I am glad you liked it, Zomis.
Those pages can be found at
www.jimloy.com , just as stated in the program info (I should have publicized better the "TAB - Program information" button
).
Well, in the way they are shown in that program, they are just a delight for the eye - for those eyes who like maths and alike - but just like any math, the nicest part is that all of them have some useful aspect. For example, the Fermat's point is the point where the sum of distances towards the three corners is minimal.
In practice, it represents the best point to connect three towns (or three houses, as well) using the minimum amount of material - electricity wires, telephony cables, water pipes and so forth.
If someone plans to use that information, I'll say here that the point can be found building two equilaterals on two sides of the triangle (they have to be built towards the outside) - the Fermat's point is the intersection between the two lines connecting the fartest corners of these equilaterals to the relative corners on the opposite side of the given triangle - just like shown in my program. It is not necessary to calculate the third equilateral - the resulting line will pass through the Fermat's point in any case.
I'll add also that if the given triangle is
not acute - that is, if there is an obtuse angle at one corner - then the best point is not the Fermat's point, but the point on the corner with the obtuse angle.
[edit: wrong, the point is valid even for an obtuse triangle, as long as the obtuse angle is not wider than 120°, see Jannik's note below - at least it wasn't my fault ]
To make the program a bit more useful, I could allow the user to specify and see the coordinates of the three points of the triangle, as well as the coordinates and the sizes of the various entities shown in the program, but once again, the biggest problem is realizing such things with C++ and put them on the screen in a good way - now I can perfectly understand the hassle when it comes to widgets, coordinates and so on... it isn't that hard, but it's extremely boring...
