Math 5270 Transformational Geometryemina/teaching/5270s13/5270_Day5_notes.pdf · Day 5, Summer 13...
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Math 5270 Transformational Geometry Day 5 Summer 13 Day 5, Summer 13 Math 5270 Transformational Geometry 1/19
Transcript of Math 5270 Transformational Geometryemina/teaching/5270s13/5270_Day5_notes.pdf · Day 5, Summer 13...
Math 5270Transformational Geometry
Day 5
Summer 13
Day 5, Summer 13 Math 5270 Transformational Geometry 1/19
Composition of rotations
Composing rotations about the same point yields a rotation.
Such rotations commute.
Composing rotations about different points yield a rotation...
Day 5, Summer 13 Math 5270 Transformational Geometry 2/19
Composition of rotations
Composing rotations about the same point yields a rotation.
Such rotations commute.
Composing rotations about different points yield a rotation...
Day 5, Summer 13 Math 5270 Transformational Geometry 2/19
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Use your geogebra to
Make an angle slider for angle α between 0◦ and 360◦
In input bar write β = 360◦ − α
Pick any two points A and B and observe the composition of
rotation about A by α, followed by rotation about B by β.
Day 5, Summer 13 Math 5270 Transformational Geometry 3/19
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Group of rotations R?
Day 5, Summer 13 Math 5270 Transformational Geometry 4/19
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Equation for the rotation not around the origin?
Day 5, Summer 13 Math 5270 Transformational Geometry 5/19
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Alternative?
Day 5, Summer 13 Math 5270 Transformational Geometry 6/19
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How can we tell two isometries are the same?
Day 5, Summer 13 Math 5270 Transformational Geometry 7/19
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Reflections
Definition
wthout coordinates
with coordinates
Hmm... I think I might need more space...
Day 5, Summer 13 Math 5270 Transformational Geometry 8/19
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Reflections
Definition
wthout coordinates
with coordinates
Hmm... I think I might need more space...
Day 5, Summer 13 Math 5270 Transformational Geometry 8/19
Equation for a reflection
Day 5, Summer 13 Math 5270 Transformational Geometry 9/19
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Equation for a reflection, take 2
Any super easy reflections you know?
Day 5, Summer 13 Math 5270 Transformational Geometry 10/19
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Fixed points, fixed sets?
Day 5, Summer 13 Math 5270 Transformational Geometry 11/19
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What happens when you compose two reflections?
Use your geogebra to observe what happens when you compose
different reflections.
Why did I say different?
Day 5, Summer 13 Math 5270 Transformational Geometry 12/19
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Day 5, Summer 13 Math 5270 Transformational Geometry 13/19
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Day 5, Summer 13 Math 5270 Transformational Geometry 14/19
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Group of reflections?
Day 5, Summer 13 Math 5270 Transformational Geometry 15/19
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Every isometry is a composition of reflections!
Day 5, Summer 13 Math 5270 Transformational Geometry 16/19
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Some of students’ work
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Congruence...
CCSS.Math.Content.HSG-CO.B.7 Use the definition of
congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
Day 5, Summer 13 Math 5270 Transformational Geometry 18/19
Congruence...
CCSS.Math.Content.HSG-CO.B.7 Use the definition of
congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
Day 5, Summer 13 Math 5270 Transformational Geometry 18/19
Day 5, Summer 13 Math 5270 Transformational Geometry 19/19
![Radiometry and Reflectance: From Terminology Concepts to ...docs.fct.unesp.br/docentes/carto/enner/PPGCC...[18:16 27/2/2009 5270-Warner-Ch15.tex] Paper Size: a4 paper Job No: 5270](https://static.fdocuments.in/doc/165x107/607434d9c04595405c48cb35/radiometry-and-reiectance-from-terminology-concepts-to-docsfctunespbrdocentescartoennerppgcc.jpg)
