Jessica Weydert

Jessie Joachim

12/12/12

450º Cone

Definition of a Straight Line: A straight line possesses reflection symmetry across itself and half-turn symmetry.

Postulates:

1. To draw a straight line from any point to any point.

Postulate 1 is false because it does not follow our definition of a straight line. We started off by drawing random points on the cone to determine which points we can or cannot connect to create a straight line based off our definition. We noticed that the point that effects our definition is either at the cone point, or a line going through the cone point. It has reflection symmetry across itself and sometimes half-turn symmetry. When looking at a line going through the cone point, you need to look at the whole line for half-turn symmetry. If the line goes through the cone point and has half turn symmetry, then the line is straight. If the line goes through the cone point but does not have half-turn symmetry, the line is not straight. Therefore, you cannot draw a straight line from any point to any point on a 450º cone. 2. To produce a finite straight line continuously in a straight line.

True because the 450º cone is infinite; therefore, any straight line will be continuous. 3. To describe a circle with any center and distance. “A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another,” (Book I of Euclid’s Elements). Postulate 3 is false because the cone point cannot be a center point of a circle. With this case, we are not able to draw straight lines from any point on the circle to any other point. Lines intersecting the cone point are not straight, so the shape is not a circle. 4. That all right angles are equal to one another.

Postulate 4 is false because there are two different types of right angles on a 450º cone. These angles include 90º and 112.5º. When two lines