All manner of Arches
갤러리
All manner of Arches
The 17th-century mathematician, scientist, engineer, architect, and Renaissance man Robert Hooke gave, on page 31 of his book A description of helioscopes, and some other instruments, an anagram for the true Mathematical and Mechanichal form of all manner of Arches for Building:
Ut pendet continuum flexile, sic stabit contiguum rigidum inversum
(As the flexible line hangs, so shall the rigid blocks of an arch stand, inverted).
We tested Hooke’s recipe by 3D-printing models of a Gothic arch and of arches in the form of an ellipse, a parabola, and a catenary curve. You can watch videos demonstrating the stability of the models and make your own using the attached STL files!
3D printed models of arches
저작권 CC BY-NC-SA-3.0
공식
- $y=\sqrt{h^2+\frac{\left(d^2-h^2\right)}{d}|x|-x^2}$
공식
- $y=h \sqrt{1-\frac{x^2}{d^2}}$
공식
- $y=h \biggl( 1-\frac{x^2}{d^2} \biggr)$
공식
- $y=h+a \left(1-\cosh \left(\frac{x}{a}\right)\right),\quad a \cosh \left(\frac{d}{a}\right)=a+h$
