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Taster Lesson For A – Level Mathematics

Taster Lesson For A – Level Mathematics. j. Investigate what happens when you remove a square from a rectangle to leave a rectangle that is in the same proportions as the original rectangle . 1. Crucifixion of San Sebastian.

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Taster Lesson For A – Level Mathematics

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  1. Taster Lesson For A – Level Mathematics

  2. j • Investigate what happens when you remove a square from a rectangle to leave a rectangle that is in the same proportions as the original rectangle 1

  3. Crucifixion of San Sebastian

  4. Some studies of the Acropolis, including the Parthenon, conclude that many of its proportions approximate the golden ratio. The Parthenon's facade as well as elements of its facade and elsewhere can be circumscribed by golden rectangles. To the extent that classical buildings or their elements are proportioned according to the golden ratio, this might indicate that their architects were aware of the golden ratio and consciously employed it in their designs. Alternatively, it is possible that the architects used their own sense of good proportion, and that this led to some proportions that closely approximate the golden ratio. On the other hand, such retrospective analyses can always be questioned on the ground that the investigator chooses the points from which measurements are made or where to superimpose golden rectangles, and that these choices affect the proportions observed.

  5. Famous Pyramids of Egypt

  6. How good is your maths? • Can you do better than 8 year old Fredrick Gauss?

  7. The Question • What is the sum of all of the whole numbers between 1 and 1,000 inclusive? • Show all of the necessary calculations on a single sheet of paper.

  8. The History • Allegedly this activity was set by a teacher as work to keep the class busy.  Unfortunately in 1885, it proved inadequate.  One student, 8 year old Frederick Gauss, solved the problem in seconds.  He later went on to become a significant mathematician.  His biography is available at:http://www.geocities.com/RainForest/Vines/2977/gauss/english.html

  9. Draw any quadrilateral Mark the midpoints and join What do you notice? Investigate.

  10. Y X Z a b O

  11. Y N P X Z M Q a b O

  12. Y N P X Z M Q a b It is sufficient to show that MQ = NP O

  13. Y N P X Z M Q a b Show that MQ = ½ (b-a) Show XZ = b - a Show NP = ½ XZ Hence NP = MQ O

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