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Math 145 Essay: The Platonic Solids and Infinity, Papers of Mathematics for Liberal Arts

San Mateo County Community College District OfficeMathematics for Liberal Arts

Two essay topics for math 145 students. The first topic is about the platonic solids, where students are required to define and name them, explain how they were determined to be the only regular solids, and discuss the concept of duality and its relation to the number of faces and vertices. The second topic is about the concept of infinity, where students must write a letter to a skeptical friend explaining the different sizes of infinity, defining cardinality, one-to-one relationship, and discussing the diagonalization method. Intended for university students and is in the form of a study guide or essay prompt.

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Pre 2010

Uploaded on 08/16/2009

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Math 145 (revised 12/2006)
2nd Out of Class Essay
3 to 5 pages, typed, double spaced with a page of explanatory illustrations either
spread through the text or as a separate sheet. Title your illustrations so that it is
easy to know which one you are referring to in the text of your paper. Use MLA
style citations.
Choose one of the two following essays:
o The Platonic Solids
Define and name the Platonic Solids
Explain how the video determined that there were not any more
Platonic Solids.
Explain how the Euler Characteristic Theorem verifies that there
are not any more Platonic Solids.
Explain the concept of duality of Platonic Solids and how it is
related to the number of faces and the number of vertices.
o Multiple Infinities
Write a letter convincing a skeptical friend that infinity does
indeed come in different sizes. Convince him/her that there are
indeed more real numbers than natural numbers. Furthermore,
convince him/her that there are sets larger than the set of real
numbers.
With in your letter use good mathematical vocabulary, define the
ideas of cardinality, one-to-one relationship, diagonalization
method (Cantor) and discuss at least different three sizes of
infinity.

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Math 145 (revised 12/2006) 2 nd^ Out of Class Essay ƒ 3 to 5 pages, typed, double spaced with a page of explanatory illustrations either spread through the text or as a separate sheet. Title your illustrations so that it is easy to know which one you are referring to in the text of your paper. Use MLA style citations. ƒ Choose one of the two following essays: o The Platonic Solids ƒ Define and name the Platonic Solids ƒ Explain how the video determined that there were not any more Platonic Solids. ƒ Explain how the Euler Characteristic Theorem verifies that there are not any more Platonic Solids. ƒ Explain the concept of duality of Platonic Solids and how it is related to the number of faces and the number of vertices. o Multiple Infinities ƒ Write a letter convincing a skeptical friend that infinity does indeed come in different sizes. Convince him/her that there are indeed more real numbers than natural numbers. Furthermore, convince him/her that there are sets larger than the set of real numbers. ƒ With in your letter use good mathematical vocabulary, define the ideas of cardinality, one-to-one relationship, diagonalization method (Cantor) and discuss at least different three sizes of infinity.