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3.125: 1 Between 1 BC and AD 5: Liu Xin [7] [11] [12] Unknown method giving a figure for a jialiang which implies a value for π ≈ 162 ⁄ (√ 50 +0.095) 2. 3.1547... 1 AD 130: Zhang Heng (Book of the Later Han) [2] √ 10 = 3.162277... 736 ⁄ 232: 3.1622... 1 150: Ptolemy [2] 377 ⁄ 120: 3.141666... 3: 250: Wang Fan [2] 142 ⁄ 45: 3 ...
The most familiar is the aforementioned 3-torus universe. In the absence of dark energy, ... " π 39 (Pi and the size of the Universe)". Numberphile. Brady Haran.
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
He also suggested that 3.14 was a good enough approximation for practical purposes. He has also frequently been credited with a later and more accurate result, π ≈ 3927 ⁄ 1250 = 3.1416 (accuracy 2·10 −6), although some scholars instead believe that this is due to the later (5th-century) Chinese mathematician Zu Chongzhi. [17]
k = +1, 0 or −1 depending on whether the shape of the universe is a closed 3-sphere, flat (Euclidean space) or an open 3-hyperboloid, respectively. [4] If k = +1, then a is the radius of curvature of the universe. If k = 0, then a may be fixed to any arbitrary positive number at one particular time.
where H is the hypervolume of a 3-sphere and r is the radius. S V = 2 π 2 r 3 {\displaystyle SV=2\pi ^{2}r^{3}} where SV is the surface volume of a 3-sphere and r is the radius.
The Friedmann–Lemaître–Robertson–Walker metric (FLRW; / ˈ f r iː d m ə n l ə ˈ m ɛ t r ə ... /) is a metric that describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected.
Table 3: Today's universe in Planck units Property of present-day observable universe Approximate number of Planck units Equivalents Age: 8.08 × 10 60 t P: 4.35 × 10 17 s or 1.38 × 10 10 years Diameter: 5.4 × 10 61 l P: 8.7 × 10 26 m or 9.2 × 10 10 light-years: Mass: approx. 10 60 m P: 3 × 10 52 kg or 1.5 × 10 22 solar masses (only ...