The diagonal of a unit square
Rational approximations to √2
Convergents of square root of 2 from continued fraction
| Bruch | Dezimalzahl | Fehler |
|---|---|---|
| 1/1 | 1,000 | 0,41421 |
| 3/2 | 1,500 | 0,08579 |
| 7/5 | 1,400 | 0,01421 |
| 17/12 | 1,41667 | 0,00246 |
| 99/70 | 1,41429 | 0,0000849 |
Spiral of Theodorus: building every square root from unit triangles
Each right triangle has one leg equal to the previous hypotenuse and one leg equal to 1. The hypotenuses are √1, √2, √3, √4, √5… Most are irrational. √2 (red) was the first proved irrational, by the Pythagoreans around 500 BC.
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Pertanyaan
Pecahan apa yang mengaproksimasi sqrt(2) dengan baik?
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1 / 10
Hasilkan digit Akar Kuadrat dari 2
√2 has no final digit
Akar Kuadrat dari 2 is irrational. Its decimal expansion never ends and never repeats. The digits shown below are verified against the pecahan berlanjut.
√2 = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))
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