Pei's Oval

Calculus Level 5

The architect I.M. Pei suggested that the most appealing oval to the human eye is ${ \left| \frac { x }{ a } \right| }^{ 1.5 }+{ \left| \frac { y }{ b } \right| }^{ 1.5 }=1.$ What is its enclosed area if $a = b = 3?$

The answer is 24.64.

1 solution

Shriram Lokhande
Jul 31, 2014

The given equation is of super ellipse . whose area is given by $A=4ab\frac{(\Gamma(1+\frac{1}{n}))^2}{\Gamma(1+\frac{2}{n})}$ By plugging in $a=b=3$ & $n=\frac{3}{2}$ $A=36\frac{(\Gamma(\frac{5}{3}))^2}{\Gamma(\frac{7}{3})}$ $\Rightarrow A=36\times 0.684455=24.64038$

Wow..Had you encountered this before??

Jayakumar Krishnan - 6 years, 10 months ago

I had to derive it using the Beta function.

Steven Zheng - 6 years, 10 months ago

Awesome.... Shriram...!

Vijay Simha - 2 years, 6 months ago

Pei's Oval

The answer is 24.64.

1 solution

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