Question

prove that the product of a rotation and a translation is a rotation

Euclidean Geometry and Transformatons

Answer #1

Write an essay comparing Euclidean Geometry with
Hyperbolic Geometry?

NON EUCLIDEAN GEOMETRY
Prove the following:
Claim: Let AD the altitude of a triangle
▵ABC. If BC is longer than or equal to AB and AC, then
D is the interior of BC.
What happens if BC is not the longest side? Is D still always in
the interior of BC? When is D in the interior?

Use postulates (axioms) to explain how Projective geometry
differs from Euclidean geometry

(Euclidean and Non Euclidean geometry)
Consider the following statements:
Given a line l and a point P not on the line:
There exists at least one line through P which is
perpendicular to l.
There exists at most one line through P which is
perpendicular to l.
There exists exactly one line through P which is
perpendicular to l.
Prove each statement or give a
counter-example E2 (Euclidean Plane), H2 ,
(Hyperbolic Plane)and the sphere S2 (Spherical
Plane)
( Consider...

EUCLIDEAN GEOMETRY
Let □ABCD be a quadrilateral on a surface satisfying the five
axioms.
Assume that m∠ABC = m∠BCD = 90, and that the rays BA and CD are on
the same side of the line BC.
Prove that if If m∠CDA = m∠DAB, then mAB = mCD. (Hint: This
proof is very similar to angle side inequality , replace isoscles
triangles with khyyam quadilateral )

What methodological techniques inherited from Euclidean geometry
had to be ignored in order to apply algebra to geometry?

what role did the fifth postulate play in the development of
non-Euclidean Geometry?

In topology, how do the intrinsic geometry differ among a
Euclidean plane, a flat torus, a Klein bottle, and a sphere?

The
conservation of energy for rolling object is: ΔK for translation
+ΔK for rotation +ΔU for gravity, why it is not 2ΔU ??
Because we add rotation and translation laws

how to prove the Uniqueness of factorization in Euclidean
domains

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