week 07 notes
TRANSCRIPT
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SME430 History of Mathematics
Week 7 - 3 Dimensional Geometry
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Itinerary
Announcements
Biographies
timeline
Discussions
Activity
Mathematics Lessons
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Announcements
Grades are in the
process of being
updated.
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From Last Week
Colbert Report Clip on Poincar
Conjecture
http://www.colbertnation.com/the-colbert-
report-videos/73352/august-22-2006/
cheating-death---fields-medal
Geometry - The mathematics of the
properties, measurement, and relationships
of points, lines, angles, surfaces, and
solids.
topology - The study of the properties of
geometric figures or solids that are not
changed by homeomorphisms, such as
stretching or bending.
http://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medalhttp://www.colbertnation.com/the-colbert-report-videos/73352/august-22-2006/cheating-death---fields-medal -
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Biographies
Apollonius of Perga, Eudoxus of Cnidus, Plato, Hypatia of Alexandria
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Timeline
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Theodosius ~160bc-~90bc - S haerics, text on eometr of s here, for astronom
Zeno of Sidon (~150bc-~70bc) - Argued against Euclid and Elements
150 B.C. 100 B.C. 50 B.C.
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Discussion -
Coordinate GeometryWhat is the
mathematical
definition/description
of analytic geometry?
How has a coordinate
system been used
throughout history?
What new mathematics
became available
because of the use of
analytic geometry (and
the perpendicular y-
axis)?
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Real World Examples
Equiangular
Spiral
. .
..
.
.
.
.
.
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Discussion -
Platonic Solids
What are the names/
properties of thePlatonic Solids?
What associations did
the Pythagoreans make
with these solids?
What is the distinction
between Platonic
solids and Archimedean
Solids?
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Archimedean Solids
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Activity
PID Sorting
A36284480-A38556458
Sphere
A38654380-A42384979
Origami
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Lesson Planning
design a mathematics
lesson for a classroom
that incorporatesEgyptian, Babylonian,
or Greek Mathematical
History.
Prepare a 3 minute
presentation describing
Topic you plan to
integrate
Objectives of the
lesson
Brief Description of
your lesson
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homework
Read Sketches
#19 - Non-Euclidean Geometry (p. 153-158)
#20 - Projective Geometry (p. 159-162)
Discussion Forum (Already Posted)
Upload History of Mathematics in Education
Presentations to Dropbox in ANGEL
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Platonic Solids
What are the names/properties of the Platonic Solids?Tetrahedron (4 sides)
Dodecahedron (12 sides)
Icosahedron (20 sides)
Hexahedron (Cube) (6 sides)
Octahedron (8 sides)
All the faces are the same regular shapes. Every vertex has the same number of faces
meeting (number of edges as well).
The angles at each vertex must add to less than 360 degrees (or else itll be flat.)
Symmetry around each vertex.
At least three faces must meet at each vertex.
What associations did the Pythagoreans make with these solids?4 elements
Tetrahedron (4) -> Fire (looks like a triangle/four necessities for fire)
Hexahedron (6) -> Earth (belief earth was flat/set on a surface, wont roll/six major
land forms on Earth)
Octagedron (8) -> Air
Icosahedron (20) -> Water (most spherical, most likely to roll out of your hand)
Dodecahedron (12) -> Universe
What is the distinction between Platonic solids and Archimedean Solids?Archimedean solids have the same properties as Platonic solids, but the faces dont
all have to be the same one shape. Each type of shape has to be congruent to all of
the same shapes in the figure.
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Lesson Planning
Grade Level: 4th
grade
Topic: Egyptian Multiplication
Objective: Students will be able to show a deeper understanding of multiplication by
being able to complete problems using Egyptian multiplication and then use standard
algorithm to check their answers.
Description: After learning the basic algorithm for the multiplication students will work
together to solve in pairs Egyptian multiplication problems. They will be asked to check
to see if they got the right answers and then explain why their answer is correct.
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