Saturday, April 28, 2012

Construction - Equilateral Triangle - I

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to


  1. "Reaching students out", hi hi! Very problem, San! And catching younger pupils even more (far as I experience it).

    Am proposing emote support to kids (for years now), and they, and no more their paents, match. Is is with the "e-tutoring" mode of work? Is it deeplier with work itself?

    Are you experiencing same atony among your boys and girls?

  2. By drawing two circles sharing the same radius you show an equilateral triangle, as in Euclid's first proposition. By connecting all four points to each other and extending the radius to the boundary of both circles you have created ten points that when connected to each other will form 14 equilateral triangles, four of which are inscribed equilateral triangles. This will allow students to see the interrelatedness and how all classification of triangles work together within the association of two circles.

  3. Sanjay, you have inadvertently drawn a hexagon. There is at least one other equilateral triangle, PQR, that satisfies the requirements. Now, what if the starting conditions are different? You are given the base of the triangle, not its centre.

  4. Your construction is one of the first drawings that a child experimenting with a pair of compasses is likely to make. How far can you take its meaning?
    (i) The three cube roots of unity in the complex plane.
    (ii) The 'Y' and 'Delta' of three-phase electricity in a phasor diagram.

  5. Aha, Sanjay. I see in your next example that you have constructed an equilateral triangle, given the base.