Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 179593 by mathlove last updated on 30/Oct/22

$$pleasprooftheelipseenvironment$$$$formullah$$$$p=\pi \sqrt{2a^2+2b^2}$$

Commented by mr W last updated on 31/Oct/22

$$whatdoyoumeanwith‘‘elipse$$$${environment}^{″}?doyoumeanthe$$$$perimeterofelipse?$$

Commented by mathlove last updated on 31/Oct/22

$$yes$$

Commented by mathlove last updated on 31/Oct/22

$$ellipse$$

Commented by mr W last updated on 31/Oct/22

$$thenyou{can}^{\prime }tprove,because{it}^{\prime }snot$$$$true.infactthereisnoclosedformula$$$$tocalculatetheperimeterofanelipse.$$

Commented by mathlove last updated on 31/Oct/22

$$thenwhatistheellipsenvironmentformullah$$

Commented by mr W last updated on 31/Oct/22

$$you{don}^{\prime }tunderstandme?ihavesaid,$$$$thereisnoformulaforcalculating$$$$theperimeterofanelipse!i.e.you$$$${can}^{\prime }tcalculatetheperimeterofan$$$$elipseexactlythroughaformula!$$

Commented by mathlove last updated on 31/Oct/22

$$goodthanks$$

Commented by MJS_new last updated on 01/Nov/22

$$\mathrm{for}\mathrm{the}\mathrm{perimeter}\mathrm{of}\mathrm{an}\mathrm{ellipse}\mathrm{we}\mathrm{have}$$$$p=4\underset{0}{\stackrel{\pi /2}{\int }}\sqrt{a^2{\cos }^{2}t+b^2{\sin }^{2}t}dt$$$$\mathrm{which}\mathrm{has}\mathrm{no}\mathrm{exact}\mathrm{solution}$$$$\mathrm{Ramanujan}\mathrm{gave}\mathrm{this}\mathrm{very}\mathrm{good}\mathrm{approximation}$$$$p\approx \pi (a+b)(1+\frac{3{\lambda }^2}{10+\sqrt{4-3{\lambda }^2}})\mathrm{with}\lambda =\frac{a-b}{a+b}$$$$$$$$\mathrm{both}‘‘{\mathrm{easy}}^{″}\mathrm{formulas}$$$$p\approx \pi (a+b)$$$$p\approx \pi \sqrt{2(a^2+b^2)}$$$$\mathrm{are}\mathrm{not}\mathrm{accurate}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com