Table of Contents

## Number order

The way you organize your numbers for math goes by many names

A number system is an ordered list of numbers, typically starting with one number: 0, also known as zero. The most common number system has ten values, beginning with 1 or 1 rather than 0. Numbers are placed after the other in line to place them, from highest to lowest.

In this ordering, each numbered position can be considered equally empty, high, middle, and low. This follows since 10=2*5; that is, every integer (any whole number) can be expressed as the sum of its digits.

The second number system does not have any commas or spaces, only congruent symbols, so 18 = 9 +9, 2 * 4 = 3+3, and 8/4 = 2. Some further properties are listed below.

These two number systems are **called positional numeral systems** because the meaning of the words is dependent upon the position of the digit in relation to the others. Since we normally write down numbers in this way, it’s very easy to understand what they mean.

However, before computers, measuring things was done according to how many points there were in the scale. Even today, *printed recipes give quantities* in terms of “hundredweight” or “pounds.” In fact, my recipe book from **twenty years ago says everything weighs** a hundredweight now.

Since weight is a unit

## Arithmetic progression

An arithmetic sequence is a series of numbers for which the difference between each consecutive number is constant. For example, considering the sequence 2, 4, 6, 8 would be an arithmetic one because there is a gap of two between each number.

The same concept applies to trends in math performance. One approach to working with ARAR (are consistently arithemetic sequences) is to consider how you could increase the interval between each new term in the set.

For analysis purposes, we will assume that these are individual terms (also known as digits). Here’s what you need to know about the vocabulary used here: Each *word represents ten letters*; words differ only by their suffixes (this includes phonetically equivalent letters), e.g., “-ORG” and “-ER”; all the words have a length of seven syllables; words can be found within articles, books, and online dictionaries.

To determine the frequency of a word, count how many times it appears in your sample text and divide by the total number of words in the article or book. To *test whether two samples come* from the same distribution, you can use a statistical test called the sign test.

## Geometric progression

A geometric progression is a sequence of **numbers multiplied together followed** by one number. For example, this **toy store sells torches** for $9.99, light bulbs for $4.99, and flashlights for $2.49.

These prices are all divided up into multiples of 11 cents. The torch cost $*11 plus whatever extra* you might want to spend.

The bulb price is $10 minus 3% sales tax, for a total of $8.90, and so on.

Thus, it’s easy to see that these prices form a geometric series, also known as an arithmetic progressions. It’s defined as follows: G(n) = n1^(k+1).

In this case, we have a base term of “$11” and then we multiply it by itself (n + 1) times to get the next value in the sequence.

For instance, the first time you go to the grocery shop you pay $11, the second time you pay $22, and the third time you pay $25. I made the math easier by adding 5 more times than it really is.

Here’s what it looks like when you graph the function:

Once you know how to calculate a geometric progression, you can use it in many places. One example is when you need to increase your *savings amount significantly*.

You can do

## Exponential progression

An example of exponential growth is the way a tree grows. When a seed is planted, it starts with one root that gradually extends its reach through the soil.

As it spreads, other roots do the same thing. Before you know it, *many new plants* have made their home inside the little branch that originally belonged to just one.

The plant’s now grown together with these other branches and this newer group of roots has become what we call a tree. It extends its existence through time by *growing outward —* only this time, instead of using the soil as food, it uses energy from photosynthesis to grow itself.

Throughout history, humans have recognized how quickly life can spread. As such, they’ve spent millions of years working out ways to prevent it. From drilling holes in rocks to **throw away potential seeds**, to building walls and fences to fill up space, our ancestors have developed tools and techniques for **keeping things small**.

Today, we also have vaccines and antibiotics to keep things under control. The problem is that these technologies are expensive. Without them, no amount of regulation will be effective.

## History of math

The history of mathematics is full of examples of how we learn the art of calculation. Many people don’t consider it to be an art form, but I feel that calculated ways of solving problems are fundamental to what **makes us human**.

We can calculate who will win when there is a fight between two men or women. We can calculate how **long something takes** to build or destroy.

We can even calculate how **many days remain** until winter ends with cold weather.

## Center of mass

In physics, center of mass is an *important concept related* to both kinematics and dynamics.

If we have two or more objects that are connected (for example, by joints) then their centers of mass will be **located differently within** their construct.

When dealing with *many objects linked together*, one can either consider them as *individual objects owned* by different people or groups of objects belonging to the same person/group.

In most situations, it doesn’t matter which approach you use, but for this section, we’ll work with several objects belonging to one person and their surrounding environment.