# Tag Info

Accepted

### How can this shape perfectly cover a cube?

The shape Using this, we can make a guess for how the cube might be folded: Once that fold is done, the shape looks more like this: A drawing of the finished product: And an animation of the whole ...
• 136k
Accepted

### How can 64 = 65?

This is a famous physical puzzle that can be tied to the fibonacci series. To answer the question as posed, the issue is that the two slopes are different ($\frac25$ vs $\frac38$). Note that all ...
• 22.3k

### How can 64 = 65?

The diagram is misleading, as it hides a gap in the middle of the second configuration. This is what we actually get if we rearrange the shapes in question. Notice that the diagonal “bows” slightly, ...
• 2,487
Accepted

### Prove that π > 3

I didn't have a knife with me, so I only used my unit circle cookie cutter to split each square like this: I then rearranged the parts into this shape: Since the angle covered by this shape is ...
• 68.2k
Accepted

### Chaos and Order: a visual puzzle in stained glass

Solved it! Spoilers ahead: P.S. I think this window is brilliant :-)
• 9,461
Accepted

### Can you fold a square into a square of one-fifth the area?

The way to do this is:
• 136k

### Join all circles together only with 6 lines

If you use just one massive line, you can make it pass through the center of all of the circles!
• 1,220
Accepted

### Turning a goat?

Here's the image equivalent: Apologies for the poor quality image. My office laptop has very limited capabilities in image editing.
• 11.6k
Accepted

### Can you perfectly wrap a cube with this blocky shape?

This seems to work: Below, I printed out the shape, and cut off the excess. The white parts are for glueing; if everything works out as planned, all of them will be covered by the coloured bits ...
• 68.2k

### Simple geometry. Or is it?

I know the answer is already given but I'd like to show an easy explanation of why the 2 planes are coplanar. Take this image: Consider two pyramids sitting side by side, and draw a line between ...
• 10.9k
Accepted

### The Jeweller's Dilemma

It is Proof/construction: Even more strongly,
• 23.6k

### Join all circles together only with 6 lines

Here's an option that uses only 4 lines. You can extend the concept to place another 2 lines if you really want 6 ...
• 1,085

### Join all circles together only with 6 lines

By mapping the puzzle onto a cylindrical topography, I've solved the puzzle using only a single straight line.
• 855
Accepted

### Is it always possible to balance a 4-legged table?

The answer is Here's why: More detailed proof:
• 136k
Accepted

### Cover 63 squares of a chess board

These should do it: Just to show another example:
• 5,130
Accepted

### Six pyramids in a cube

The answer is because the volume of a pyramid is proportional to its height, and we know that each pair of opposite pyramids together has the same total height. Therefore, all three pairs of pyramids ...
• 1,981

### Can you perfectly wrap a cube with this blocky shape?

The shape can be folded like this
• 10.7k

• 11.6k
Accepted

Explanation:
• 536
Accepted

### Help the prisoners

You can't. Color them like a checkerboard - the top-left-front cell is black, and the ones adjacent to it are white, and the ones adjacent to those are black... Each prisoner in a white cell must ...
• 136k

### Turning a goat?

I've found a simpler solution that doesn't rotate the entire goat! See the image below for a visual explanation.
• 2,834
Accepted

### Create a 3 inch measurement

I can do it in folds, by
• 4,361

### Odd-looking circle

He has made a rapid escape from the scene because he actually didn't know what a "circle" was. No wait.
• 591
Accepted

### Join all circles together only with 6 lines

I think this is one possible solution:
• 751

### The Jeweller's Dilemma

It is possible! How is that polyhedron? WTF!? How!? It is hard to understand? So let's visualize that with $k = 90^\circ$: Let's see some properties of this particular polyhedron: Ok, but how ...
• 8,828

### Folding paper into corners

I managed to make Like so:
• 20.9k
Accepted

• 5,259

### A new way to cut a pizza

This paper by Joel Haddley and Stephen Worsley answers a slightly different question - finding monohedral disc dissections where not all pieces touch the centre - but the results generally apply to ...
Accepted

### Cut the disk with a hole in four equal pieces

Here's one solution: I assumed the radius of the hole's curvature matches the curvature radius of the circle, the hole's straight side is equal to the circle's radius, and its curved edges meet the ...
• 515
$\hskip 1.5in$ This is an image of an arrow sweeping each of the successive angles in the star. Notice that, after it traces all $5$ angles, its orientation is reversed - meaning it has rotated \$180^{...