Background Research:

Geometry: This is a branch of mathematics going through questions of shape, size, relative position of figures, and the properties of space.

The "Infinite Chocolate Bar" Riddle:

The Infinite Chocolate Bar trick involves cutting a chocolate bar into 6 pieces then rearranging it into a certain order somewhat resulting in an "extra piece" that seems to come out of nowhere.

The Big Picture: (The Subject)

• Geometry, Shapes, Dimensions, Puzzles, Chocolate

The Main Principles:

• Area and Dimensions of a Shape

Units:

• # of singular pieces of Hershey's™ Chocolate

Figures:

• *none

Introduction

The main purpose of our "Infinite Chocolate" experiment is to demonstrate how changing the parts of a whole chocolate bar can leave certain pieces of chocolate out.

Safety:

Be careful using the steak knife for you may accidentally cut and injure yourself or others.

Pictures

Essential Understanding

What Happened?

One square of the chocolate is then removed and set aside. However when the pieces are reassembled, in a different format this time, it resembles a full bar.

But How?

The trick works by spacing out the volume. By dividing the bar up and rearranging it, you are displacing enough chocolate to remove a whole chunk from the bar. This missing layer is equivalent to the square taken away, but is hardly noticeable because the viewer counts each square - and doesn't actually measure the chocolate bar. Unfortunately, although it seems that additional chocolate has been produced from thin air, it means that you have just as much chocolate as before.

Who Uses This?

This trick is used by illusionists, in order to play an optical illusion and mess with our brains.

How Does it Benefit Society?

This little experiment forces us to not count the total amount of little chocolate squares, but to measure the whole chocolate bar itself.

What are Some Benefits for the Future?

This riddle can help you with understanding the concepts of geometry and the puzzles it has to offer.

Investigation Questions

1. What geometric principles are applied to the chocolate in this demonstration?

Change in shape and volume are principles that were applied to the chocolate that made it infinite. When you geometrically change the slope of a chocolate bar from one side of chocolate to the other, you can create an infinite number of changes in the shapes for the volume of the chocolate bar.

2. How can this transformation be represented by one equation?

There are two formulas for area that are used in this experiment. The first is the area of a rectangle which is base times height. The second equation is the area of a triangle which is base times height divided by two.

3. Is the chocolate really infinite?

Yes, When all the pieces are broken off from the bar, while rearranging, the bar is ever so slightly increased in size, along the slant line while the other parts rearrange. If you don't increase the chocolate bar as stated above, the cubes don't really match up, and would leave a bit of space in between them. That's where the infinite chocolate comes from.

4. What makes the demonstration successful?

When a diagonal cut is made from the second bar on the left side up to the third bar on the right, it allows the person moving the chocolate to take out an extra layer along the width of the bar, making the third from row smaller. This missing layer is equivalent to the square taken, but it isn't noticeable since the viewer doesn't count each piece.