The cache is not hidden at the posted coordinates and it is not necessary to visit the place to get the final coordinates.
We were inspired to create this cache by chain clues found in some of the caches of the geocacher who hid the most caches in Crete.
A catenary curve with U-like shape is similar to a parabola. However, a parabola is formed when an inclined plane intersects a rotating cone at a certain angle, it is described by the equation y=ax2+bx+c, where a≠0. For example, satellite dishes or car headlights have a parabola shape.
The catenary curve (Greek: Η αλυσοειδής καμπύλη, I alysoeidís kampýli, chain-like curve) arises from the balance of gravitational forces along a chain or cable when it is supported only at its ends under its own weight. It is also sometimes called a funicular curve.
Mathematically, a catenary curve is described by the function:
y= B · cosh(x/B)= ½ · B · (e-x/B + ex/B) ,
where B ≠0 is a constant that depends on the physical properties and the span of the hanging chain, cosh is hyperbolic cosine and e is the base of the natural logarithm.
Flipping the chainline upside down creates the most stable possible shape of a free-standing arch. The catenary curve or catenary arch can be encountered in various aspects of nature, architecture and engineering.
In nature, filaments can often be seen hanging freely between two fixed points and shaped by gravity into catenaries. For example, silk in the spider web, suspended lianas or mosses or lichens hanging between tree branches. Catenary arches occur when forces and material distribution naturally align to create stable, efficient structures. In Arches National Park, Utah you can see Landscape Arch, elsewhere volcanic lava tubes occur. Certain ant and termite species construct tunnel systems or mounds with arched entrances.
In architecture are catenaries used in elegant suspension bridges or vice versa to create self-supporting arches in buildings. For example, the Clifton Suspension Bridge, which has spanned the Avon Gorge and the River Avon since 1864, also the traditional construction of old Irish huts or snow igloos resembles the arc of a catenary. The ruins of the modernist Celler wine press building in Sant Cugat del Vallès, Spain and the Gateway Arch in St. Louis, Missouri, which is a near-perfect catenary. By the way, the mathematical expression of the shape of the curve is engraved on the inside of this arc.
In engineering, catenaries are seen in the design of high voltage power lines, where suspended electrical wires naturally form this curve.
The catenary curve can be seen in the cross-section of tented roofs.
A beautiful example of a striking roof is on the Cathedral of St. Barbara in Kutná Hora in the Czech Republic. It is one of the most famous Gothic churches in Central Europe and is a UNESCO World Heritage Site. It was built between the 14th and 16th centuries and dedicated to St. Barbara, the patron saint of miners, reflecting the town's historical wealth derived from silver mining.
Source: Wikipedia
How to find the final coordinates
Enter the Latin name of catenary curve into the Certitude checker to reveal the final coordinates and hint.
Just in case, a local cacher will provide maintenance assistance.