The Lemon Fool

This image has 16 circles in it -

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

Can you spot them?

Itsallaguess

Yes

Weird though

John

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

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

UncleEbenezer wrote: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.

jfgw wrote:

UncleEbenezer wrote: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

redsturgeon wrote: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

Gengulphus wrote:

redsturgeon wrote: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

redsturgeon wrote:
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!

Itsallaguess wrote:This image has 16 circles in it -

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

Can you spot them?

Itsallaguess

Is it a sail boat?

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.

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

BrummieDave wrote: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