Download MA 125: Introduction to Geometry: Quickie 1. (1) How many (non

MA 125: Introduction to Geometry: Quickie 1.
(1) How many (non-coplanar) points in R3 uniquely describe a
sphere?
(2) Given 4 non-collinear points in the plane, can we always find an
ellipse which goes through all four points? What do you think?
(3) For which angles θ is the map RO,θ the identity map?
(4) Can the reflection map be described as the composition of rotation maps?
(5) Show that translation by the vector (0, 2) can be described as
composition of two reflections.
(6) Can translation by the vector (0, 2) be described as the composition of exactly three reflections?
(7) Let f be an isometry. Show that f is injective. Is f also surjective?
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