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The curve given by (t-sinh(t)cosh(t), 2 cosh(t)), t real.

Q: What is the evolute of a catenary?

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The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.

apparently, it is called catenoid.

One is the "Gateway To The West" arch in St. Louis, Missouri. It is also possible McDonalds Restaurants have a double inverted catenary arch shape. It resembles a letter M in script form.

No shape is mathematical really unless it has been created by a mathematical formula, but is certainly a geometric shape. But anything which is a 2D or 3D shape is geometric. My improvement: A catenary curve from a mathematical equation such as cosh x, is a mathematical and natural shape. Maby each other arch can be approximated by a mathematical formula.

Slack, in high power transmission lines, refers to the difference between the length, L, of a conductor hanging between two towers, and the direct distance (span length), S, between the attachment points on those towers. Rather than give slack its own variable, it is simply written (L-S). In his book "Electric Power Generation, Transmission and Distribution, Vol 1", Leonard L. Grigsby gives the following approximate equations for slack: L-S = 8D^2/3S, where: - D is the mid-span sag (how far the conductor sags below a line drawn directly between the attachment points at mid-span) The alternate equation is: L-S = S^3/(24*W^2) = S^3*w*2/(24*H^2), where: - w is the conductor weight per unit length - H is the horizontal tension (constant) throughout the conductor catenary, and - W = H/w is known as the "catenary constant" These equations are only approximations. Exact catenary equations involve hyperbolic sines and cosines, and these parabolic equations are approximations for those. The are relatively accurate as long as sag is less than 5% of span length.

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it evolves into donphan

Catenary

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The general formula of a catenary is y = a*cosh(x/a) = a/2*(ex/a + e-x/a) cosh is the hyperbolic cosine function

A catenary is the shape formed by a hanging chain or cable under its own weight. In wind turbine alignment, the catenary is important because it helps to position the turbine blades in a way that maximizes their efficiency in capturing wind energy. By aligning the turbine blades along the catenary curve, the blades can better adapt to changing wind conditions and generate more power.

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A equation is santa clause

sphere

The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.

A catenary is the curve formed by slack wire - telephone cables are a good example. So a catenary tow is one where, simply put, the towline is attached to shackles of anchor cable in order to ensure that a belly of towline (providing spring) hangs between the two ships.

If: A=Horizontal distance betwen ends (at same height) B=Depth of catenary C=radius of curvature at lowest point L=length along catenary M=Mass per unit length Tm=Tension at ends of catenary To=Tension at lowest point. (Also horizontal component of tension at any point) Then: C=To/M, and B=C(cosh(A/2C)-1)