GEOSKETCH+PAD+&+the+Flange+Point





I was messing around with sketchpad, trying to find a new point of concurrency for any triangle. I call it the flange point. See if you can figure out how it is made. I will cut and paste a copy here, but USM students, you can go to the K drive under flange for the actual sketchpad document. Pips to first to discover its secret, and more for comparisons and properties of the flange point.

Here is what Ishaan came up with, but it is NOT the final solution. He (or anyone) can still earn the pip by coming up with how the radii of the circles in step 2 are defined. I did give Ishaan pips for his ideas on the properties Construction of the Flange Point On Sketchpad Step 1: Given 3 points A, B, and C Step 2: Make 3 circles with origins at A, B, and C. Each circle must overlap with two other circles. Step 3: Make points where these circles intersect each other. Step 4: Draw lines between these points. Step 5: The Flange point is the point at which these lines intersect. Ishaan, you may want to clarify what you mean by the conceptual flange point. I think it is too broad. Conceptual Flange Point Step one: Given 3 points A, B, and C. Step two: Think of three lines that are perpendicular to AB, BC, and AC, AND intersect with each other. Step three: The point at which these lines intersect is the Flange point. Interesting Properties: In an equilateral triangle, the Flange point will be at the point where the angle bisectors intersect.

In an isosceles triangle, If two sides are longer than the third, the Flange point will be inside the Triangle. In this isosceles triangle, The longer the long two sides are compared to the third short side, the closer the Flange point gets to the point where they intersect (the origin of the most acute angle) but never reaches it. In an isosceles triangle, if the two sides are shorter than the third, the Flange point will be outside the triangle If the length of these two sides add up to the third (meaning the triangle has become a line) the Flange point goes infinitely far away.

If we imagine three boxlike structures extending to infinity that share one edge with each of sides of the triangle, you find that the Flange point must remain within these boxes. Ishaan