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Constructing the Applet from Scratch (For Developers)

Autor:Serkan Ozel
This code creates a "snapping" effect that helps users easily construct a perfect equilateral triangle. In simple terms, the code says: "If the user drags the vertex A very close to a pre-calculated perfect spot (A_1 or A_2), then automatically move A to that exact spot."

How It Works

This script runs continuously in the OnUpdate tab for point A, meaning it checks the condition every time A is moved.
  1. The Target Points (A_1 and A_2): Before writing this script, the developer would have created two hidden points, A_1 and A_2. These points represent the two mathematically perfect locations where vertex A would form an equilateral triangle with the other two vertices (let's call them B and C).
  2. The Snapping Zone: The Distance(A, A_1) < 0.2 part creates an invisible "snapping zone" or radius around the target point A_1. The number 0.2 is the threshold; you can make it larger for a more accurate snap or smaller for greater precision.
  3. The Action:
    • If(Distance(A, A_1) < 0.2, SetValue(A, A_1)): This line checks if the draggable point A has entered the snapping zone around the first target point A_1. If it has, the SetValue(A, A_1) command is executed, which instantly moves A to the exact coordinates of A_1, creating a perfect equilateral triangle.
    • The second line does the exact same thing for the other possible target point, A_2.
An analogy is to think of the perfect spots A_1 and A_2 as having small, invisible magnets. When you drag the vertex A close enough, it gets pulled in and locks perfectly into place.

How to Construct the Perfect Spots (A_1 and A_2)

There are a few ways to create these hidden target points. The most classic method uses intersecting circles:
  1. First Circle: Select the Circle tool. Create a circle with its center at point B and its radius extending to point C. This ensures every point on this circle is the correct distance from B.
  2. Second Circle: Create another circle with its center at point C and its radius extending to point B.
  3. Find the Intersections: The two points where these circles intersect (A_1 and A_2) are the only two locations in the plane that are the correct distance from both B and C to form an equilateral triangle.
Your idea of using a perpendicular bisector is a great start because it correctly identifies the line of symmetry for an isosceles triangle. To adapt it for an equilateral triangle, the height must be precise. The height of an equilateral triangle with side length s is (s  √3) / 2. So, you would construct a circle on the perpendicular bisector with a radius of (length of base * √3) / 2 to find the perfect spots. The two-circle method is often simpler to construct in GeoGebra.

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