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Math 3379 Paper 1
A discussion of the similarities and differences between MacLane’s axioms
(attached) and the SMSG axioms (in the Notes).
In this paper you are expected to compare and contrast these two systems of
axioms.
They are both designed for high school students – any student taking
geometry, not just gifted and talented.
They are both designed to create Euclidean
geometry.
The paper should be 700 words (
25 words).
Captions do not count nor do
citations count in the word count.
14 point type and double spaced, please.
Some ideas to discuss are:
Where do Euclid’s postulates show up in both of the systems?
Which postulate(s)
do not show up?
How is the Axiom of Continuity in MacLane’s Axioms logically equivalent to the
SMSG Plane Separation axiom in SMSG?
Write a definition of half plane and
discuss Plane Separation explicitly.
Attempt to prove the Plane Separation Axiom
from SMSG using MacLane’s axioms.
It is a theorem in MacLane’s system.
Just
a sketch or some ideas would do.
Include a sketch of the setup for The Continuity
Axioms.
What possible benefits do having negative angles create and how does having them
simplify the wording of axioms in MacLane’s list? Look at A2 in MacLane’s; are
there cases to consider about which ray is in the middle?
Discuss the measurement of angle rr, for a given ray r.
Discuss why
The measure of angle rs is the negative of the measure of angle sr.

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