Although this remarkable feature of KSEG is treated in the documentations by KSEG’s author, Ilya Baran, of MIT, it can be such an important feature that it deserves a section on its own.

Motivation

One of the chief problems of using figures in teaching geometry is that only rarely can the note-taker (you, the student!) figure out the order in which the details (parts) of a figure were added to produce the final result. Preparing videos is one possibility. But that is very demanding of resources, and has to be watched many times by the learner to follow the steps. An alternative is to "journal" the construction. Baran chose to do the latter. It is possible to see, and even edit, the recipe of a construction in its entirety. Highlighting a detail in the script locates the geometrical object it refers to in the figure, and vice versa. This feature has two immediate uses, one obvious, the other more subtle.

Konstructions

KSEG constructions are ordinarily saved as .seg files. It is, however possible to ask for a KSEG Construction (Menu KSEG → File → Copy as Construction) to be made from a .seg file under construction. The unfortunate technical use by Baran of the word "Construction" here can be ameliarated by referring to such files (with suffix .sec) as KSEG "konstructions." We will continue to call the product of KSEG a geometrical "construction", whether it is a .sec or .seg file, to distinguish it from a picture of a construction, such as a .png file.

thales3pts.png

Click on image to download the thales3pts.sec KSEG konstruction.

On the left you see three marked points $ A,B,C $ which might be the right vanishing point, the left vanishing point of a rectangle, and $ C $ the zenith of the horizon $ (AB) $. Equivalently, $ C $ would be the third vanishing point for a drawing in 3-point perspective. There is a Thales triangle above the horizon, and a 45 degree line (marked by the square), pointing to the 45 degree diagonal vanishing point.

This construction is actually quite time consuming if you have to do it three times to obtain the 3-point perspective frame. Here are all the construction lines in KSEG that have been hidden:

thales-unhidden.png

Construction lines hidden from view in the thales3pts.sec konstruction.

Extending the utility of KSEG

The subtle use of konstructions is to extend the KSEG language. As you build a konstruction from scratch, or copy a .seg file as a konstruction, points that were freely chosen are so labelled in the script. You can edit these lines (pull-down → Construction → Make Given) so that the entire konstruction can be applied to another construction with the "given" points as inputs.

To use the thales3pts.sec konstruction, for example, highlight three points in the new construction, in the correct order, and apply thales3pts.sec (pull-down → Play). You may have to change directories to where the .sec file is located before it shows up in the menu. The Thales triangle appears.