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In practical applications it is often small: for example the triangles of geodetic survey typically have a spherical excess much less than 1' of arc. [14] On the Earth the excess of an equilateral triangle with sides 21.3 km (and area 393 km 2) is approximately 1 arc second. There are many formulae for the excess.
For example, two proportional vectors have a cosine similarity of 1, two orthogonal vectors have a similarity of 0, and two opposite vectors have a similarity of -1. In some contexts, the component values of the vectors cannot be negative, in which case the cosine similarity is bounded in [ 0 , 1 ] {\displaystyle [0,1]} .
In all the formulas stated below the sides a, b, and c must be measured in absolute length, a unit so that the Gaussian curvature K of the plane is −1. In other words, the quantity R in the paragraph above is supposed to be equal to 1. Trigonometric formulas for hyperbolic triangles depend on the hyperbolic functions sinh, cosh, and tanh.
The result is shown in Figure 1. Figure 1. The paraboloid y = x z is shown in blue and orange. The paraboloid x = y z is shown in cyan and purple. In the image the paraboloids are seen to intersect along the z = 0 axis. If the paraboloids are extended, they should also be seen to intersect along the lines z = 1, y = x; z = −1, y = −x.
Cos is an American sketch comedy/variety television series that debuted on ABC in September 1976. It was hosted by comedian Bill Cosby and featured an ensemble cast who performed sketches each week. The show was unsuccessful in the Nielsen ratings and was cancelled by November 1976 and replaced with The Hardy Boys/Nancy Drew Mysteries .
Lyone Foundation, COS [1] Dominique Lyone (11 September 1954 – 25 October 2024) was an Australian businessman. He was the Chairman and Founder of COS ; Australia’s largest family owned B2B supplier of office products.
1 [21] 20 Episode 20 – Dinner party 26 February 2025 Wednesday 7:30 pm 2,814,000 1,817,000 1 [22] 21 Episode 21 – Commitment 2 March 2025 Sunday 7:00 pm
More than 1,000 prison guards flooded Albany on Tuesday, chanting a defiant message as pressure mounted on them to stop their wildcat strike: “Hold the line.” The unsanctioned strike entered...