### Background on forced perspective photography

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

Size Wise uses this camera trick to help you do real-world proportional reasoning while you take funny photos of your friends and make measurements.

In some activities, you’ll explore the ratios of image sizes of various things onscreen. It’s fun to physically control what the image size will be and start to visualize these ratios. In other activities, you will explore the more complicated proportional relationships between image size, object height and object distance. Depending on which variables are manipulated in each activity and which are held the same, you will explore relationships that are either directly proportional or indirectly proportional.

### What’s Going On?

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

Image Size is related to Object Height / Object Distance

Direct Proportion

In some activities, you make everything look the same size and manipulate object size and object distance. For example, you may arrange everyone in class to look the same size onscreen, or you may line up their height with the virtual giraffe. If you hold 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 one value increases, the other value increases. In order to match image sizes, objects that 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 different distances in front of the camera. For example, when a you move back further and further from the camera in the course of multiple pictures. In this case, you’re holding 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 one value increases, the other value decreases. In order to make someone appear 1⁄2 as big, she has to stand 2x as far away.

### Math in the Real World

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

### Language

It’s very easy to look at a forced perspective image and say something like, “Look, she’s the same size as the Leaning Tower of Pisa!” But of course they only look like they’re the same height. Neither the actual person nor the building has changed size at all. Extra care with language is required to distinguish between the size of an image and the height of an actual object. But since both image size and object height are values that you talk about in these activities, it’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 is the difference between what your right and left eyes see. Since your two eyes are in slightly different positions, they see slightly different views of the world in front of you. Your brain interprets those differences to place things in 3D space. Since the camera has 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 from how objects overlap, how they interact with the background, or whether things are in 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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