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Table of Contents

- Introduction To Zero In Maths!
- Introduction To The Number E In Maths
- Introduction To The Number I In Maths
- Introduction To The Number Pi In Maths
- Cool Math Games: Have Fun Learning To Remember Pi
- Introduction To The Golden Ratio
- Introduction To The Perfect Numbers In Maths
- Introduction To The Prime Numbers In Maths
- How to remember number sequences
- Ideas For Math Learning

Maths has existed since the dawn of time, according to the discovery of the Lebombo bone which is a baboon fibula that is over 35,000 years old. It is perhaps **the first calculation** of the calendar or menstrual cycle as it is a tally stick with 29 marks on it. It may also be proof of the first knowledge of prime numbers and multiplication.

While **mathematics may remain a mystery** to many of us. Math theorem like knowing the square root of each number, negative numbers, differential equations, fractions, an exponential statistics, logarithm, complex numbers, differential equations, mathematical modelling and other math concepts. Are seen by many mathematicians as an essential way to understand and analyse our world.

**Learning mathematics sometimes requires a certain degree of estimating**, but because its based on theorems which use logic. Its results can be described **objectively as correct** even if they are strange. This is true especially in terms of Geometry, Trigonometry (trig), Arithmetic, algebra or infinite calculus: our brains sometimes **have trouble understanding many of the concepts **of these numbers. But they often sound more complex than they really are, like the addition, subtraction, multiplication and division that used to seem impossible in middle school math. *With time you can learn to understand and answer all math questions.*

Today we introduce some of the most unique numbers of our time. Introducing zero, the number, the number I, pi, the gold ratio, Prime numbers and perfect numbers!

The simple number zero has a huge and long history. Photo Source: Unsplash

The simple number zero has a huge and long history which has been developed over centuries. **Coming from mathematicians in India** and finding its way to Europe where it was banned by the church for fear of it representing the devil. Slowly it began to be used by merchants on the streets and before long it grew into the zero that we know and use today.

- In Hindu, it was known as Shunya
- Then it was known in Arabic as Sifr
- In Latin it became Zephirum
- And later the word Zero was born

**Zero, the incarnation of emptiness**, the absence of quantity and nothingness, has many cultural, popular and philosophical representations. Both positive and negative, zero is neutral and is the only integer that returns the result to zero when multiplied by any other value!

Here Are Several Symbols Of This Value:

- The lack of value, the free,
- The completeness (100%),
- Renewal (hence the expression “starting again”),
- The egg: fertility, femininity, the fetus,
- The cycle, etc.

The number * e* has

- The ratio 2/7, for example, is equal to 0.285714285714285714 …
- Among all the decimals after the comma,
**the demonstration shows**the recurring sequence 285714 is reproduced to infinity.

- Among all the decimals after the comma,
- E, however, is equal to
*=*71828182845904523536028747135266249775724709369995957 …- There are more than 8,000 billion possible decimals that do not have a logical sequence.

Maths has existed since the dawn of time. Photo Source: Unsplash

The search for the square roots of negative numbers has led to the invention of complex numbers such as *i**. *The number I is **a purely imaginary number was invented to help scientists and mathematicians solve equations when the solution didn’t exist.** The number *i**, therefore,* makes it possible to envisage the extraction of the square root of a real number: the **root**** of -4 = 2i.**

Now **a set of complex numbers** is considered to be an extension of the set of real numbers which contain an imaginary number denoted *i. E**xponent (a; b) *such that *i** = square root of -1* and *i² = -1, * with the square of ( – *i) * as -1. The principle is that any number can be written in the form a + i *b,* where a and b are real, negative or positive numbers. The square root of -4 is, therefore, equal to 2 *i.*

- Any number of the form b
*i**,*where b is different from 0 is a pure imaginary. - This is why the numbers “square root of -4 = 2
*i”, ”*square root of -16 = 4*i”*etc. are imaginary numbers. - If the square root of -1 does not exist, we can not estimate exact or approximate decimals as we do for the
**roots of positive numbers**(example, the square root of 5 = 2,236). - The number i is thus a concept allowing to conceive a whole family of square roots of negative numbers.

Pi, **also known as the Archimedes constant,** is an irrational number. The Greek letter π was chosen from the Greek name περίμετρος which means perimeter, π is the symbol for pi. The simple definition of the number Pi is that it is defined as the ratio between the circumference (c) of a circle and its diameter (d). c/d=pi

Pi has been studied for thousands of years.

- Austrian astronomer C. Grienberger discovered pi to 38 digits of accuracy (3.1415926535897932384626433832795028841)
- British Mathematician and physicist Isaac Newton and German mathematician Gottfried Wilhelm Leibniz changed the calculating method and discovered pi to 15 digits of accuracy using calculus’ infinite series (3.14159265358979)
- British mathematician Abraham Sharp
**discovered pi to 71 digits of accuracy in 1699**(3.1415926535897932384626433832795028841971693993751058209749445923078164) - British astronomer John Machin discovered pi to a 100 digits in 1706 (3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679)

known in Arabic as Sifr. Photo Source: Unsplash

If you want to try to **impress your friends** by *reciting a maximum of 75 decimals of π. T*here are several methods, including the memorization of simple poems called piems (Pi +Poems). These Transformations correspond the number of letters in each of the word lines to create a sequence of number lines when put together will read the Pi numbers to a certain point (for example ‘the’ = 3, a word of 10 letters is 0):

- Now I defy a tenet gallantly (3.14159)
*The decimal just is added after the 3* - Of circle canon law: these integers
- Importing circles’ quotients are, we see,
- Unwieldy long series of cockle burs
- Put all together, get no clarity;
- Mnemonics shan’t describeth so reformed
- Creating, with a grammercy plainly,
- A sonnet liberated yet conformed.
- Strangely, the queer’st rules I manipulate
- Being ollowed, do facilitate
- Whimsical musings from geometric bard.
- This poesy, unabashed as it’s distressed,
- Evolvéd coherent – a simple test,
- Discov’ring poetry no numerals jarred.

Wikipedia: Piphilology

This gives you **a grand**** total of the first 75 digits of pi, **as easy as telling time! It’s not enough to get into the record books but it is enough to impress any person with your amazing math skills, share it, and people might think that you are mathematically gifted including your math classroom peers or a math tutor covering your private math learning course. Just be discrete, or they might ask you to solve another Conceptual math problem.

A golden ratio is an irrational number roughly equal to 1.61803, which is represented by the Greek letter φ. The number creates a very specific equation to determine the golden ratio.

- a+b/a=a/b =φ

From this equation, you can build something called the golden spiral. Which is a logarithmic spiral that can be found in nature. In fact this spiral pops up so much throughout history, nature and well even our DNA, that some mathematicians think that the golden ratio may be a divine number.

When All **factors of a number, excluding the number itself,** add up to that number, it is known as a perfect number. Factors are the numbers lower than that number which can divide into it evenly. A perfect number is a very rare number, until today only 51 of them have been found.

For example:

- 6 is the first perfect number
- 6 can be evenly divided by 4 factors: 1, 2, 3 and 6
- To find out if 6 is a perfect number, we add up all the numbers less than the number itself: 1+2+3=6
- 6 is a perfect number

They show up in a **very sparse way across the number spectrum** with 6, 28, and 496 being the only three perfect numbers which are less than 1000. New numbers are being discovered every year maybe you will find one and make the record books.

A prime number is a number **which can only be divided** (equally without creating decimals or rounding) by 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are examples of prime numbers.

For example:

- 2 is a prime number because the factors of 2 are 1 and 2
- 1/2 = 2
- 2/2 = 2

Some facts:

- The only even prime number is 2.
- No prime number greater than 5 ends in a 5.
- Zero and 1 are not accepted prime numbers.

Mnemonics are simply **a memory technique** which makes it easier to remember things which otherwise are not easy to remember. They can be like a logic game with interactive math which can make math fun. *They can also be used to make complex numbers or sequences easier to remember.* Mnemonics can help you learn math, remember your shopping list, or phone numbers. It is a memory tool that can **help you with your math lessons**.

If you have visual memory instead, you can associate numbers with objects or characters :

- 0 to a round,
- 1 to a pencil,
- 2 to a swan,
- 3 to a seahorse or a camel,
- 4 to a sailboat,
- 5 to a snake,
- 6 to a snail,
- 7 on a cliff,
- 8 an hourglass,
- 9 to a balloon hanging on a string.

Let See What The Example Gives Us:

**Swan seahorse snake cliff**= 2, 3, 5, 7,

- If you repeat this, then you would have created a fantastic memory system that you can use for any number sequence in maths.
- You can either complete the sequence to 100+, or you can say 2 pencils to mean 20. You can make it as you would like to.

Designing your study program to split up the math that you are having trouble with will make it easier to remember. **You can use math worksheets, get creative** and use your own number system, do some puzzles, quizzes, learn fun math facts, practice your equation notation…etc.

- Go to online math website and download printable worksheets
- Learn number patterns in a fun way like the piem above
- Find easy games for kids and work your way up to harder math problems
- Create a nickname for intimidating math, for example, change Trigonometric functions to Trig F. it even sounds cool
- Buy engaging textbooks with lots of exercises
- Attend
**free math study groups** - Watch math videos and practice solving what you learn
- Ask your math teacher for the core standards to pass the class and ask for math help specifically for the part you are struggling with.

As a learner, you must learn to recognise how you prefer to learn and which methods give you the best results. High school math onwards is challenging, it is not basic math like counting, multiplying, dividing, adding or subtraction. The more you the practice, the higher the **Probability that you will achieve mastery** in your Mathematics education and curriculum.

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