QBasic 64 : Arithmetic Stuff

Mine! Mine! Mine! It’s my stuff.  Infants and even seagulls  intuitively learn how to count by tracking and accounting for their stuff.  Arithmetic was invented to keep track of stuff.

Children are delighted when they increase or add to their stuff.  It is no wonder addition was the first arithmetic operation to be created.  In QBasic the addition symbol is “+”

Children are sad when they have to give up or subtract their stuff.  In QBasic the subtraction symbol is “-“.

Happy days are here again when children learn multiplication  is a form of accelerated addition.  In QBasic the “*” is the symbol for multiplication.

Another sad event is when we have to give up or divide stuff.  Think of multiplication in reverse.   

In QBasic the “/” is the symbol for multiplication. 

Examples of QBasic arithmetic would be:

Num1 + Num2 = Ans1

Ans – Corr = Diff1

Num 1 * Num2 = Prod1

Prod1 / Num2 = Quot1

  

These are the four basic arithmetic operators in QBasic.

Mine mine mine (Finding Nemo) posted by as0k

George Carlin Talks About "Stuff" posted by CappyNJ

The Number Family

The number family is large a collection of numbers, actually an infinite collection numbers.  Some numbers  are prime while the majority are composites of other numbers.  Every family has it’s negative members but they are usually offset by the positive members.  There is only one zero in the family it is neither negative or positive.  

The earliest numbers were simple whole counting numbers.  Some people call them the natural numbers but there was nothing natural about zero which didn’t come into use in Western mathematics until about 1200 AD.  Are the un-natural numbers zombie numbers, vampire numbers or invisible numbers?

The un-natural numbers are a little complicated to conceptualize. They are real numbers and can be very rational at times and irrational at other times.  Integers are whole numbers which can be positive, negative or zero.  (In QBasic we can define variables as integer numbers.)

Rational numbers are really ratio-nal numbers because they can be expressed as a ratio of integers and do not have a denominator of zero, ¼, 7/27, or 5/1.  Rational number can also be divided and expressed as decimals although some quotients result in very annoying repeating decimals which go repeating for infinity and beyond but are predictable. (In QBasic we define non-integer numeric variables as floating numbers.)

Most disturbing are the irrational numbers.  The most famous irrational number is pi or for really hungry people, pie.  Pi is a mathematical constant of the ratio of a circle’s circumference to its diameter.  The quotients of irrational numbers do not repeat but go on forever and ever like fairy tales.

The discovery of irrational numbers was not a fairy tale.  The Greek philosopher Hippasus is believed to have discovered irrational numbers in the 5^th century BC when tying to compute the square root of the number two.  Pythagoras  (yes, from the famous theorem a^2+b^2=c^2 where “^” is exponentiation in QBasic) and his Pythagorean School did not believe in irrational numbers.  Rumor has the Godfather of the Pythagorean gang was very upset with Hippasus who ended up sleeping with the fishes. 

There is a conspiracy theory Hippasus was drowned in the ocean for revealing the existence of irrational numbers.  When programming in computers, keep your mind open for all possibilities. Some people believe Humpty Dumpty did not fall off the wall, he was pushed.  

“The Godfather - Luca Brasi Sleeps with the Fishes” - Posted by TheFilmSpectrum.

“Humpty dumpty was pushed” – Posted by FAproduckshins

A Lot of Something About Nothing - Zero

Most people are familiar with Roman numeral counting such as I, II, III, IV, V… representing our number of 1,2,3,4,5……

So then, what is the Roman numeral for zero?

There is no Roman numeral for zero as zero did not come into play into Western mathematics until about 1200 A.D.  The ancients did not really require the use of zero in their arithmetic.

Although zero is nothing, our mathematics is nothing without it.

The divisibility rule for zero is undefined.  Try dividing a number on your electronic calculator or in a computer program and it will return an error code.  Undefined is a term used when mathematicians have problems explaining a concept.  

Below is an interesting video “Zero and One” posted by TheAlexmeister:

For a historical perspective, the “Math Movie Zero” posted by SpookyKat4 provided different insight:

You Can’t Handle The Truth: Ten

Children are most familiar with ten as the base of the decimal number system we commonly use in our mathematics. 

Scientists, mathematicians, anthropologists, sociologists, historians and philosophers all tend to agree we use base ten as our number  system because humans have ten fingers or digits. Really? They are in denial.  You want answers?  Do you really want me to answer the question why we use base ten?  You think you’re entitled to the truth?  You can’t handle the truth!

The truth of why we use base ten is stinky feet.  Humans have twenty digits, on two hands and two feet.  Why not use the digits on our toes for advanced counting?  You would double the size of your number system with a base twenty system. 

However, people of the ancient past stepped in a lot of doo-doo and other nasty stuff.  Even the most primitive people wore shoes of some type so not only did their feet smell but it was a hassle taking on and off your shoes every time you had a number ( >=  ) greater than or equal to eleven to manipulate in a calculation.  This is one reason why humans invented the abacus, so they didn’t have to use their toes for counting.  The abacus was the first computer made of wood.

It was the most decent act of human kindness to our noses use ten the base of our number system.  The divisibility rules for then are simple.  If a number ends in zero, it is divisible by ten.

Classic Movie Line #15” posted by DiNap44. “funny commercial ! (stinky feet)” posted by seknight86.

Love Potion Number Nine

There’s something magical about the counting numbers, 1,2,3,5…

They are whole numbers and almost seem natural to us.  Did you ever notice almost everything we enumerate are whole numbers.  You never see sports jerseys with numbers such as 3.2, 9.8,  4 and one fourth, 50% or the square root of sixteen.  My favorite sport jersey numbers are three (Anthony Paultanis), six (Al Kaline) and nine (Gordie Howe).

The barcodes (UPC or Universal Product Code) you see on almost every product you can buy at a store are whole numbers.  Vehicle license plates displayed on the back of cars and your social security numbers are whole numbers.  Home addresses and locker numbers in school are whole numbers.

The last single digit counting number is nine.  Nine is a composite number with factors of three.  The divisibility rule for nine is similar to three.  Add the digits of the number and if it is divisible by nine the entire number is divisible by nine.

In the very olden days, “Love potion number nine” by the searchers was a hit posted by barbieaslenkho. 

I think the greatest athlete to wear the number nine on a sports jersey was Gordie Howe of the Detroit Red Wings hockey team.  Nicked named “Popeye” by his teams mates for his muscular build, he went on to play for other hockey expansion teams in Houston and Hartford.  He played hockey with his sons and retired from professional hockey at the age of fifty-two.  I watched Gordie Howe in many games.  When he took a hit from someone, he didn’t retaliate right away.  He would “take your number” and cream that player later in the game.  When he went into the hospital for minor surgery, everyone in the National Hockey League thought he was going in to get his elbows sharpened.  A video posted by NYIandersFan21.

Byte Me!

In early personal computers, eight was and still is a magic number . It is a composite number and it is the cube of two: 2 x 2 x 2 =8 or two raised to the third power.

                                   

You see and use bytes all the time.  The file is fifty kilobytes or there is three gigabytes of memory on my memory stick or you have a gigabyte of random access memory(RAM).

A byte is a unit of data eight binary digits (0,1) long that represent a character such as a letter, number or symbol.  Bytes can from combinations of 256 characters which form our alphabet, numbers and special symbols.  Yes, two raised to the 8^th power is 256. (2x2x2x2x2x2x2x2=256)

Byte are used to measure random access memory in computer.  In 1969, one of the most powerful computers had a RAM of four kilobytes that launched men into space sending them to the moon.

Today’s kids have two gigabytes or RAM and they are lost in space playing on computers Minecraft or Facebook.  With all the time kids spend on computers, parents would like to send them to the moon.

The divisibility rule for eight is if the last three digits are divisible by eight, the entire number is divisible by eight. Well, use a calculator. 

Below is a video posted by WOODSYMAN which a good introduction to bytes:   

Since you are working on electronic projects using circuit boards, this video gives a little different perspective about the flow of electricity.  Posted by KarBytes:

Sieben Zwerges

Snow White and the seven dwarfs.  Heigh -ho. Heigh-ho, it’s off to work we go. Seven is a prime number but you’ll need to work to figure out if a number is divisible by seven.

Here is the rule, take the last digit in a number.  (a) Double that number then (b)subtract the doubled number from the rest of the digits.  (c) If that number is divisible by seven then the entire number is divisible by seven.

For example,  672: a) 2*2=4     b) 67-4=63     c) 63/9=7  okay

                      357: a) 7*2=14   b) 35-14=21   c) 21/3=7  okay

This is a technique you’ll need if you’re ever stuck on a deserted island in the middle of some ocean,  if there a thermonuclear holocaust which wipes out civilization as we know it or if you are taking a manual math test. Otherwise, since you live in the 21^st Century, just use a calculator.

Schneewitchen und die sieben Zwerge posted by lemmatt:

Four Dimensions

Four is the first composite number.  Four and two are good friends.  Two times two is four.  Two is a factor of four.  Two plus two is four.  Two squared is four.

For the ancients there were four elements, fire, air, water and earth.

We live in a four dimensional universe that appears to be three dimensional.  The is up, down and sideways, or X,Y and Z. 

Einstein considered time a fourth component of dimension.  Even though we cannot see time we sense know we are moving through time and space.

When you think of the divisibility rules for four just remember fours best friend two.  If the last two digits of a number is divisible by four, the entire number is divisible by four. 

Three: Getting Crowded

The number three is three times the number one.

Two is company but three’s a crowd.

Not that two is romantically in love with one or one is romantically in love with two.  One, two and three are the Three Amigos of Prime Numbers.  It is the first and last time you will see three consecutive prime numbers.

With three things gets complicated.  To determine if a number is divisible by three you need to add all the digits in the number to obtain the sum.  If the sum is divisible by three, that number is divisible by three. 

The Three Amigos Salute should be learned by all school children. (Posted by antonioorlandojr)

Two: Double Your Pleasure

The number two is double or twice the number one.

Two is the first even number and that make two a big shot in the world of even numbers.  Every even number is a composite number of two and is divisible by two.  In other words, two is the only even prime number.

If the last digit of a number is even, it is divisible by two. 

Two is usually easy to multiply.  Two is almost as popular as one.

For whatever reason, two is a big number for people on earth.  Humans have two legs, two arms,  two eyes and two ears. Since we have only one mouth but two ears, maybe listening is more important than talking.

“Here’s tip you’ll appreciate, it pays to have a smile that’s bright that make you look bright and make you feel just right….Double you pleasure, double your fun”....but for God’s sake, brush your teeth twice a day.

Video post by Videos78rpm:

One Is The Loneliest Number

It is the only one, the first one, the most famous one, the number one.  True that one is the first odd number but it makes one the ultimate prime number.    

Loved by children because it is easy to multiply and divide. It has a special property that is easy to understand.  Children cherish the identity property because any number times one is the same number.  Any number divided by one is the same number.  Easy…

Yet, most students in mathematics don’t recognize one when they see it.  One is a master of disguises. For this reason, the number one has undergone extensive psycho-therapy because children do not really understand one.   One is used extensively to manipulate fractions or has one calls fractions, mini me’s.

One can appear to small such as 2/2,  20/20 or very large 1,000,000,000/1,000,000,000 but they are just one.  One can be used to add and subtract fractions and simplify  fractions because one hates complicated fractions. One can be used to manipulate equations.

One is the most versatile number of all the numbers but the most misunderstood.  This make one the loneliest number.  

“One Is The Loneliest Number - Three Dog Night (Lyrics)” Posted by xxdaydreamerxx11: