1. Mathematical Contributions from Across the Globe
Math 105 Term Project
By: Alexandra Reynoso, Ho-Sung Kang, Lilia Jimenez, and Samantha Abbott

2. Thesis
The mathematical contributions of Mesoamerica, Ancient Egypt, the Islamic Empire, and Ancient Greece has added to the global understanding of mathematics as a whole.

3. Mesoamerica and South America

4. Mayan and Inca Number Systems
Inca method of tying knots

5. Mesoamerica: Mathematics Uses in Daily Life
Math was used as an important way to structure life
Was key to the Mesoamericans' sophisticated knowledge of astronomy
Was needed both for calculating the movements of celestial bodies and for using the calendric counting systems, which were themselves inextricably tied to religion
Numbers important in religious and spiritual practices
Page 13 of Codex Borbonicus

6. Ancient Egypt Much of Ancient Egyptian mathematics was practical
Mathematical achievement known through papyri
Mathematics usually applied:
Bookkeeping and administration
Architecture (pyramids)
365 day calendar

7. Ancient Egypt: Counting Hieroglyphs
= = = = =104
= = =107
3105 = 3*(1000) =

8. Ancient Egypt: Mathematics in Construction
Geometry was utilized in construction
circumference and surface area (Rhind papyrus and Moscow papyrus)
Pyramid construction: evidence of rectangular coordinates

9. Islam
Ranged from Persia, the Middle East, parts of India, Central Asia, Iberia, and North Africa
Exposure and synthesis of mathematical developments from India and Greece
Introduction of fundamental algebraic methods
Esfahan’s Friday Mosque

10. The mihrab of Madrasa Imami
Math in Islamic Art
The prohibition of depicting human forms in art lead to the use of geometric figures in architecture.
They used what is now referred to as quasicrystalline geometry
Symmetrical polygonal shapes
Can extend indefinitely
6 sided star polygon pattern
The mihrab of Madrasa Imami
Located in Iran

11. Islam and Algebra Baghdad mathematician Muḥammad ibn Mūsā al-Khwārizmī
Wrote Algebra et Almucabal (825 CE)
He verbally wrote out the solutions for each problems
Included some of Euclid’s geometric concepts
Solved these six equations in the first part of his work:
ax2 = bx, ax2 = c, bx = c, ax2 + bx = c,
ax2 + c = bx, and bx + c = ax2

12. Ancient Greece
As the Greek empire began to extend its realm of influence into Asia Minor, Mesopotamia, and further, the Greeks astutely adopted and adapted useful elements from the societies they subjugated
The ancient Greek numeral system, known as Attic or Herodianic numerals, was completely developed by about 450 BC and in customary use
possibly as early as the 7th
Century BC

13. Ancient Greece: Geometry and the Concept of Proof
Most of Greek mathematics was predicated on
geometry. The 6th Century BC mathematician
Thales is generally considered to have been the
first to set guidelines for the abstract
development of geometry.
The most significant single contribution of the Greeks was perhaps the concept of proof, and the deductive method of using logical steps to prove or disprove theorems from initially assumed axioms

14. Ancient Greece: Pythagoras
The 6th Century BC mathematician Pythagoras has become identified with the advent of Greek mathematics
The central proverb of Pythagoras's school was “all is
number” or “God is number,” and the Pythagoreans
effectively practiced a type of numerology or
number-worship, regarding each number to have its
own character and meaning
Pythagoras is primarily recognized for what has
become known as the Pythagorean Theorem, which maintains that for any right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the square of the other two sides (a2 + b2 = c2)

15. Bibliography
Al-Hassani, Salim. "New Discoveries in the Islamic Complex of Mathematics, Architecture and Art." New Discoveries in the Islamic Complex of Mathematics, Architecture and Art. 1 Jan Web. 2 Apr <
Dacey, James. "Ancient Islamic Architects Created Perfect Quasicrystals." Ancient Islamic Architects Created Perfect Quasicrystals. Physicsworld.com, 31 Jan Web. 16 Apr <
Evans, Brian. Development of Mathematics Throughout the Centuries : A Brief History in a Cultural Context. Somerset, NJ, USA: Wiley, ProQuest ebrary. Web. 27 April 2015.
“Greek Mathematics.” The Story of Mathematics. Luke Mastin, Web. 17 April
2015.
“Greek Mathematics- Pythagoras.” The Story of Mathematics. Luke Mastin, 2010.
Web. 17 April 2015.
Hosch, William L. "Islamic Contributions." The Britannica Guide to Algebra and Trigonometry. New York, NY: Britannica Educational Pub. in Association with Rosen Educational Services, Print.
"Islamic Mathematics." The Story of Mathematics. Web. 2 Apr <
Lumpkin, Beatrice. "Mathematics Used in Egyptian Construction and Bookkeeping." Mathematical Intelligencer 24.2 (2002): Academic Search Elite [EBSCO]. Web. 18 Apr
Scott, Williams W. "The Mathematics of Ancient Egypt." Department of Mathematics, University at Buffalo. University at Buffalo, Web. 20 Apr