Four Dimensional Hats: A Visual Wonder!

[Image courtesy of Brilliant.org.]

The mobius strip is one of the simplest objects in the world, and yet, the most mind-bending. If you take a strip of paper, add a single twist, and tape the ends together, you transform a two-sided object into a single-sided object. It becomes one continuous surface.

(We’ve discussed the concept briefly in the blog before, but in bagel form.)

But did you know that you can take that idea a step further and end up with this?

[Image courtesy of math.union.edu.]

This is a Klein bottle, an object with one continuous surface. If you trace a path along the surface, you will traverse from the “inside” to the “outside” and back again without breaking stride.

Yes, the word “bottle” is a bit of a misnomer, since this won’t actually hold any liquids; they would just flow along the surface, going “inside” and back “out” without pooling anywhere. This is a result of a mistranslation, as the German word “flache” (surface) was translated as “flasche” (bottle).

This limerick sums up the Klein bottle nicely:

A German topologist named Klein
Thought the Mobius Loop was divine.
Said he, “If you glue
The edges of two,
You get a weird bottle like mine.”

[Image courtesy of Pinterest.]

Although the Klein bottle can’t quite exist as a three-dimensional object — since the object has to pass through itself, which can only happen in four dimensions — we can come close enough to create some impressive approximations, like the glass “Klein bottles” pictured above.

YouTuber and physics student Toby Hendy has even managed to create a technique to knit yourself a Klein bottle hat! Check it out:

Although it’s not an optical illusion, it’s still a visual puzzle for the eyes and the mind, one that has captured the imaginations of mathematicians, artists, and many others throughout the years.


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It’s Follow-Up Friday: Blind Spot edition!

[No, not THAT Blindspot. Though friend of the blog David Kwong works on that show…]

Welcome to Follow-Up Friday!

Follow-Up Friday is a chance for us to revisit the subjects of previous posts and bring the PuzzleNation audience up to speed on all things puzzly.

And today I’d like to return to the subject of optical illusions.

[Image courtesy of Geekologie.]

We’ve discussed optical illusions many times in the past, covering everything from the Necker Cube to the Dress, but today’s illusion is a little bit different.

The 12-dot optical illusion pictured above, also known as a Hermann grid, has been making the rounds lately, and although many puzzlers have accused people of using a video or an animated gif instead of a simple picture, that’s simply not true.

This is a static picture, but our eyes are not designed to capture 12 dots in view at once, so the others vanish when you focus on one dot in particular.

And the folks at ASAP Science have an explanation for this phenomenon! As it turns out, this illusion and others involve both how your brain processes visual information and how the natural structure of your eye creates a blind spot that some optical illusions exploit.

Check out the full explanation here:

So next time someone shares one of these optical illusions, you’ll be ready to explain how they work and show off your puzzly knowledge.


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You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

It’s Follow-Up Friday: Carpet Conundrum edition!

Welcome to Follow-Up Friday!

By this time, you know the drill. Follow-Up Friday is a chance for us to revisit the subjects of previous posts and bring the PuzzleNation audience up to speed on all things puzzly.

And in today’s post, I’d like to return to the subject of visual puzzles.

We’re keeping it simple today. In this photo that’s been making the rounds on Facebook and Reddit, can you find the iPhone?

Let us know if you spotted it! It’s tougher than you might think!

Happy Friday!


Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!