Euclidean & Non-Euclidean Geometries Part 4: Axioms

I bought twelve new markers thinking that I would use each of them for one video, and throw it away, so that I would always be writing with a nice, clear, legible black marker. So much for thinking. I may try chalk and a board next.

For a list of the undefined terms, see Part 3.

The following representations of axioms (or postulates) and definitions are flawed because typographical limitations prevent them from being displayed in a manner that mathematicians would approve. Suggestions welcome.

EUCLID'S POSTULATE I. For every point P and for every point Q not equal to P there exists a unique line m that passes through P and Q.

DEFINITION. Given two points A and B. The segment AB is the set whose members are the points A and B and all points that lie on the line AB and are between A and B. The two given points A and B are called the endpoints of the segment AB.

EUCLID'S POSTULATE II. For every segment AB and for every segment CD there exists a unique point E such that B is between A and E and segment CD is congruent to segment BE. ("Any segment AB can be extended by a segment BE congruent to a given segment CD.")

DEFINITION. Given two points O and A. The set of all points P such that segment OP is congruent to segment OA is called a circle with O as center, and each of the segments OP is called a radius of the circle.

Continued in Part 5.

Category:

Howto & Style

Tags:

• Geometry
• logic
• axiom
• postulate
• definition

[azzuwan78]

Great job!

Thank you for taking time to do this series.

[ashboxtoo]

Nice Circle

Thanks for this series :)