A rectangle with rounded edges is not an oval

For the discussion of math. Duh.

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rtg928
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A rectangle with rounded edges is not an oval

I was having an argument about this with a girl in my class (not a math class). In the class the desks were set up so that they formed the shape of a rectangle with rounded edges. She said that this was the same thing as an oval but I pointed out that ovals don't have parallel lines while rectangles do. I told some people IRL about this argument and at first even they believed that a rectangle with rounded edges was an oval so this must be a common misconception. Anyone know why this is?

TaintedDeity
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Re: A rectangle with rounded edges is not an oval

It depends what you mean by rounded. If the corners are replaced with quarters of a circle then, sure, the shape isn't an oval but if the corners of the rectangle are replaced with the quarters of an oval of the right size... you've got an oval
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jaap
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Re: A rectangle with rounded edges is not an oval

Like this oval? Or this one? Or any of these?

Oval is not a mathematical term, as it is not precisely defined shape. Originally it meant egg-shaped, but nobody now insists on an oval being pointier at one end than on the other. The word can be used for any rounded convex oblong shape.

greengiant
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Re: A rectangle with rounded edges is not an oval

Huh, I never knew oval covered so many shapes but Wikipedia agrees with jaap. In fact in the 'common english' section it says "Sometimes it can even refer to any rectangle with rounded corners".

It's weird that a squircle wouldn't seem to fit the definition of an oval, but a rounded square would.

aleph_one
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Re: A rectangle with rounded edges is not an oval

Squares with rounded corners are so inelegant. Their boundary paths are not even infinitely differentiable!

jestingrabbit
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Re: A rectangle with rounded edges is not an oval

greengiant wrote:It's weird that a squircle wouldn't seem to fit the definition of an oval, but a rounded square would.

What's weirder is that people have gone and invented the word squircle.
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tckthomas
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Re: A rectangle with rounded edges is not an oval

I thought oval is a circle that is stretched in one direction? So any rectangle with corners replaced with arcs wouldn't be an oval in my definition unless the corners being replaced spans the whole rectangle.

EDIT: mine would be ellipse and not an oval

squareroot
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Re: A rectangle with rounded edges is not an oval

greengiant wrote:It's weird that a squircle wouldn't seem to fit the definition of an oval, but a rounded square would.

I don't see why not; it's a closed, convex, plane curve with an axis symmetry, differentiable, and it's not an ellipse..
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Eebster the Great
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Re: A rectangle with rounded edges is not an oval

aleph_one wrote:Squares with rounded corners are so inelegant. Their boundary paths are not even infinitely differentiable!

Are you sure about that? I don't see why it couldn't have a smooth boundary and straight sides.

It probably wouldn't be analytic, though.

aleph_one
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Re: A rectangle with rounded edges is not an oval

Well, it doesn't work to round off the corners as circles, as these have nonzero curvature everywhere, so the place where the line and the circle meet will have an undefined second derivative. There probably is an smooth way to join two perpendicular line segments, considering that there are smooth bump functions, but I can't see it offhand.

Eebster the Great
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Re: A rectangle with rounded edges is not an oval

aleph_one wrote:Well, it doesn't work to round off the corners as circles, as these have nonzero curvature everywhere, so the place where the line and the circle meet will have an undefined second derivative. There probably is an smooth way to join two perpendicular line segments, considering that there are smooth bump functions, but I can't see it offhand.

Well it would probably have to be somehow exponential, but yeah, I can see your point about the standard circular rounding.

jobriath
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Re: A rectangle with rounded edges is not an oval

If it makes the OP feel any better I also have the stricter (stretched-circle) definition in my head. Similarly, oblong sounds rounded to me. An American friend insisted that a rhombus was basically an oblong square, and I couldn't agree. I'm British, he's American---regional difference?

Eebster the Great
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Re: A rectangle with rounded edges is not an oval

jobriath wrote:If it makes the OP feel any better I also have the stricter (stretched-circle) definition in my head. Similarly, oblong sounds rounded to me. An American friend insisted that a rhombus was basically an oblong square, and I couldn't agree. I'm British, he's American---regional difference?

A rhombus isn't an oblong square, though . . . a rectangle is.

jaap
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Re: A rectangle with rounded edges is not an oval

jobriath wrote:An American friend insisted that a rhombus was basically an oblong square, and I couldn't agree. I'm British, he's American---regional difference?

A rhombus, as a mathematical term, should have all sides of equal length i.e. a square is stretched along its diagonal. If you stretch a square diagonally but each half by a different amount, then you get a kite. I haven't ever noticed rhombus being used colloquially to mean a kite shape (I lived in Britain for 15 years).

phlip
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Re: A rectangle with rounded edges is not an oval

I've only heard the term "oblong" to refer to a rectangle, not a rhombus... and even then, only from osmosis from educational shows made in the States, never from local stuff.

In school, iirc, we were taught the word "oval" first, for an ellipse, but I think when it was actually taught in Geometry proper, with actual definitions and whatnot, it was under the name "ellipse". I don't think it was ever explained that "oval" was a more general term for things vaguely shaped like that, whereas "ellipse" is a more specific term... if it was, I evidently didn't pick up on that, 'cause I learned that from this thread.

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DavCrav
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Re: A rectangle with rounded edges is not an oval

I've seen the word "stadium" to refer to a rectangle with corners replaced by quarter-circles. e.g., the Bunimovitch stadium.

Rocket22
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Re: A rectangle with rounded edges is not an oval

I would refer to any square, rectangle, parallelogram, or geometric shape with curved corners and straight sides as a compound radius. This term may be used more in the architectural field than in geometry which may be why the learned mathematicians (far more qualified than me) on this thread are having to be inventive with terms such as a squircle (which is very clever). An example of a compound radius is seen in the shape of an entryway arch where the side walls and the header are straight but the two corners are curved. Another example would be in designing the neck of a stringed instrument where the top of the neck may have a tighter, more narrow curve while the bottom near the bridge has a wider curve. The two outer lines connecting the outsides of those two curves would not be parallel but would look like a cross section of a tee-pee with the top and bottom cut off.

Eebster the Great
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Re: A rectangle with rounded edges is not an oval

Does that mean this shape, which Wikipedia says is an oval in the formal sense used in technical drawing, would be a "compound radius"? It has no straight edges, but every point on it is on (at least) one arc.

Cleverbeans
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Re: A rectangle with rounded edges is not an oval

tckthomas wrote:EDIT: mine would be ellipse and not an oval

Don't forget to tell that girl you were mistaken. Humility is important in mathematics because we all make mistakes and if we ignore them instead of correcting when pointed out to us then we'd make no progress.
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Re: A rectangle with rounded edges is not an oval

Cleverbeans wrote:
tckthomas wrote:EDIT: mine would be ellipse and not an oval

Don't forget to tell that girl you were mistaken.
tckthomas wasn't the OP, though.
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brenok
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Re: A rectangle with rounded edges is not an oval

gmalivuk wrote:
Cleverbeans wrote:
tckthomas wrote:EDIT: mine would be ellipse and not an oval

Don't forget to tell that girl you were mistaken.
tckthomas wasn't the OP, though.

Also, telling her about a mistake they made 6 years ago would be pretty strange.

cphite
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Re: A rectangle with rounded edges is not an oval

brenok wrote:
gmalivuk wrote:
Cleverbeans wrote:
tckthomas wrote:EDIT: mine would be ellipse and not an oval

Don't forget to tell that girl you were mistaken.
tckthomas wasn't the OP, though.

Also, telling her about a mistake they made 6 years ago would be pretty strange.

I can just picture it... there she is, standing alone in some park, he walks up to her and says "You were right."

"I was... what?" she says, reaching tentatively for something in her purse.

"The desks. They were in fact in the shape of an oval."

"The... desks... who are you?"

"You were right. Just because the lines were parallel doesn't mean that... No, wait!" *Psssst!* "MY EYES!!! AGGGGGHHH!!!"

He falls to the ground in pain, trying to cry the burning from his eyes, the quick sound of her footsteps fading quickly away...

Trebla
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Re: A rectangle with rounded edges is not an oval

cphite wrote:I can just picture it... there she is, standing alone in some park, he walks up to her and says "You were right."

"I was... what?" she says, reaching tentatively for something in her purse.

"The desks. They were in fact in the shape of an oval."

"The... desks... who are you?"

"You were right. Just because the lines were parallel doesn't mean that... No, wait!" *Psssst!* "MY EYES!!! AGGGGGHHH!!!"

He falls to the ground in pain, trying to cry the burning from his eyes, the quick sound of her footsteps fading quickly away...

That's pretty much the exact scenario I was imagining... except in mine there was kissing instead of mace in the face. Falling to the ground still followed, but in a different manner.