Download as PPSX, PPTX
![Pi (rather than some other Greek
letter like Alpha or Omega) was
chosen as the letter to represent the
number 3.141592... because the letter
[ ] in Greek, pronounced like our
letter 'p', stands for 'perimeter](https://image.slidesharecdn.com/history-150727161357-lva1-app6891/85/History-14-320.jpg)
Uploaded byst.arnolds higher secondarooly school
History
The document discusses the history and development of pi. Pi is the mathematical constant that represents the ratio of a circle's circumference to its diameter. Ancient civilizations like Egypt and Greece were aware of pi as a constant ratio slightly higher than 3. Archimedes calculated pi more accurately in ancient Greece. Over centuries, mathematicians have calculated pi to increasing numbers of decimal places. Pi is ubiquitous in formulas used by many fields like engineering and has no discernible pattern in its decimal representation.
More Related Content
History
- 2.
- 3.
- 4.
- 5. The Definition ofPi The 16th letter of the Greek alphabet is P or p, corresponding to the roman p. .
- 6. The Definition ofPi The 16th letter of the Greek alphabet is P or p, corresponding to the roman p. A number, represented by said letter, expressing the ratio of the circumference of a perfect circle to its diameter. The value of pi has been calculated to many millions of decimal places, to no readily apparent pattern.
- 8. Beginning of Pi It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and its interest here is that it gives π = 3. Not a very accurate value of course and not even very accurate in its day.
- 9. Beginning of Pi The earliest values of π including the 'Biblical' value of 3, were found by measurement. In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 4(8/9)2 = 3.16 as a value for π.
- 10. What is pi? Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter
- 11. What is pi? Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter
- 12. What is pi? Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter Circumference = The distance around a circle
- 13. What is pi? Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter Circumference = The distance around a circle Diameter = The width of a circle
- 14. Pi (rather thansome other Greek letter like Alpha or Omega) was chosen as the letter to represent the number 3.141592... because the letter [ ] in Greek, pronounced like our letter 'p', stands for 'perimeter
- 16. The historyof pi is complicated. No one “invented” pi. It was discovered rather than made. The use of pi developed as the use of mathematics developed.
- 17. The historyof pi is complicated. No one “invented” pi. It was discovered rather than made. The use of pi developed as the use of mathematics developed. Ancient Egyptians and Greeks knew the ratio of the circumference to the diameter of a circle is the same for all circles and is slightly higher than 3.
- 18. The historyof pi is complicated. No one “invented” pi. It was discovered rather than made. The use of pi developed as the use of mathematics developed. Ancient Egyptians and Greeks knew the ratio of the circumference to the diameter of a circle is the same for all circles and is slightly higher than 3. Though the estimate of ancient civilizations was close to pi it was not until Archimedes, a Greek mathematician and physicist, who more accurately calculated pi.
- 19. How Pi wasdeveloped. Archimedes found that if he drew circles in polygons and calculated the inner and outer polygon’s perimeters and calculated the values that the estimate of pi was 3.1419. The second major advancement in understanding pi came with the development of calculus. Polygon=geometric figure with three or more sides or angles.
- 20. Archimedes (Known for hiswork with Pi)
- 21. Archimedes (Known for hiswork with Pi) 287 BC – 211 BC
- 22. Archimedes (Known for hiswork with Pi) 287 BC – 211 BC Spent most of his life in Syracuse, Sicily.
- 23. Archimedes (Known for hiswork with Pi) 287 BC – 211 BC Spent most of his life in Syracuse, Sicily. Studied in Alexandria, Egypt under the followers of Euclid.
- 24. Archimedes (Known for hiswork with Pi) 287 BC – 211 BC Spent most of his life in Syracuse, Sicily. Studied in Alexandria, Egypt under the followers of Euclid.
- 25. Archimedes Invented WarMachines used in the defense of Syracuse, compound pulley systems, planetarium, water screw, water organ, burning mirrors.
- 26. Archimedes Invented WarMachines used in the defense of Syracuse, compound pulley systems, planetarium, water screw, water organ, burning mirrors.
- 27. Archimedes Invented WarMachines used in the defense of Syracuse, compound pulley systems, planetarium, water screw, water organ, burning mirrors.
- 28. Archimedes Invented WarMachines used in the defense of Syracuse, compound pulley systems, planetarium, water screw, water organ, burning mirrors.
- 29. Archimedes Invented WarMachines used in the defense of Syracuse, compound pulley systems, planetarium, water screw, water organ, burning mirrors.
- 30. The Notation ofpi The first to use the symbol π with its current meaning was William Jones in 1706. He was a Welsh mathematician. Euler adopted the symbol in 1737 and it soon became a standard. William Jones Leonhard Euler
- 31. Augustus de Morgan English mathematician born in India Looked at Shanks’ 707- digit calculation of pi. Noticed that there was a suspicious shortage of 7s. In 1945 Ferguson discovers that Shanks had made a mistake in the 528th place, which lead to all the following digits to be wrong. De Morgan
- 32. How Many Numbers? 1699 – Only 71 digits were correctly discovered. • 1719 – 112 digits were found to be correct in France.
- 34. There areno repeating parts in Pi. This means that at no part during the 1.2411 trillion counts of Pi did the pattern begin to repeat itself. It is the only number like this in the world.
- 35. There areno repeating parts in Pi. This means that at no part during the 1.2411 trillion counts of Pi did the pattern begin to repeat itself. It is the only number like this in the world. So far, the largest count of Pi was done by a supercomputer at the University of Tokyo in Sept of 2002. 1.2411 trillion decimal digits were calculated. That looks like 1,241,100,000,000 numbers
- 37. The area ofa circle = πr2
- 38. The area ofa circle = πr2 Circumference of a Circle = πd or 2πr
- 39. The area ofa circle = πr2 Circumference of a Circle = πd or 2πr Surface Area of a Sphere, Volume of a Cone, Cylinder and Sphere all are formulas that involve π.
- 40. Use Pi toFind:- Right Cylinder – V = πr2h SA = 2πr2 + 2πrh Right Cone – V = 1/3 πr2h SA = πr (l + r) Sphere – V = 4/3 πr3 SA = 4πr2
- 41. Circumference Circumference isthe distance around the outside of the circle. To find distance we would use the formula circumference= pi x diameter As you know diameter is the width of a circle. For example Jim the engineer needs to design a metal tube that has a diameter of 15 feet. Jim needs to find the circumference of the circle in order to make a metal tube to fit around it. Jim would use the formula c=pi x d Circumference = 3.14 x 8 = 25.12 The circumference Jim is looking for is 25.12 feet.
- 42. Area Area=pi xthe radius squared. The radius of a circles is the distance from the center most point to the edge of that circle. For example. Tim the architect has to build a circular column that has a radius of 5 feet. What would be the area of the entire column? To calculate this Tim would take pi x 5 squared 3.14 x 5 squared = 78.5 Therefore the area of the circular column is 78.5 feet. <= radius
- 43. Volume To findvolume we would use the formula volume = pi x radius squared x height. Tom the agriculturist needs to know the volume of a dipping vat for his cows to safely and comfortably fit in. Before he can calculate he needs to know the radius and the height of the structure before he can begin building. Tom measures the radius at 5 feet and the height at 9 feet. Therefore Tom’s formula would look like Volume=3.14 x 5 squared x 9 3.14 x 5 squared x 9 = 706.5 feet cubed
- 44. Some peoplewere “dedicated” enough to actually spend incredible amounts of time and effort continuing the calculation of pi. 1699: Sharp gets 71 correct digits 1701: Machin gets 100 digits 1719: de Lagny gets 112 correct digits 1789: Vega gets 126 places 1794: Vega gets 136 places 1841: Rutherford gets 152 digits 1853: Rutherford gets 440 digits 1873: Shanks calculates 707 places of which 527 were correct
- 45. Pi in theProfessions. Agricultural professionals may use pi to determine the area covered by a pivot irrigation system or storage facility. The would use the formula Architects and construction works would both use the formula for Area extensively. They also use the formula for volume extensively to fill columns of concrete and to know the space a building would take up.
- 46. Pi in theProfessions. Engineers use advance formulas that include pi. These are just some of the formulas an engineer would use. Moving around structures such as landmasses and buildings would require the use of some of these formulas. Engineers would probably use pi more than other professions.
- 47.
- 48. Summary Pi isthe mathematical constant whose value is the ratio of a circle’s circumference to its diameter. The use of pi dates back to 1900 BC with ancient Egypt and Greece. It has taken 100’s of different algorithms to help estimate pi’s number because it is a repeating decimal. Pi has been developed along with the development of mathematics. There are many different applications for pi. Many different professionals such as engineers, agriculturalist, and construction workers use pi. Pi day is celebrated on 3/14 of every year because pi = 3.14
- 49. “Probably nosymbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi.” William L. Schaaf, Nature and History of Pi
- 50.