File:Comparison catenary parabola.svg
Summary
Comparison of a catenary (black dotted curve) and a parabola (red solid curve) with the same span and sag. The catenary represents the profile of a simple suspension bridge, or the cable of a suspended-deck suspension bridge on which its deck and hangers have negligible mass compared to its cable. The parabola represents the profile of the cable of a suspended-deck suspension bridge on which its cable and hangers have negligible mass compared to its deck. The profile of the cable of a real suspension bridge with the same span and sag will lie between the two curves. The catenary and parabola equations, plotted between x=-1 and x=1, are <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f62eb94927f50e2299c9425c4356a4bdda8a619e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:10.641ex; height:2.509ex;" alt="{\displaystyle y={\text{cosh }}x}"> and <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad50cad095170c986635e7c1d1100bf1e3cd8385" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:24.068ex; height:3.176ex;" alt="{\displaystyle y=x^{2}[({\text{cosh }}1)-1]+1}">, respectively.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:14, 4 January 2017 | | 512 × 144 (14 KB) | 127.0.0.1 (talk) | Comparison of a catenary (black dotted curve) and a parabola (red solid curve) with the same span and sag. The catenary represents the profile of a simple suspension bridge, or the cable of a suspended-deck suspension bridge on which its deck and hangers have negligible mass compared to its cable. The parabola represents the profile of the cable of a suspended-deck suspension bridge on which its cable and hangers have negligible mass compared to its deck. The profile of the cable of a real suspension bridge with the same span and sag will lie between the two curves. The catenary and parabola equations, plotted between x=-1 and x=1, are <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mtext>cosh </mtext></mrow><mi>x</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y={\text{cosh }}x}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f62eb94927f50e2299c9425c4356a4bdda8a619e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:10.641ex; height:2.509ex;" alt="{\displaystyle y={\text{cosh }}x}"></span> and <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo>=</mo><msup><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mtext>cosh </mtext></mrow><mn>1</mn><mo stretchy="false">)</mo><mo>−<!-- − --></mo><mn>1</mn><mo stretchy="false">]</mo><mo>+</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y=x^{2}[({\text{cosh }}1)-1]+1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad50cad095170c986635e7c1d1100bf1e3cd8385" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:24.068ex; height:3.176ex;" alt="{\displaystyle y=x^{2}[({\text{cosh }}1)-1]+1}"></span>, respectively. |
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