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WonderScience fact

Pi, the ratio of any circle's circumference to its diameter, can never be written out in full. Its digits after 3.14 go on for ever without settling into a repeating pattern, because pi is irrational: no fraction of two whole numbers equals it exactly.

Mathematics

Science

The story behind the card

People have approximated pi for thousands of years. Around 250 BC the Greek mathematician Archimedes trapped it between 3 10/71 and 3 1/7 by drawing many-sided shapes inside and outside a circle. The Swiss scientist Johann Heinrich Lambert proved in the 1760s that pi is irrational. In 1882 Ferdinand von Lindemann went further, showing that pi cannot be produced from whole numbers by any finite combination of arithmetic and roots. That settled an ancient puzzle: with only a compass and straight edge, it is impossible to draw a square with exactly the same area as a given circle. The Welsh mathematician William Jones first used the symbol π for this number in 1706. Computers have now calculated hundreds of trillions of digits, yet NASA's engineers use just 15 decimal places for their most precise spacecraft navigation.

Türkçe oku
Bir çemberin çevresinin çapına oranı olan pi sayısı hiçbir zaman tam olarak yazılamaz. 3,14'ten sonraki basamakları, tekrar eden bir düzene girmeden sonsuza dek sürer; çünkü pi irrasyonel bir sayıdır, yani iki tam sayının oranı olarak yazılamaz.

İnsanlar pi sayısını binlerce yıldır yaklaşık olarak hesaplıyor. MÖ 250 dolaylarında Yunan matematikçi Arşimet, çemberin içine ve dışına çok kenarlı şekiller çizerek pi sayısının 3 10/71 ile 3 1/7 arasında olduğunu gösterdi. İsviçreli bilim insanı Johann Heinrich Lambert 1760'larda pi sayısının irrasyonel olduğunu kanıtladı. Ferdinand von Lindemann ise 1882'de daha da ileri giderek pi sayısının, tam sayılardan sonlu sayıda dört işlem ve kök alma ile hiçbir şekilde elde edilemeyeceğini gösterdi. Böylece çok eski bir soru da yanıtını buldu: Yalnızca pergel ve cetvelle, bir çemberle tam olarak aynı alana sahip bir kare çizmek imkânsızdır. Bu sayı için π simgesini ilk kez 1706'da Galli matematikçi William Jones kullandı. Bilgisayarlar bugün pi sayısının yüz trilyonlarca basamağını hesapladı; NASA mühendisleri ise en hassas uzay aracı hesaplarında bile yalnızca 15 ondalık basamak kullanıyor.

Sources and further reading

Background reading: Pi
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