Rata-rata aritmetika–geometrik

Dalam matematika, rata-rata aritmetika–geometrik atau purata aritmetika–geometrik dari dua bilangan real positif $x$ dan $y$ didefinisikan sebagai berikut: Misalkan $x = a 0$ dan $y = b 0$ , maka barisan $(a n)$ dan $(g n)$ didefinisikan sebagai

{\begin{aligned}a_{n+1}&={\frac {1}{2}}(a_{n}+b_{n}),\\b_{n+1}&={\sqrt {a_{n}b_{n}}}\,.\end{aligned}}

Rata-rata aritmetika–geometrik dari $x$ dan $y$ dilambangkan sebagai $M (x, y)$ , terkadang sebagai $agm(x, y)$ atau $AGM(x, y)$ .

Rata-rata aritmetika–geometrik dapat diterapkan dalam algoritma cepat untuk fungsi eksponensial dan trigonometri, serta konstanta matematika, khususnya dalam menghitung $π$ .

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