Chapter 2: An ancient theorem and a modern question: Difference between revisions
Chapter 2: An ancient theorem and a modern question (edit)
Revision as of 22:18, 16 May 2020
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==== Euclidian Postulates ==== | ==== Euclidian Postulates ==== | ||
# A straight line segment can be drawn joining any two points | # A straight line segment can be drawn joining any two points. | ||
# Any straight line segment can be extended indefinitely in a straight line. | # Any straight line segment can be extended indefinitely in a straight line. | ||
# Given any straight line segment, a circle can be drawn having that segment as its radius | # Given any straight line segment, a circle can be drawn having that segment as its radius. | ||
# All right angles are congruent. | # All right angles are congruent. | ||
# If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate. | # If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate. | ||