### Background on forced perspective photography

Forced perspective photography is a trick of the camera that can make things look wildlyÂ bigger or smaller than they really are. The effect works by arranging things at varyingÂ distances in front of the camera. Objects that are further away look smaller. ObjectÂ that are closer look bigger.

Size Wise uses this camera trick to help youÂ do real-world proportional reasoning while youÂ take funnyÂ photos of yourÂ friends and make measurements.

In some activities, you’llÂ explore the ratios ofÂ image sizes of various things onscreen. Itâs fun toÂ physically control what the image size will be and start toÂ visualize these ratios.Â In other activities, youÂ will explore the moreÂ complicated proportional relationships between image size, object height and objectÂ distance. Depending on which variables are manipulated in each activity and which areÂ held the same, youÂ will explore relationships that are either directly proportional orÂ indirectly proportional.

### Whatâs Going On?

The primary relationship you’llÂ be exploring can be expressed this way:

Image Size is related to Object Height / Object Distance

Direct Proportion

In some activities, youÂ make everything look the same size and manipulate objectÂ size and object distance. For example, youÂ may arrange everyone in class to look theÂ same size onscreen, or youÂ may line up their height with the virtual giraffe. If you holdÂ image size constant, then

Object1 Height / Object1 Distance = Object2 Height / Object2 Distance

Here, there is a direct relationship between object height and object distance: as oneÂ value increases, the other value increases. In order to match image sizes, objects thatÂ are 2x as tall have to be positioned 2x as far away.

Indirect Proportion

In other activities, the object remains the same and it gets positioned at differentÂ distances in front of the camera. For example, when a youÂ move back further andÂ further from the camera in the course of multiple pictures. In this case, youâre holdingÂ object size constant, so:

Image1 Size * Object1 Distance = Image2 Size * Object2 Distance

Here there is an indirect relationship between image size and object distance: as oneÂ value increases, the other value decreases. In order to make someone appear 1â2 asÂ big, she has to stand 2x as far away.

### Math in the Real World

Because these activities use real-world measurements, the mathematical relationshipsÂ will be approximate and not exact. Even though more accurate measurements will yieldÂ more precise data, there are lots of opportunities for error. YouÂ will need toÂ become comfortable with approximations. Graphing data can help reveal relationshipsÂ that are hidden in abstract numbers, since human beings are skilled at recognizing visualÂ patterns.

### Language

Itâs very easy to look at a forced perspective image and say something like, âLook, sheâsÂ the same size as the Leaning Tower of Pisa!â But of course they only look like theyâre theÂ same height. Neither the actual person nor the building has changed size at all. ExtraÂ care with language is required to distinguish between the size of an image and theÂ height of an actual object. But since both image size and object height are values that youÂ talk about in these activities, itâs often vital to be clear.

### Why Does This Effect Work Better in Photos Than in Real Life?

Your brain uses more than just image size to judge distances. A very important signal isÂ the difference between what your right and left eyes see. Since your two eyes are inÂ slightly different positions, they see slightly different views of the world in front of you.Â Your brain interprets those differences to place things in 3D space. Since the camera hasÂ only one lens, it strips away any extra information from having two eyes.

There are other things that affect how you judge distances. Your brain gets clues fromÂ how objects overlap, how they interact with the background, or whether things are inÂ focus. Controlling for these things can make the forced perspective trick work better.

### Tutorial

Here’s a brief tutorial to help you get up and running with Size Wise.

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