2.3 Game 2302-0330 scale factors, ratios, and proportions

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
• Discussion
  • Scale factors
  • Ratios
  • Proportions
• Run the scripts
• Miscellaneous

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The module provides a brief tutorial on scale factors, ratios, and proportions.

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1 . Screen output for Listing #1.
• Figure 2 . Screen output for Listing #2.
• Figure 3 . Screen output for Listing #3.

Listings

• Listing 1 . Exercise on scale factors
• Listing 2 . Circumference is proportional to radius.
• Listing 3 . Area is proportional to radius squared.

General background information

Mathematical expressions are used in physics to describe relationships that are difficult to express in words. The expressions use algebraic symbols to representquantities that consist of numbers and units.

Measurements are important

Conclusions that are drawn in physics and other sciences ranging from chemistry to the social sciences are often based on measurements such as length,width, weight, salinity, population, density, etc.

Each number in an equation often represents the results of a measurement, which is made in terms of a standard. The units indicate which standard was usedto make the measurements.

Knowledge of units is critical

A number that is used to indicate the result of a measurement is of little value unless we know the units in which the measurement was made. For example,it isn't very useful to know that the length of an object is 125 unless we know whether the units are meters, centimeters, millimeters, or miles.

The Google calculator

Although I won't go into detail in this module, I will tell you that the Google calculator is very good at helping you to keep track ofunits. For example, if you enter the following expression in the Google search box,

3 ft + 1 yd + 36 inches

The following result will be displayed immediately below the search box:

(3 ft) + (1 yd) + (36 inches) = 2.7432 meters

Discussion

We often express the relationship between two items using a scale factor.

Scale factors

For example, we might say that that a colt doubled its weight in one year. Thismeans that the colt's weight after one year was equal to the colt's weight at birth multiplied by a factor of two. The factor is the number by which aquantity is multiplied or divided when it is changed from one value to another.

Ratios

The factor is the ratio of the new value to the old value. Regarding the colt mentioned above, we might write: