and several other graphs that only exist for testing purposes.