Need some geometry help

[Jerry Bruette]

If an oval and a circle have the same circumference do they have the same area?

[Mel Fulks]

No. Couple pieces of string cut at same length will quickly convince you.

[Mike Henderson]

Use Mel's suggestion and then compute the area of an ellipse and the area of a circle. That is, use some string tied together which will be the circumference of both your ellipse and your circle. Lay the string down and arrange it in a circle or an ellipse.

The area of an ellipse is A=pi*a*b where a is the major "radius" and b is the minor "radius"

The area of a circle is A=pi*r^2.

So the equations are the same when a=b.

Anyway, lay the string into an ellipse, measure a and b and insert into the equation. The lay the same string into a circle, get the radius (r) and compute the area. See if they are the same.

Mike

[Bill Dufour]

A circle or a square have the largest area for circular or rectangular objects of a given. circumference.
Bill D

[Alan Rutherford]

You can do it in your head with no math. Picture a cricle. Now stretch that circle into an oval. Keep stretching and you can see that the area is getting smaller and will approach zero.

[Patty Hann]

You can do it in your head with no math. Picture a cricle. Now stretch that circle into an oval. Keep stretching and you can see that the area is getting smaller and will approach zero.
That is cool. I never thought of explaining it that way.

[Jim Koepke]

An ellipse:


a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.

Can also be defined by the angle at which the plane on which a circle is drawn is viewed.

Sets of ellipse templates, for drafting, are often marked in degrees.

504373

jtk

[Dave Zellers]

If an oval and a circle have the same circumference do they have the same area?

I have to ask the most obvious question if you don't mind.

What are you working on that would cause you to ask this? Circles are the most curious of all shapes.

[Jerry Bruette]

I'm trying to find the square footage of a food plot so I know how much fertilizer and seed I need. It has an irregular shape and I thought I could possibly use the measure of the perimeter to figure the area.

I thought I could use an GPS app on my phone until I realized the accuracy of the app was plus or minus 30 meters. Haha the plot isn't even 30 meters in any direction. I ended up just pacing it off in two directions and treating it more like a rectangle. Close enough for the deer I hunt.

[Dave Zellers]

Maybe break the plot up into pieces that make sense area wise. A little more here, a little less there... averaging can be pretty accurate.

[Patty Hann]

Maybe break the plot up into pieces that make sense area wise. A little more here, a little less there... averaging can be pretty accurate.

^^ This is probably the best way to figure it ^^
(It's actually the way you basically solve a "find the area" problem using integral calculus)

[Jerry Bruette]

Maybe break the plot up into pieces that make sense area wise. A little more here, a little less there... averaging can be pretty accurate.

That's pretty much what I did. I paced a couple tracks for the length and about three for the width and averaged them.

[Jerry Bruette]

^^ This is probably the best way to figure it ^^
(It's actually the way you basically solve a "find the area" problem using integral calculus)

Calculus? Haha, I didn't even have Geometry in high school. Believe me I need the KISS system.

[Patty Hann]

Calculus? Haha, I didn't even have Geometry in high school. Believe me I need the KISS system.

That''s what I was saying..."use the ^^[above]^^ method" (break it into pieces that Dave suggests)

(But also it really is how integral calculus works)