Geometrical Classics

About Basic

Some of my Web files are BASIC programs written in either GW-BASIC or QuickBASIC. To run them, you will need to download them to your own disk, then load BASIC and run the program. If you're not familiar with BASIC this will show you how to access BASIC and run the programs.

Program names that end in G are GW-BASIC. They will also run in QuickBASIC. Program names that end in Q are QuickBASIC. These are newer versions and will NOT run in GW-BASIC

All these programs employ low resolution color graphics. Any monitor with graphics capability will display them.

If you wish to modify the programs (for example, upgrade to higher-level graphics) you are advised to consult a BASIC language reference.

You can copy, use and modify the programs freely provided you do not remove the author credit.

Carlyle Circles:

A nifty geometrical construction for solving quadratic equations.
Access program carlyleq.bas QuickBASIC Version 1.0 14 Jan 1997

Classic Curves

Envelopes:

Families of lines and circles that outline much more complex curves. Example: draw a line and a point not on the line. Now draw a line from the point to the line, and a second line at right angles to the first. Do this repeatedly. The lines will outline a parabola, and the point is the focus of the parabola.

Morley Triangle:

Trisect the angles of a triangle. Join the intersections of the trisectors. The result is an equilateral triangle regardless of the shape of the initial triangle!

Steiner Chains:

Draw two circles, one within the other. They need not be concentric. If you draw a chain of circles tangent to the outer and inner circles, each touching their neighbors, in almost all cases the chain will not close. The last circle will not fit exactly. But, if you can construct a chain that closes, it will close regardless of where the first circle is located.

You can find the parameters for the circles the hard way, by brute force. Using a technique called inversion geometry, the problem becomes fairly simple.

The Deltoid

The deltoid is a three-cusped curve that is generated by a point on the circumference of a circle of radius r rolling along the inside of a circle of radius 3r. It is therefore a hypocycloid, and can be generated using one of the envelopes programs. But it also can be generated in a surprising way that this program displays. Like Morley's Triangle, it is a surprising way of getting regular three-fold symmetry from an asymmetrical triangle. It should come as no surprise that there is a connection to Morley's Triangle.

All about Triangles

The altitudes, angle bisectors, medians, edge bisectors, and a lot of other lines of triangles all intersect at common points. A hundred years ago there was a whole separate branch of geometry called Triangulation Geometry, devoted to ferreting out progressively more subtle properties of triangles. This vein eventually played out (although fascinating, triangles are finite and pretty simple, at that). This program displays some of the interesting properties of triangles.

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Last Update 1/6/1997