This article provides a summary of the topics covered in the GVSU course Nature of Modern Mathematics. Please make sure to respect the ownership other people's material. This includes the syllabus to the course. Do not simply copy it to this article or upload it without their permission. Please make sure to read the writing guidelines.

Overview of the CourseEdit

The text used for this course is Journey Through Genius by William Dunham. [1]

Summary of TextbookEdit

Hippocrates' Quadrature of the LuneEdit

Key PeopleEdit

Key TermsEdit

Great TheoremsEdit

All of the great theorems in the main textbook used for this course.

The Quadrature of the LuneEdit

Hippocrates argument rested upon three preliminary results:

  • The Pythagorean theorem
  • An angle inscribed in a semicircle is right.
  • The areas of two circles or semicircles are to each other as the squares on their diameters.

\[\frac{\text{Area (semicircle 1)}}{\text{Area (semicircle 2)}}=\frac{d^2}{D^2}\]


15,000-10,000 BCEdit

  • Agricultural Revolution

2,000 BCEdit



  1. Journey Through Genius