The History of Mathematics Blog: https://historyofmathsblog.wordpress.com/ 247554: John Incoll

Mathematics Where it began, where I began Thinking back on my own time through schooling, I could not recall how, why and where mathematics began being used. Was it something pre-coded in our brains somehow? I never took it upon myself to learn the history of mathematics, till now. This presentation explores the history of Mathematics, the language of the universe. Callaway (2013)

Prehistoric Mathematics The oldest known mathematical tool is the Lebombo Bone, discovered in the Lebombo Mountains of Swaziland, Africa, dated approximately 35,000 BC. It consists of 29 notches cut into a baboon’s fibula, but this is mere counting and tallying rather than mathematics as such (Akshat, 2017). I would argue that regardless of the evidence our prehistoric ancestors would have had a general concept about amounts, and would have instinctively known the difference between one and two and many antelopes. Lebombo Bone Mastin (2010)

Mathematics Documentary | Decoding the Language of the Universe | History Films https://www.youtube.com/watch?v=zff3fhb-BGs History Films (2015)

Sumerian/Babylonian Mathematics Sumerians developed the earliest known writing system called cuneiform script, they used a wedge shaped object to inscribe on. The Sumerians and Babylonians needed to describe large numbers for the measurement of plots of land, they attempting to chart the course of the night sky thus developing the lunar calendar. They used small clay cones to represent one, a clay ball for ten, and a large cone for sixty. Over time they replaced the objects with cuneiform equivalents so they could have numbers written with the same object that they used for the words in the text (Mastin, 2010).

Egyptian Mathematics Egyptians introduced the first fully developed 10 numeration system as early (if not earlier) as 2700 BCE. The way their system worked was “a stroke for units, a heel-bone symbol for tens, a coil of rope for hundreds and a lotus plant for thousands, as well as other hieroglyphic symbols for higher powers of ten up to a million” (Mastin, 2010). The image on the bottom right shows an example of how the Egyptian mathematics used multiplication 3 by 6. Take the combination of blocks on the 1’s side which add up to 6 (2 + 4), and count up the corresponding blocks on the 3’s side (6 + 12), to give a total of 18 (Mastin, 2010)

Pythagoras Theorem Pythagoras is a well-known mathematician, most famous for his concept of geometry and is mainly remembered for what has become known as Pythagoras’ Theorem Pythagoras was the first to establish “the sum of the angles of a triangle is equal to two right angles and that for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides” – Famous People, 2017. Written as an equation: a2 + b2 = c2 and shown in the diagram on screen. the Pythagorean Theorem by our area factor and come up with a relationship for any shape. The actual line section itself can be any portion of the shape. You could choose the circle's radius, diameter, or circumference and it would give a different area, but the formula 3-4-5 would remain the same.

Medieval Mathematics - Fibonacci Fibonacci is best known for his number sequence, which is now known as Fibonacci Sequence. This is something I remember learning about in primary school, I believe I only learnt about it briefly (or maybe I can only briefly remember) but it is actually an interesting concept. The way the number sequence works is by adding the last two numbers you will be able to predict what you will get next, for instance: 1,1,2,3,5,8 or in mathematical terms: Fn = Fn-1 + Fn-2 (Mastin, 2010).

historical mathematics with culture After doing some extensive research and readings I have discovered the vast diversity in culture throughout the mathematical history, although the teachings have compiled from different cultures wherever you are, a triangle is still a triangle with angles which add up to 180 degrees all over the world (Bishop, 1988). The history of mathematics give students the opportunities to investigate different ancient cultures and societies. With this, the use of historical mathematic practices in a mathematics classroom gives students the ability to compare the different types of approaches to the same formula and/or algorithm made by different vast variety of cultures throughout the different time periods.

Applying in the Classroom The Ancient Egyptian numbers seems intriguing and could potentially be used in many different ways. Using the legend at the top of the worksheet, students will be able to work out the answers. Students could connect this algorithm to real life situations. As a cross-curriculum exercise, art could be incorporated into the lesson by students having to draw the answers as well as write them.

Further Question What are your thoughts on implementing cultural mathematics in the classroom? Can you see any benefit of incorporating the history of mathematics into the classroom? Discussion, do you think the Pythagorean Theorem worth implementing in the classroom?

References Akshat (2017). Prehistoric mathematics. Retrieved from http://akshat- historyofmaths.blogspot.com.au/2011/07/prehistoric-mathematics.html Azad, K (2008). Surprising Uses of the Pythagorean Theorem. Retrieved from https://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/ Bishop, A J (1988) Vol. 19, No. 2, Mathematics Education and Culture (May, 1988), pp. 179-191 Callaway, E (2013). Shocks to the brain improve mathematical ability. Retrieved from http://www.nature.com/news/shocks-to-the-brain-improve-mathematical-abilities-1.13012 History Films (2015). Mathematics Documentary | Decoding the Language of the Universe | History Films. Retrieved from https://www.youtube.com/watch?v=zff3fhb-BGs Mastin, L (2010). The Story of Mathematics. Retrieved from http://www.storyofmathematics.com/story.html The Famous People (2017). Pythagoras Bibliography. Retrieved from http://www.thefamouspeople.com/profiles/pythagoras-504.php