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

Table of contents

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:

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
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Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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