MTH 405 Midterm 16/3/2011 1. A specific area for the area of various polygons is the one for the area of a regular polygon. The setup and initial steps to creating the proof require a geometric approach that would otherwise make proving a big challenge. For example‚ a polygon with n sides is broken up into a collection of n congruent triangles‚ this geometric setup is key in reaching an easy solution for the area. The algebraic aspect comes into play when it comes to deriving the equation
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Carl Friedrich Gauss Carl Friedrich Gauss was a German mathematician and scientist who dominated the mathematical community during and after his lifetime. His outstanding work includes the discovery of the method of least squares‚ the discovery of non-Euclidean geometry‚ and important contributions to the theory of numbers. Born in Brunswick‚ Germany‚ on April 30‚ 1777‚ Johann Friedrich Carl Gauss showed early and unmistakable signs of being an extraordinary youth. As a child prodigy‚ he was
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Western civilizations. Many achievements of the ancient Greek civilization have positively affected the west. Roots in the most influenced areas of math‚ art‚ philosophy‚ and drama can be traced back to the ancient Greeks. The ancient Greek mathematician Euclid influenced mathematics in a large way after developing the Pythagorean theorem. His theorem (written around 300 B.C.) stated that “If two straight lines cut one another‚ the vertical‚ or opposite‚ angles shall be the same” (Doc. 5). Euclid
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attendance at school often isn’t‚ and a minority of parents choose home-schooling‚ e-learning or similar for their children. Contentsn the West‚ Ancient Greek philosophy arose in the 6th century BC. Plato was the Classical Greek philosopher‚ mathematician and writer of
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When you think of the people that most influenced your life today‚ Ada Lovelace is almost certainly not a name that pops into mind. But her effect on the modern world cannot be denied. Every time that you send an email‚ listen to Spotify‚ or go on Instagram‚ you are experiencing the long lasting effect of Ada Lovelace on the world today. Because of her work in computer programming‚ civil rights‚ and mathematics‚ she is the most influential person in history. Ada Lovelace’s life was filled
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various ways of incorporating Banks’ five dimensions into teaching Mathematics. One way of incorporating content knowledge into teaching Math according to Strutchens‚ is to teach students about Benjamin Banneker‚ an African American self-taught mathematician. After discussing Banneker’s background student can “have fun solving some of the puzzles he created” (1995). Knowledge construction is the second dimension and can be incorporated into teaching Math by allowing students to build and construct
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understanding of cultural heritage. This can be seen in China‚ the oldest systematic math originated from Zhan guo period. A book called ”Mo Jing” recorded many definitions and math ideology. Through the study of math‚ we can find out famous mathematicians like Liu Yi‚ Zhu Shijie and Shen Kuo so as to learn the history of math and prompt our understanding of Chinese culture. As we can see‚ learning math can transit the culture and academic heritage. In the second place‚ calculation is believed
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Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know little about his achievements. There is nothing that is truly accurate pertaining to Pythagoras’s writings. Today Pythagoras is certainly a mysterious figure. Little is known of Pythagoras’s childhood. Pythagoras’s father was Mnesarchus‚ and his mother was Pythais. Mnesarchus was a merchant who came from Tyre. Pythais was a native of Samos. As
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A Beautiful Mind Film Analysis This movie is based on the true story of the brilliant mathematician John Forbes Nash Jr. He made remarkable advancements in the field of mathematics at a young age and had a very promising future. Unfortunately‚ John Nash had problems deciphering the difference between reality and hallucinations. He had a mental disorder known as Schizophrenia. Schizophrenia is a severe‚ complex illness that causes hallucinations and can affect a person’s ability to think clearly
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inventions and coming up with great ideas. He was a very smart person‚ and had invented some useful inventions for human kind for what is still used today. BC. He was a physicist‚ engineer‚ inventor‚ astronomer and a Greek mathematician. Archimedes is one of the greatest math mathematicians of all time. He has been given credit for the invention of the lever even though it was used thousand of years before his time despite the fact that he did not invent it. He only gave an explanation of the principal
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