Cosmology – Construction Assignment 1 – Triangles

Due Wednesday, September 13.

You will need a compass, a straight-edge, and four sheets of paper for this assignment. When you use the compass to draw a circle, draw the entire circle. Also consult Schneider’s book if you have questions. Pages 22-3 and 43-9 will be particularly useful.

1. The Vesica Pisces – This is a very simple construction. Using a sheet of paper in a horizontal position (that is, the long part of the sheet at the bottom) draw a line about 3 inches long in the center of the page, parallel to the long edge of the paper. Then placing the point of the compass at one endpoint of the line and the pencil at the other endpoint draw a complete circle. Then draw another circle using the endpoints in the opposite order. The almond shaped piece inside both circles is called a Vesica Pisces.

2. The Equilateral Triangle – Repeat the construction in number 1. Then using the straight edge, connect the endpoints of the line with which you started to the point of intersection of the circles that lies above the line. The resulting triangle is an equilateral triangle. If you then connect the endpoints of the line with the bottom point of intersection of the circles, the figure that results is a rhombus, a parallelogram all of whose sides are of the same length.

3. The 30-60-90 Right Triangle - Repeat Construction 2 up to the point of producing the equilateral triangle. Draw a line through the upper intersection of the circles (call that point A) and the right endpoint of the beginning line. Continue this line until it intersects the right hand circle (call that point B). Draw a second line that connects the two points of intersection of the two circles. Call the bottom point of intersection C. Finally draw a line between points B and C. You have produced a 30-60-90 right triangle DABC.

4. The hexagon. – Complete the construction found on page 45 in Schneider. You will have then produced a hexagon in each of the two initial circles.