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

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.

Mesoamerica and South America

Mayan and Inca Number Systems Inca method of tying knots

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

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

Ancient Egypt: Counting Hieroglyphs = 1 = 10 =100 =1000 =104 = 105 =106 =107 3105 = 3*(1000)+100+5 =

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

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

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

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

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

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

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)

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. 2007. Web. 2 Apr. 2015. <http://www.muslimheritage.com/article/new-discoveries-islamic-complex-mathematics-architecture-and-art>. Dacey, James. "Ancient Islamic Architects Created Perfect Quasicrystals." Ancient Islamic Architects Created Perfect Quasicrystals. Physicsworld.com, 31 Jan. 2012. Web. 16 Apr. 2015. <http://physicsworld.com/cws/article/news/2012/jan/31/ancient-islamic-architects-created-perfect-quasicrystals>. Evans, Brian. Development of Mathematics Throughout the Centuries : A Brief History in a Cultural Context. Somerset, NJ, USA: Wiley, 2014. ProQuest ebrary. Web. 27 April 2015. “Greek Mathematics.” The Story of Mathematics. Luke Mastin, 2010. 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, 2011. 32-35. Print. "Islamic Mathematics." The Story of Mathematics. Web. 2 Apr. 2015. <http://www.storyofmathematics.com/islamic.html>. Lumpkin, Beatrice. "Mathematics Used in Egyptian Construction and Bookkeeping." Mathematical Intelligencer 24.2 (2002): 20-26. Academic Search Elite [EBSCO]. Web. 18 Apr. 2015. Scott, Williams W. "The Mathematics of Ancient Egypt." Department of Mathematics, University at Buffalo. University at Buffalo, 2008. Web. 20 Apr. 2015.