Base-Ten: Because we have ten fingers.

Spencer Olmsted
513 Central St NE
Olympia, WA 98506
(solmsted at yahoo)

2009-Current: 5th grade math and science teacher at Pioneer Elementary School in Olympia, Washington.

2006-2009: 5th grade teacher at L.P. Brown in Olympia.

Fall 2005: student taught in the 4th grade at Morning Star Elementary School in Bozeman, Montana.

Links place content further down the page.

Geometry

Field trip to the Tinsley House at the Museum of the Rockies

The circumscribed triangle is made from the diameter of the circle and two segments meeting on the circle.

The two smaller triangles inside are isosceles.
The sum of the angles in ABC is 2α + 2β = 180° so α + β = 90°
Angle B is a right angle.

Any trianlge circumscribed by a circle with one side being the diameter of the cirlce will be a right triangle.

The altitude of a right triangle is related to the two line segments it creates in the hypotenuse.

The circle, the right triangle, and Pythagoras.

Looking at the altitude of the large triangle, we can say: a² = (c+b)(c-b) = c²-b²
which means that

The circle, the right triangle, and the equilateral triangle.

A 30-60-90 degree triangle is half of an equilateral triangle.

The side opposite the 30° angle will be half of the hypotenuse. All 30-60-90 degree triangles are similar and thus share this relationship.

This also shows why the area of an equilateral triangle is √3/4 * a side length