Shar va doira nisbati (Arximed teoremasi)

Arximed shar sirt yuzasi to'rttaga mos doira yuzasiga teng ekanligini isbotladi: S = 4πr², A_doira = πr², demak S = 4 × A_doira. Masalan, r = 3 sm: doira yuzasi = 9π, shar sirti = 36π = 4 × 9π. Bu natija Arximed tomonidan miloddan avvalgi III asrda kashf etilgan. U bu teoremani qabrida tasvirlanishini vasiyat qilgan.

S_shar = 4πr² = 4 × A_doira

Shar sirt yuzasi to'rtta xuddi shu radiusli doiraga teng. Arximed topgan munosabat. Shar hajmi V = (4/3)πr³.