The Ghostly Presence of Famous Mathematicians

Feda

Niyaz

Mathew

“Math Projects” Assignment

The Ghostly Presence of Famous Mathematicians

http://www.biographybase.com/biography/Al_Khwarizmi.html

http://www.muslimheritage.com/topics/default.cfm?ArticleID=631

Mohammed Ibn-Musa al-Khwarizmi was born around 780 and died around 850. Not much is known about his life. Yet, during the period of Islamic Dynasty in which Al-Khwarizmi lived, an academy was established in Baghdad that is called the House of Wisdom. In that academy, many scholars preserved most of the Greek mathematics and science that eventually led to the stimulation and reinforcement of learning in Europe.

Alkhwarizmi was one of these scholars. He was known as the Father of Algebra and as the mathematician who brought the concept of zero to the Western world

He founded the concept of the algorithm in mathematics and the word "algorithm" is an English translation of his name. He also made major contributions to the fields of algebra, trigonometry, astronomy, geography and cartography.

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He developed algebra in linear and quadratic equations. His most famous - Hisab al-jabr w'al-muqabala, which means "Science of the completion and the balancing”, is from which we got the name for algebra itself. The Al-jabr wa'l-muqabala began with a discussion of solving equations of first and second degree

The process takes place by using the two operations of al-jabr and al-muqabala.

Here "al-jabr" means "completion" and is the process of removing negative terms from an equation. For example, using one of al-Khwarizmi's own examples,

"al-jabr" transforms x² = 40 x - 4 x² into 5 x² = 40 x.

The term "al-muqabala" means "balancing" and is the process of reducing positive terms of the same power when they occur on both sides of an equation.

For example, "al-muqabala" reduces 50 + 3 x + x² = 29 + 10 x to 21 + x² = 7 x

As we see here, the term algebra is only one half of what this process should be called. It was supposed to be called algebra and almuqabala.

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Another intervention was introducing the Hindu-Arabic numerals ( 1, 2, 3, 4, 5, 6, 7, 8, 9) to medieval Europe. The Hindu-Arabic numerals and the place value of numbers were introduced in 500s AD. After around 20 years, Alkhwarizmi, wrote about it in his book but also included an explanation of the use of zero in the same meaning we use these days and which was still confusing to people at that point of history.

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He also used a geometric proof to solve the equation x² + 10 x + 39= 0 by completing the square. He begins with a square of side x, which therefore represents an area x² (Fig 1). To the square he adds 10x and this is done by adding to the four sides of the square four rectangles each of width 10/4 and length x (Fig 2). Fig 2 has area x² + 10 x but from the above equation that is equal to 39. To complete the outside big square he adds four little squares of area ⁵/₂ × ⁵/₂ = ²⁵/₄ each. As a result, the outside big square in Fig 3 has an area of 4 × ²⁵/₄ + 39 = 25 + 39 = 64. Which means that the side of the outside big square is equal to 8. But the same side is of length ⁵/₂ + x + ⁵/₂ so x + 5 = 8, and hence x = 3.

2) Strengths:

- This project is well designed for those students who enjoy the imaginative process of artistic creation. (S)

- It is also helpful for the students to get a historical perspective of mathematics. (S)

- It gives the students the opportunity to learn who were the mathematicians that invented certain topics, hence giving them a human connection to topics learned in mathematics. (T, S)

- The end result of the figure is much better than a poster of some research topic. (T, S)

Weakness:

- The project may take too long, and it may cost the students some money, if they

are not able to use the materials provided for them in their art classes. (S)

- The end result of building a figure may be nice, but it is not so interactive. (T, S)

- The students would have to make the figure and in addition have to do extra research to find out more about the life of the mathematician. It may be too much work. (S)

- With a life-size model, it would be hard to transport the figure and the class space may be limited. (S)

- The project may not involve a lot of mathematical content for the student to learn. (T, S)

- This also may be hard to mark from the teachers view. (T)

T – Teacher’s perspective

S – Student’s perspective

3) After looking at the strengths and weaknesses of the given project we have decided to modify it from building a model of a famous mathematician to conducting an interview with a famous mathematician.

Students would work in pairs to research a famous mathematician of their choice. They would research and then present the information found to the rest of the class in a short 5-10 min interview. While conducting the interview students would pose as an interviewer and the mathematician in question. The student posing as the mathematician would be strongly encouraged to dress up as the mathematician.

As well as the interview students would be expected to make a poster with a brief summary/description of the interview/mathematician researched, which would be posted in the classroom. The poster should contain a graphic of the famous mathematician. Both the poster and the interview should answer basic questions such as what era was the mathematician alive and what were some of their most famous/well known contributions to the world of mathematics?

This project can be done at any high school grade level, however the higher the grade level the more in depth and detail the interview/poster would need to be. The purpose of this project is to acknowledge the mathematicians that have formed the mathematics that we use today and to add a human touch to the math classroom by adding some decorations to the walls. Students will be marked on the information contained in both their interview and on their poster, as well as their creativity and their presentation (a rubric would need to be developed that would be appropriate for each grade level that this project would done at).

The Project’s Marking Rubric

Students work	Mark distribution	Marking
Interview	Organization, presentation and participation of both students	5 Marks
Poster	Layout and attractiveness	5 Marks
Creativity	Bringing new and exceptional ideas	5 marks
Informative content	For both the poster and the interview. Information about the mathematician life (5 marks) Information about the mathematician work (5 marks)	10 marks
Final score		Out of 20 Marks