week 07 notes

8/9/2019 Week 07 Notes

1/22

SME430 History of Mathematics

Week 7 - 3 Dimensional Geometry


2/22

Itinerary

Announcements

Biographies

timeline

Discussions

Activity

Mathematics Lessons


3/22

Announcements

Grades are in the

process of being

updated.


4/22

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


5/22

Biographies

Apollonius of Perga, Eudoxus of Cnidus, Plato, Hypatia of Alexandria


6/22

Timeline


7/22

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.


8/22

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)?


9/22

Real World Examples

Equiangular

Spiral

. .

..

.

.

.

.

.

- -


10/22

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?


11/22

Archimedean Solids


12/22

Activity

PID Sorting

A36284480-A38556458

Sphere

A38654380-A42384979

Origami


13/22

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


14/22

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


15/22


16/22

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.


17/22

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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