16 circles

[Itsallaguess]

This image has 16 circles in it -

https://i.redd.it/3ul70f62uoez.jpg

Can you spot them?

Itsallaguess

[redsturgeon]

Yes

Weird though

John

[UncleEbenezer]

The clue is in the number, if they're not immediately apparent.

But those 'circles' are from the pixellated days of about 1980!

[jfgw]

The clue is in the number, if they're not immediately apparent.

But those 'circles' are from the pixellated days of about 1980!

Polygons rather than circles. I might be being a bit too pedantic though.

Julian F. G. W.

[redsturgeon]

The clue is in the number, if they're not immediately apparent.

But those 'circles' are from the pixellated days of about 1980!

Polygons rather than circles. I might be being a bit too pedantic though.

Julian F. G. W.

Isn't any circle just a polygon with a infinite number of small sides?

John

[Gengulphus]

Isn't any circle just a polygon with a infinite number of small sides?

No - that's a loose description of something that is true, but no more than a loose description.

One mathematically accurate way (not the only one) of expressing that truth is that a circle of radius R centred at a point P is the limit as N tends to infinity of any series of N-sided regular polygons with side length 2*pi*R/N centred at the same point P. But in general, the limit of a series of Xes need not be an X itself, so such a limit need not be a polygon itself, and in this case the circle is not itself a polygon.

Another example of that general principle is the series of rational numbers (*) 1/1, 3/2, 7/5, 17/12, 41/29, 99/70, ..., where each term is produced from the previous one by changing a/b to (a+2b)/(a+b). The limit of that series is SquareRoot(2), which is not a rational number.

(*) I.e. numbers that can be expressed as fractions, without necessarily having to lie between 0 and 1.

Gengulphus

[redsturgeon]

Isn't any circle just a polygon with a infinite number of small sides?

No - that's a loose description of something that is true, but no more than a loose description.

One mathematically accurate way (not the only one) of expressing that truth is that a circle of radius R centred at a point P is the limit as N tends to infinity of any series of N-sided regular polygons with side length 2*pi*R/N centred at the same point P. But in general, the limit of a series of Xes need not be an X itself, so such a limit need not be a polygon itself, and in this case the circle is not itself a polygon.

Another example of that general principle is the series of rational numbers (*) 1/1, 3/2, 7/5, 17/12, 41/29, 99/70, ..., where each term is produced from the previous one by changing a/b to (a+2b)/(a+b). The limit of that series is SquareRoot(2), which is not a rational number.

(*) I.e. numbers that can be expressed as fractions, without necessarily having to lie between 0 and 1.

Gengulphus

You can tell who is and is not a mathematician here

Would it be true though that any representation of a circle on an LED screen will be a polygon?

John

[UncleEbenezer]

You can tell who is and is not a mathematician here

Well, I'm a long-lapsed mathematician, and he regularly impresses me.

Would it be true though that any representation of a circle on an LED screen will be a polygon?

John

No. As with those circles, it'll involve more than a mere geometric shape: for example, it might use anti-aliasing. And that's with the assumption that an LED screen is necessarily a rectangular grid of fixed pixels!

[BobbyD]

This image has 16 circles in it -

https://i.redd.it/3ul70f62uoez.jpg

Can you spot them?

Itsallaguess

Is it a sail boat?

[BrummieDave]

That's a great illusion and shows just how easily the brain can be fooled by the eyes.

I stared at it for a good three minutes before I saw the gorilla walking across the screen.

[cinelli]

This reminds me of those pictures which were popular a few years ago. If you stared at them in the right way you would see three-dimensional dinosaurs. Try this one for size:

http://www.vision3d.com/sghidden/dino.html

Cinelli

[BobbyD]

That's a great illusion and shows just how easily the brain can be fooled by the eyes.

I stared at it for a good three minutes before I saw the gorilla walking across the screen.

My favourite is this one.

Which square is darker A or B?

https://images.chesscomfiles.com/proxy/upload.wikimedia.org/wikipedia/commons/6/60/Grey_square_optical_illusion/https/e8340fa1aa.PNG

https://en.wikipedia.org/wiki/Checker_shadow_illusion