Ellipse and triangle Announcing the arrival of Valued Associate #679: Cesar Manara ...
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Ellipse and triangle
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Maximize the area of the inscribed triangleMaximum area of a rectangle inside a triangleFind the ellipse inscribed in a triangle having the maximum areaMinimal area of triangleOptimize triangle on ellipseLargest rotated ellipse inscribed in a rectangleLargest area of the triangle that can be inscribed in ellipseThe maximum area of a hexagon that can inscribed in an ellipseTriangle and Circle maximization problemRight triangle minimum area problem without calculus
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Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.
I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.
real-analysis optimization
edited Mar 23 at 22:40
Rócherz
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
$endgroup$
add a comment |
$begingroup$
Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.
I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.
real-analysis optimization
edited Mar 23 at 22:40
Rócherz
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
$endgroup$
$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
3
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08
add a comment |
$begingroup$
Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.
I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.
real-analysis optimization
edited Mar 23 at 22:40
Rócherz
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
$endgroup$
Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.
I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.
real-analysis optimization
real-analysis optimization
edited Mar 23 at 22:40
Rócherz
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
edited Mar 23 at 22:40
Rócherz
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
edited Mar 23 at 22:40
Rócherz
3,0263823
edited Mar 23 at 22:40
Rócherz
3,0263823
edited Mar 23 at 22:40
Rócherz
3,0263823
3,0263823
asked Mar 23 at 21:53
m2017mm2017m
94
asked Mar 23 at 21:53
m2017mm2017m
94
asked Mar 23 at 21:53
m2017mm2017m
94
94
$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
3
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08
add a comment |
$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
3
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08
$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
3
3
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08
add a comment |
0
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$begingroup$
What tringle is referred to by the word "equilateral" in the title?
$endgroup$
– user
Mar 23 at 21:56
$begingroup$
sorry, that was mistake
$endgroup$
– m2017m
Mar 23 at 22:01
3
$begingroup$
Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
$endgroup$
– Ethan Bolker
Mar 23 at 22:06
$begingroup$
I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
$endgroup$
– user
Mar 23 at 22:08