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Tag Archives: triangle
Spectral Golden Spiral II
Image
3 April 2016
Tagged geometry, Golden, Mathematics, rainbow, ratio, spectral, spectrum, spiral, triangle
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Polygons Related to the Golden Ratio, and Associated Figures in Geometry, Part 1: Triangles
There are two isosceles triangles which are related to the golden ratio, [1 + sqrt(5)]/2, and I used to refer to them as the “golden acute isosceles triangle” and the “golden obtuse isosceles triangle,” before I found out these triangles … Continue reading
On Triangle Congruence, and Why SSA Does Not Work
Those who have taught geometry, when teaching triangle congruence, go through a familiar pattern. SSS (sidesideside) triangle congruence is usually taught first, as a postulate, or axiom — a statement so obvious that it requires no proof (although demonstrations certainly … Continue reading
Posted in Education, Mathematics
Tagged angle side side, congruence, congruent, conjecture, counterexample, disproof, Education, geometry, HL, Mathematics, proof, right triangle, school, side side angle, SSA, theorem, triangle
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A Polyhedral Demonstration of the Fact That Twenty Times Four Is Eighty
The Platonic solid known as the icosahedron has twenty triangular faces. This polyhedron resembles the icosahedron, but with each of the icosahedron’s triangles replaced by a panel of four faces: three isosceles trapezoids surrounding a central triangle. Since (20)(4) = … Continue reading
Posted in Mathematics
Tagged eighty, four, geometry, icosahedron, Mathematics, multiplication, polyhedra, polyhedron, trapezoid, triangle, twenty
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The 98190 Triangle
In a previous post (right here), I explained the 187290 triangle, derived from the regular pentagon. It looks like this: I’m now going to attempt derivation of another “extraspecial right triangle” by applying halfangle trigonometric identities to the 18º angle. After … Continue reading
Posted in Mathematics
Tagged 98190, geometry, Mathematics, right triangle, special right triangle, triangle, trigonometry
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A Comparison of the Areas of Some of the Triangles Formed By Connecting Three Noncollinear Triangle Centers
The five most wellknown triangle centers are the centroid (where a triangle’s medians meet), the orthocenter (where the lines containing the altitudes meet), the incenter (where a triangle’s three interior angle bisectors meet), the circumcenter (where the perpendicular bisectors of … Continue reading
Posted in Mathematics
Tagged 9point, area, center, centroid, circle, circumcenter, Euler line, geometry, incenter, Mathematics, ninepoint, orthocenter, triangle
2 Comments