SpiroChart 2.0 is a spreadsheet which generates a fascinating variety of spiral designs and angular patterns, based on numbers selected by the user. This edition of SpiroChart was created using Microsoft Excel 4.0.
Directions
To manipulate the graphics, open SpiroSheet ABC and the Main Chart. Try changing the numbers in outlined cells, and watch what happens!
Hints and Tips
A degree interval of 1 will generate the smoothest curves for figures having a relatively small number of loops. Increasing the degree interval makes the figures more angular.
The number of points (or line segments) in the figure is limited by the number of rows of formulas in the spreadsheet. You may add more rows of formulas to increase the number of points and line segments which can be drawn. This can be helpful if you would like to reduce the degree interval to make a smoother curve and still have a complete figure.
For the adventurous: By changing the user-selected numbers in small increments, a series of charts can be generated and saved as a set of PICTs, which can then be assembled into a QuickTime movie using a shareware utility like MooVer. A sample movie is included with this collection.
Concept behind SpiroChart
SpiroChart traces a curve which is followed by a point on a wheel spinning at one end of a rod of arbitrary length. The entire rod is being pivoted about the opposite end. Imagine holding a pinwheel in your hand with your arm horizontally extended as you turn in place. If you could trace the path followed by a point on the pinwheel as it spins and you turn, you would get one of the many curves drawn by SpiroChart. The wheel may spin in the plane of the chart (as a level turntable) or it may be rotated 90 degrees to face the direction of motion. The orientation of the wheel may be further changed so that it is spinning at an arbitrary angle out from the rod axis.
Paying for SpiroChart
The original idea for SpiroChart came while I was volunteering in South America as a teacher of high school mathematics. To obtain financial support for continuing my service overseas, I am making this edition of SpiroChart available to you as CharityWare. If you enjoy using SpiroChart, you are invited to show your appreciation by sending a tax-deductible contribution of $15 or more to Engineering Ministries International (EMI). Your donation will support my personal involvement in the design of water supply and sanitation systems, shelters, clinics and schools in underdeveloped and developing countries. (This year, for example, I travelled to Central America to help design a multi-purpose building to serve children scavenging off a municipal garbage dump. The building will include a clinic, a kitchen and feeding area, and a few small classrooms.)
You may send your contribution to
Engineering Ministries International
110 South Weber
Colorado Springs, CO 80903
Please indicate that these funds are intended specifically for the support of Paul Koch. All moneys received in this way will be used only for essential travel expenses.
Your generosity today will result in facilities serving the underprivileged for many years to come! Thank you!
Paul Koch
P.O. Box 4256
Lincoln, NE 68504
USA
P.S. SpiroChart is also provided under the category of GratuityWare. As an alternative to making a donation EMI, you may send a gratuity in any amount or currency to my regular mailing address.
Legal Considerations
In regard to the development of SpiroChart, I claim any rights to which I am entitled, including all portions which I may legally copyright. SpiroChart may be distributed freely, but it may not be included with or used to develop any products for sale (whether commercial or not-for-profit) without written permission from the author.
Version History
2.0. Consolidated most of the previous four spreadsheets into one. Added third dimension to calculations. Added charts which showed wheel orientation and profiles of the figure from two directions.
1.6. Four different spreadsheets with somewhat different capabilities.
1.0. One spreadsheet implementing a simple polar equation.
