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Starting with 5, every second Fibonacci number is the length of the hypotenuse of a right triangle with integer sides, or in other words, the largest number in a Pythagorean triple, obtained from the formula (+) + (+ +) = +.
For example, a 10 cm (3.9 in) circular would have a maximum precision approximately equal to a 31.4 cm (12.4 in) ordinary slide rule. Circular slide rules also eliminate "off-scale" calculations, because the scales were designed to "wrap around"; they never have to be reoriented when results are near 1.0—the rule is always on scale.
The greatest mathematician of antiquity is often held to be Archimedes (c. 287 – c. 212 BC) of Syracuse. [80] He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series , in a manner not ...
Ancient Egyptian mathematicians had a grasp of the principles underlying the Pythagorean theorem, knowing, for example, that a triangle had a right angle opposite the hypotenuse when its sides were in a 3–4–5 ratio. [60] They were able to estimate the area of a circle by subtracting one-ninth from its diameter and squaring the result:
An excited state of the 12 C nucleus exists a little (0.3193 MeV) above the energy level of 8 Be + 4 He. This is necessary because the ground state of 12 C is 7.3367 MeV below the energy of 8 Be + 4 He; a 8 Be nucleus and a 4 He nucleus cannot reasonably fuse directly into a ground-state 12 C nucleus.
The triple point is at a temperature of 273.16 K (0.01 °C; 32.02 °F) and a pressure of 611.657 pascals (0.00604 atm; 0.0887 psi); [71] it is the lowest pressure at which liquid water can exist. Until 2019 , the triple point was used to define the Kelvin temperature scale .