Some of my Web files are BASIC programs written in either GW-BASIC or QuickBASIC. Torun them, you will need to download them to your own disk, then load BASIC and run theprogram. If you're not familiar with BASIC this will show you howto access BASIC and run the programs.
Program names that end in G are GW-BASIC. They will also run in QuickBASIC. Programnames 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 graphicscapability will display them.
If you wish to modify the programs (for example, upgrade to higher-level graphics) youare advised to consult a BASIC language reference.
You can copy, use and modify the programs freely provided you do not remove theauthor credit.
A nifty geometrical construction for solving quadratic equations.
Access program carlyleq.bas QuickBASIC Version 1.0 14 Jan 1997
Families of lines and circles that outline much more complex curves. Example: draw aline and a point not on the line. Now draw a line from the point to the line, and a secondline at right angles to the first. Do this repeatedly. The lines will outline a parabola,and the point is the focus of the parabola.
Trisect the angles of a triangle. Join the intersections of the trisectors. The resultis an equilateral triangle regardless of the shape of the initial triangle!
Draw two circles, one within the other. They need not be concentric. If you draw achain of circles tangent to the outer and inner circles, each touching their neighbors, inalmost all cases the chain will not close. The last circle will not fit exactly. But, ifyou can construct a chain that closes, it will close regardless of where the first circleis located.
You can find the parameters for the circles the hard way, by brute force. Using atechnique called inversion geometry, the problem becomes fairly simple.
The deltoid is a three-cusped curve that is generated by a point on the circumferenceof a circle of radius r rolling along the inside of a circle of radius 3r. It is thereforea hypocycloid, and can be generated using one of the envelopes programs. But it also canbe generated in a surprising way that this program displays. Like Morley's Triangle, it isa surprising way of getting regular three-fold symmetry from an asymmetrical triangle. Itshould come as no surprise that there is a connection to Morley's Triangle.
The altitudes, angle bisectors, medians, edge bisectors, and a lot of other lines oftriangles all intersect at common points. A hundred years ago there was a whole separatebranch of geometry called Triangulation Geometry, devoted to ferreting out progressivelymore subtle properties of triangles. This vein eventually played out (althoughfascinating, triangles are finite and pretty simple, at that). This program displays someof the interesting properties of triangles.
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Last Update 1/6/1997