Gothic Arch Tangency Properties using SketchPad

Gothic Arches: SketchPad Files

These ideas came from me trying to find some none-trivial problems for applying Pythagoras' Theorem to. Some can be quite demanding algebraically and really do need some thought. Unfortunately, in the Gothic era, Master Masons who were responsible for such designs were not particularly forthcoming in sharing their knowledge with others and jealously guarded their ideas - often on pain of death!. Their construction techniques were also just that: constructions - with compass and straightedge. I have only been able to find such constructions for the most rudimentary arch types but if any historians/architects/etc. out there know of any resources then I would love to hear from you.

Notes:
(1). On opening any of these scripts enclosed in the above pages you may not actually see them! - What you may see instead is a blank Sketch File probably called "Sketch01.gsp". If you are unfamiliar with SketchPad all that you need to do is to click on the "Restore" Button in the top right of the active Sketch file Window Toolbar.
(2). All of these filenames in this page are LONG! - Therefore, if you want to preserve these (Because Version 3.* of SketchPad does not use long filenames) you must either RIGHT-CLICK on the file links within the above directories and then choose "Save Target As...". This allows you to save the file directly to a disk/drive or after using a LEFT-CLICK select the "Save this file to disk" Option Box rather than selecting the "Open this file from its current location". If you choose this last option then Geometer's SketchPad will automatically open - if you have it! - but then after viewing the file if you then try to save it you will not be able to use a long filename.

Scripts GSP Version3

D - Double Symmetrical Internal Variable Arch Script.gss
This script constructs the two congruent arches shown below from the two points A and B.

D - Quintic Internal Variable Arch - Independent Middle Arch.gss
This script constructs the five arches shown below from the two points A and B. The middle arch has a width and height independent from the other four that are congruent.

D - Single Variable Arch Script.gss
This script can be used as the outermost arch to any number of internal configurations.

D - Single Variable Arch with Two Crossing Internal Arches.gss
A different type of window in which the inner arches are similar and are varied independently to the outer arch.

D - Single Variable Arch with Two Separate Internal Arches.gss
A more traditional double arch window

D - Tangent Circle to any Arch and Two Inner Arches (All Arches Present).gss
For this script to draw the tangent Circle inside the typical double arch (see above) the double arch must first be present.

D - Tangent Circle to any Arch and Two Inner Arches (No Arches Present).gss
Same arch type as above but only two starting Points are needed.

D - Triple Internal Variable Arch - Independent Middle Arch.gss
This script constructs the three arches shown below from the two points A and B. The middle arch has a width and height independent from the other two that are congruent.

D - Triple Symmetrical Internal Variable Arch Script.gss
This script constructs the three congruent arches shown below from the two points A and B.

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For GSP Version 4 scripts click here. Then put the file "Arches Scripts.gsp into your GSP 4 "Tools Folder". All of the Gothic Arch Scripts will then be available from the same folder in the Tools dropdown menu whatever file is open.
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