Q: What is an Arch of an inverted catenary shape?

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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.

yes

A form of arch defined by a moving point which remains equidistant from a fixed point inside the arch and a moving point along a line. This shape when inverted into an arch structure results in a form which allows equal vertical loading along its length. A parabola is the graph of a quadratic equation. Mathworld has some nice drawings. Need a link? You got it. A Parabola is the set of all points that are equidistant from a point and a line. The line is called the directrix and the point is called the focus. Each point on the parabola is as far from the directrix as it is from the focus. It is the same shape of a curve you will find in the reflector of a flashlight bulb, or in the arc of a baseball when it is thrown or hit.

triangles are the second strongest shape next to the arch

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.

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It is a catenary, as defined by the following mathematical equations: y = cosh(x) or y = (e^x + e^-x)/2 A catenary is the shape which a flexible linear object with constant mass will naturally hang in when it's endpoints are fixed. The classic example is a cable or a chain. Catenary's have a practical application in arch construction because the force of the weight of the higher portions of the arch is always directed into the lower portions of the arch, making it very self supporting. This is why the Arch is constructed as a catenary, and why it is still standing.

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.

The "inverted arch" is used when a sideways, or inward load, is to be resisted. The "common arch" supports a vertical load.

Tacoma narrow bridge.

sphere

The St. Louis Arch is in the shape of a hyperbolic cosine function It is often thought that it is in the shape of a parabola, which would have a quadratic function of y = a(x-h)^2 + k, where the vertex is h, k.

there are not very many you go up to then top in an elevator that is shaped like a pod

A catenary is produced by hanging a chain from two points some distance apart. The equation for a catenary is the hyperbolic cosine. One simple example of a catenary can be found if you look at the power lines running between two poles. A parabola is produced by putting a hanging chain or cable under an equally dispersed load. An example of this can be seen on a suspension bridge, the cable hanging from two towers with the road below hanging from vertical cables attached to the main suspension cables.

The Gateway Arch in St. Louis, Missouri was created from a competition winning design submitted by Eero Saarinen. The design was tweaked through several stages until the final flattened catenary arch was agreed upon.

The Gateway Arch in St. Louis, Missouri was created from a competition winning design submitted by Eero Saarinen. The design was tweaked through several stages until the final flattened catenary arch was agreed upon.

An inverted kite is still a kite.

The Gateway Arch is a 630-foot-high monument in St. Louis, in the U.S. state of Missouri. Clad in stainless steel and built in the form of a flattened catenary arch, it is the tallest man-made monument in the United States, Missouri's tallest accessible building, and the world's tallest arch.