the.com/catenary
the shape a chain makes when it stops fighting gravity and starts cooperating
means The curve formed by a hanging chain, rope, or cable that droops freely under its own weight while supported at both ends.
from From Latin 'catena,' meaning chain — the same root that gives us 'concatenate' (to link together) and the prisoner's 'chains.' The mathematical sense was coined in the late 17th century when thinkers like Huygens, Leibniz, and Johann Bernoulli worked out the true shape of a hanging chain, proving it was not a parabola, as Galileo had supposed, but its own distinct curve.
- flip it
- upside down, it's the strongest arch possible
- not a parabola
- looks identical, fooled mathematicians for decades
- gateway arch
- St. Louis built a giant inverted catenary
- the math
- hyperbolic cosine, hidden in every hanging wire
- galileo's miss
- he guessed parabola, got it wrong
gateway arch — 630-foot monument in st. louis completed in 1965, shaped as an inverted weighted catenary
suspension bridge cables — golden gate bridge and brooklyn bridge use catenary curves for their main suspension cables
power lines — electrical transmission lines across landscapes naturally hang in catenary curves between poles