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Project on submitted by :- Kabir Singh Class :- 9-B Roll no. 12. What Is. In non-mathematical terms, pi is simply the greek letter " pi", and is written like this:.

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  1. Project on submitted by:- Kabir Singh Class :- 9-B Roll no. 12

  2. What Is In non-mathematical terms, pi is simply the greek letter "pi", and is written like this: However, when referring to Mathematics, pi represents one of the most important constants, not just in theoretical Maths, but in practical situations too. This constant is the ratio of a circle's circumference to its diameter, commonly approximated as 3.14.

  3. The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter. The constant, sometimes written pi, is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century. π is an irrational number, which means that it cannot be expressed as a ratio of two integers (such as 22/7 or other fractions that were commonly used to approximate π); consequently, its decimal representation never ends and never repeats. 

  4. Rational Or Irrational? Irrational number An irrational number is a number which cannot be expressed exactly in any algebraic or arithmetical form. That might sound scary, but it just means a number that would carry on infinitely if you were to try to write it out as a decimal. So with pi, you get 3.1415926535...., on to infinity. A quick and easy approximation to π is 22/7 22/7 = 3.1428571... But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.

  5. Common Application Pi is commonly seen in mathematical formulae. The most well known formula that involves pi is: where c is the circumference of a given circle, and d is the diameter of a given circle.

  6. In basic terms, this is the definition of pi, as the ratio of a circle's circumference to its diameter. It is also the first equation in which pi was ever used. Another extremely common formula that relies on pi is also to do with a circle, specifically the relationship between a circle's area and radius: where A is a given circle's area, and r is a given circle's radius.

  7. Aside from these two, there are many other formulae in the study of solid geometry which involve pi, and a few of these are detailed below with brief explanations: Volume = πr2h • and its surface area is: • the area of the top (πr2) + • the area of the bottom (πr2) + • the area of the side (2πrh). Therefore without the top or bottom (lateral area), the surface area is: A = 2πrh. With the top and bottom, the surface area is: A = 2πr2 + 2πrh = 2πr(r + h).

  8. Hollow right circular cylinder VolumeV  =  π×h×(R² − r²) = π × h × (D² − d²) ⁄ 4 Lateral outer surface arealS = 2×π×R×h Lateral inner surface areals = 2×π×r×h Lateral total surface areal  =  lS+ls = (2×π×R×h)+(2×π×r×h) = 2×π×h×(R+r) AreaA  =  2 × B + l = (2 × π × (R² − r²)) + (2 × π × h × (R + r)) = 2 × π × (R² − r² + h × (R + r)) = 2 × π × (R+r) × (R − r+h) Base areaB = π × (R² − r²) Base outer perimeterP  =  2×π×R Base inner perimeterp  =  2×π×r

  9. SPHERE Volume:- Surface Area Of A Sphere:-

  10. HEMI-SPHERE Volume of Hemisphere = (2/3)πr³Curved Surface Area(CSA) of Hemisphere = 2πr²Total Surface Area(TSA) of Hemisphere = 3πr²

  11. CONES

  12. Approximate Values At Various Stages 1. The ancient Egyptians used an approximation of pi in their monuments, as the Great Pyramid of Giza was built so that the circle whose radius is equal to the height of the pyramid has a circumference equal to the perimeter of the base (it is 1760 cubits around and 280 cubits in height). 2. Some says Egyptians knew the vaue of of pi, and the approximation was 256/81 3. As early as the 19th century BCE, Babylonian mathematicians were using π ≈ 25/8, which is about 0.5 percent below the exact value. 4.The IndianastronomerYajnavalkya gave astronomical calculations in the ShatapathaBrahmana (c. 9th century BCE) that led to a fractional approximation of π ≈ 339/108 (which equals 3.13888..., which is correct to two decimal places when rounded, or 0.09 percent below the exact value).

  13. 5. Ptolemy, using a regular 360-gon, obtained a value of 3.141666...., which is correct to three decimal places. 6. The Chinese mathematicianLiu Hui in 263 CE computed pi to between 3.141024 and 3.142708 .However, he suggested that 3.14 was a good enough approximation for practical purposes. Later he obtained a more accurate result π ≈ 3927/1250 = 3.1416 7. In 499 CE India, mathematician Aryabhata calculated the value of pi to five significant figures (π ≈ 3.1416)

  14. Thank You

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