Contents

# Units

## Introduction

Math Touch has an automatic, extenisble, dimensional-analyzing unit-conversion engine built into its core. Math Touch keeps a database of units, categorized by their dimension, and automatically converts values you enter to and from the appropriate units. This means, you don't need to enter "consistent" units into equations. (i.e. you can use "m" and "km" in the same equation but still arrive at the correct answer) And you may even mix units from different systems. (i.e. mixing "mph" with "meters"). When Math Touch needs to calcualte a value for you, it will check what your preferred unit is for the dimension of the result, and automatically convert the solution to that unit. In fact, when calculating trig functions, Math Touch will automatically convert to radians as necessary, if your value is in degrees. In general, Math Touch will prevent you from entering a unit in the wrong dimension into an equation by giving you a warning. It can, in certain cases handle units it doesn't already know, either by cancelling them out, or by recognizing them as a prefix to a unit it does know.

The one requirement for making this work is that you must always type the units of the numbers you enter. For instance, when entering the length of something into an equation, you may not enter "12" but must specify the units like so: "12 m" or "12 in". A number without a unit is interpretted as dimensionless, which is sometimes its own dimension! (For instance, if you must enter an angle, and you merely type "π", Math Touch will assume "π radians") Always enter units afer typing a number, i.e. type "12 in" not "in 12". Any precisions or imaginary values must also be entered before the unit names.

For more information about how Math Touch performs dimensional analysis, recognizes units, the warnings Math Touch will give you for errors, or how you can modify the database of units, see the appropriate subsections below:

Dimensional Analysis

The Unit Database

Unit & Dimension Warnings

## Dimensional Analysis

Dimensional analysis can be a confusing term at first, but basically it means keeping track of the physical significance of units. There are "base" dimensions and "Composite" or "derived" dimensions. "Base" dimensions are completely independent from each other. Composite dimensions are made up of base dimensions.

### Base Dimensions

Depending on your unit system, different dimensions are base and composite, but in Math Touch, the base dimensions are: Length, Time, Mass, Temperature, Electric Charge, Memory, Angle (dimensionless).

### Composite Dimensions

All other dimensions are composed of base dimensions. For instance, "Speed" is Length divided by Time. "Momentum" is Mass times Speed. "Acceleration" is Speed divded by Time.

## The Unit Database

Math Touch maintains an extensive database of physical units, conforming to the United States' National Institute of Standards and Technology (www.nist.gov) standards. As part of this standard, the SI (Systeme Internationale, i.e. International System) such as meter are reconciled with the Imperial (i.e. English) units, such as foot.

### Recognizing Units

When you enter a physical value for any variable, Math Touch will attempt to determine its units. For your text that doesn't appear to be numbers, Math Touch will separate the units names by spaces that you have typed, then looks for the those unit names in the database. Thus, while spaces in the names of your units are allowed, either the name, plural or symbol of a unit should be unique and have no spaces. Plurals are optional. Names and symbols are not optional unless you are creating a composite unit to be set as the preferred unit, (i.e. creating a new unit with a definition of "m/s" but no name, plural or symbol, then setting it as the preferred unit in the Speed dimension). Capitalization differences are respected, but if not matching unit is found requiring capitalization to match, a second search will be done without requiring that capitalizaiton match.

Values are sometimes entered as a combination of other units. For instance, acceleration due to gravity at the Earth's surface is approximately "9.812 m/s^2". The carrot ("^") indicates a power, which in general will be an integer. Entering this text exactly as shown here will work, and there are also special characters to enter the superscript 2 power.

Regarding the division symbol, there are two caveats: 1) it is not necessary to separate the division symbol "/" with spaces from units names, and 2) the division symbol may be used only once for each value, entirely separating the units in the nominator on the left, from the units in the denominator on the right. For instance, "1.57 m kg/s s" would be recognized identical to "1.57 m kg s^-2", not a reduced "1.57 m kg". When displaying such unit values, Math Touch always uses a division symbol to display such composite units, and always lists each unit symbol only once, using a superscript to indicate a non-unity power. This is not exactly the standard form in science, but is generally more convenient to read in limited space.

In version 1, Math Touch does not perform math function when entering values, nor does it allow mixed unit notation. I.e., you may not enter "2 m + 1 in" , nor "5 lb 3 oz", nor "5º 2'". Such notations work at different purposes to Math Touch's main objective. The "2 m + 1 in" example would require "interpretation" which is not allowed on the iPhone, and the "5 lb 3 oz" is would technically be multiplication, which is not the user's intent.

### Creating or Modifying a Unit

To create or modify a unit, when viewing the units in a dimension, tap the "Edit" button. To modify a unit, select it; to create a new unit, tap the "+" button, then "New Unit." This will take you to the unit editting page. Once there, you are free to change the name (i.e. "foot"), plural form (i.e. "feet"), symbol (i.e. "ft"). For new base units, the "definition" is left empty. For units that depend on other units, enter the dependence in the "definition" field (i.e. "12 in"). Most unit conversions are "pure," which means their significant figures as entered do not impact the precision of the result. Once you have entered the appropriate text and dismissed the keyboard by pressing "Done", the "Pure switch" is visible. By default it is "On," but if your conversion has an associated precision, turn it off and Math Touch will consider the precision of your entry.

If you enter a name, plural or symbol that has been already used, Math Touch will refuse to allow it, since unique text is the only way Math Touch is able to recognize units you enter. This means that all of your symbols must have a unique name and symbol.

Here are the rules for new and modified unit names, symbols and plurals. 1) Names, symbols and plurals may not begin with numbers or math operators, such as -, +, ^, ±, /, !, or ., and they may not contain any superscript number or character. Numerical multipliers such as "π", "∞" and "i" as unit names may cause confusion with numbers and should be avoided as first characters. 2) All names, symbols, and plurals must not conflict with any other unit's name, symbol or plural. Differing in capatalization only is allowed. For instance, "c" and "C" would be allowed as unique symbols. A single unit may use the same text as its name, symbol and plural, but this is only seldom useful. 3) Symbols may not contain spaces. While names and plurals may contain spaces, hyphens are the suggested substitute. Math Touch will read units you type by splitting them at the spaces, so when a unit name contains a space, it will never be recognized. You may not use mathematical operators besides the hyphen-minus, such as "+", "/", ".". 4) While subscript 0 is available, other subscripts are not supported. 5) While most unicode characters are supported, the iPhone's keyboards may limit the characters you can use. Use the special keyboard to use some common characters the iPhone's regular keyboard does not support.

### Dimensions

The Math Touch units database is sorted by dimension. You may create new dimensions, re-name and re-sort them and delete them.

### Setting Prefferred Units

You may use units from different unit systems freely, they will be automatically converted as necessary. When units are calculated, however you have the choice that they be initially displayed in a preferred unit.
There are two preferences related to preferred units. The first is the unit system. If you prefer "SI" or "English" or "cgs" units, you may select your preference in the "Preferences" item in the information menu (the "i" menu). Simply select the system name you prefer, and all future calcualted units will be converted to the preferred unit in the appropriate dimension.
The second preference is for each dimension. In each unit system, each dimension has a preferred unit. To change the preferred unit in a particular dimension, go to the definition of the unit in the unit database, and edit it. Tap the "Set as Preffered Unit in System button," which will bring up a list of unit system names and the corresponding preferred unit name in each system. Select the system or systems in which you would like to set the current unit as the preferred unit.
Finally, any time a value is calculated, a unit conversion button appears next to it, you may tap this button and type in the units you prefer to see the value instantly converted.

### Offset Units

Degrees Celcius and Fahrenheit are not regular "units" per se, but they are so commonly used that Math Touch makes a special exception. They're already built-in, so you probably won't need to bother with them. Just remember that when using offset units, there are differences in absolute values and relative values. Note whether you see the "∆" character in the symbol's name, you probably want to enter a difference. If you have a difference in two values of 30 ºC, and you enter that value, Math Touch will think you had a difference of 303 K, not 30 K, which was your intent. Kelvin (K) and Rankine (R) are the "real" units that relate to Celcius and Fahrenheit, respectively. Consider using K and R instead of ºC and ºF when entering differences of temperature. As a side-note, it is remarkably common to use 100 ºC. However, this number has only one significant figure, many times, when specifying 100 ºC, it is the user's intent to specify "100. ºC" instead.

### Logarithmic Units

In version 1, "logarithmic" units (i.e. dB) are not supported in Math Touch.

## Unit & Dimension Warnings

### Wrong Dimension Warning

Many equations have variables that must be in a particular dimension. If you enter a value that is not in the required dimension, Math Touch will give you a warning and will not allow the value to be set. Math Touch will, however, suggest a unit for you to use in the warning pop up.

### New Prefix Unit

In the SI system, common unit symbols, like "m" can have prefixes that act as power-of-ten multipliers. For instance, "km" means "1000 m" and "mm" means "0.001 m". Because there are many units that use prefixes, and other common unit names that interfere with the prefix symbols, the prefixed units are generally not included in Math Touch when it is purchased from the AppStore. (One exception is "kg") However, if Math Touch encounters a unit name it does not know, it will look to see if the name appears to have a "prefix." If Math Touch finds a matching prefix and unit name, it will actually create the new unit definition, insert it in the database, and warn you that it has done so. This means that if you made a typo and accidentally created a new unit, you know to go find the unit and remove it. In general, it is not necessary to remove the automatically generated units, as they will always be a "correct" unit. The second time you use a prefix unit, you will not be warned, because the unit will already be in the database.

### Unknown Unit Name

If Math Touch encounters a unit name it does not know, it will create a temporary unit with an unknown dimension. While variables requiring a unit in a particular dimension will not allow such a value to be used, there are cases in which units cancel, allowing Math Touch to compute your answer without needing to know what the units are.