Choice of Topic:
My choice of topic will explore the amalgamation of traditional spectacles and cosmetic to create contact lenses.

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Reasons for the Choice of Topic

Contact lenses are chosen as the example of amalgamation as it combines traditional spectacles with cosmetic, making it much more convenient for people. It is very popular and common among people.

In examining the issue on late coming, it is observed that many a time, alarm clocks fail on the late comers as they claim to not hear the alarm ring, hence they oversleep. My objective is the amalgamation of bed and alarm clock to solve the problem of people not hearing the alarm rings which results in late comings.

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|Feasibility of Project | |How can the proposal be carried out? |Evaluation | | | | |Strategy 1: Every individual will be able to use this bed |Strategy 1: Users will have a better reliance on this product| |with build-in alarm as it will have different functions for |where the bed will vibrate to wake them up as this involves | |the users to set to meet their needs. For example, they can |the touch of the body which is a stronger disturbance. | |set the degree of vibration. | | | | | |Strategy 2: The bed will still be a normal bed but with an |Strategy 2: Users do not need to worry about the comfort | |additional mechanism which can cause it to vibrate. To stop |ability of the bed as it will remain the same. Only when...

...The History of Pi
The History of Pi
Most individuals who have a general mathematical education that touches on the basics of geometry commonly know pi. The definition of pi is the ratio of the circumference to the diameter of the circle (Smoller, 2001). The majority of the population, however, does not realize the history associated with the symbol, which not only spans throughout the centuries but throughout the millenniums. The Babylonians, Egyptians, Archimedes of Syracuse, Leonardo of Pisa, Francois Viete, Leonhard Euler, Asian mathematicians such as Liu Hiu, Tsu Ch’ung-Chih, Arya Bhatta, Gottfried Leibniz, Isaac Newton, William Jones, John Machin. George Buffon and Srinivasa Ramanujan, have all played a role in the enriched past of this important mathematical symbol.
The ancient Babylonians dates back to the 18th century BCE and reigned in Mesopotamia. The Babylonia, even though it declined drastically in the 17th century, existed until 539 when the Persians consumed Babylonia (Kjeilen, 2009). During this time, they made magnificentstructures with archways that held religious emphasis. The Babylonians used a developed mathematical system, which included six as the root number as opposed to 10 which are commonly used today (Kjeilen, 2009). Even though the Babylonians has a variation on their mathematical system, they calculated the area of a circle by taking three times the square of its radius. One old...

...What is π?
Webster's Collegiate Dictionary defines π as "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265"
A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behavior in different situations. In order to understand where π fits in to the world of mathematics, one must understand several of its properties: π is irrational and π is transcendental.
The History of π
In the long history of the number π, there have been many twists and turns, many inconsistencies that reflect the condition of the human race as a whole. Through each major period of world history and in each regional area, the state of intellectual thought, the state of mathematics, and hence the state of π, has been dictated by the same socio-economic and geographic forces as every other aspect of civilization. The following is a brief history, organized by period and region, of the development of our understanding of the number π.
In ancient times, π was discovered independently by the first civilizations to begin agriculture. Their new sedentary life style first freed up time for mathematical pondering, and the need for permanent shelter necessitated the...

...History of Pi
There are many people who have discovered and proved what pi is. As time goes on people discover more and more of the seemingly random numbers. Four of the people who proved pi are the Liu Hui, Archimedes of Syracuse, James Gregory, and the Bible.
The first proof I will be talking about is Liu Hui’s. Liu Hui was a Chinese mathematician whose method for proving pi was to find the area of a polygon inscribed in a circle. When the number of sides on the inscribed polygon increased, its area became closer to the circumference of a circle and pi. For finding the side length of an inscribed polygon Liu Hui used a simple formula. (13Ma3)
To find the side length of an inscribed polygon of 2n sides, if the side length of a polygon with n sides is known he used the following formula:
In this formula k stands for a temporary variable, and Sn stands for the side length of an inscribed polygon with n sides. (13Ma3)
We will start with a hexagon inside of a circle. The radius of the circle is one, the area is pi. The side length of the hexagon is 1. To calculate the next k value, all we need to do is do an addition and a square root like in the following:
The area of a regular polygon is A=1/2nsa. The n stands for number of sides, s stands for side length, and a stands for apothem. As the number of sides increases, the apothem becomes closer and closer to the radius so...

...A Script for Archimedes Play
Curtain opens and Father is reading a newspaper.
At Ahmed’s house
Mohamed : (Bouncing the ball and enters the stage)
Ahmed, Aren’t you coming to play today?
Ahmed : (From inside)
One more to do……….
Mohamed : (to the audience)
Maths is always his favourite subject
Ahmed : Do you know today we learnt something very interesting for maths.
Father : (Interrupting and getting up from the chair)
What did you learn today, Ahmed?
Ahmed : How to find the area of a circle by using a formula pi x r2
Mohamed : What is pi?
Ahmed : It is a value 22/7.
Father : Do you like to know about the person who discovered pi?
Ahmed & Mohamed : Oh! Yes father.
Father : (sitting on a chair, Mohamed and Ahmed sitting on the floor)
The person who discovered this is Archimedes. He was the greatest Greek mathematician of the ancient world. He lived from 287BC to 212BC. His life story is very interesting.
Mohamed : Can you please tell us one story?
Father : King Heron was ruling the country at that time…………………………
(The curtain closes and the Narrator speak in front of the closed curtain)
Narrator : During the ruling time of King Heron, lived a famous mathematician whose theorems and philosophies became worldwide. He was no other but Archimedes the Greek mathematician. On one such day, the King ordered the goldsmith to make him a golden crown.
(the...

...Pi has always been an interesting concept to me. A number that is infinitely being calculated seems almost unbelievable. This number has perplexed many for years and years, yet it is such an essential part of many peoples lives. It has become such a popular phenomenon that there is even a day named after it, March 14th (3/14) of every year! It is used to find the area or perimeter of circles, and used in our every day lives. Pi is used in things such as engineering and physics, to the ripples created when a drop of water falls into a puddle, Pi is everywhere. While researching this topic I have found that Pi certainly stretches back to a period long ago. The history of Pi was much more extensive than I originally imagined. I also learned that searching for more numbers in Pi was a major concern for mathematicians in which they put much effort into finding these lost numbers. The use for Pi was also significantly larger than I originally anticipated. I was under the impression that it was used for strictly mathematicians which is entirely not true. This is why Pi is so interesting.
The history of Pi dates back to a much later period than I thought. Ancient Egypt and Babylon are one of the first places that Pi was first founded. When discovered it showed that these ancient Pi values were within one percent of it's actual...

...Pi is an ancient and wonderful Number to the World of Mathematics invented with the Geometrical structure Circle.
CIRCLE
It is felt that the creation of the Circle is not created by the man himself but came through the inspiration of Nature itself. The shape of Sun, Full Moon, Eyes are some examples for it.
Some basic things :
There are 3 major parts to remember.
Radius : The straight line drawn to the Circumference of the Circle from the Centre point.
Diameter : Diameter is the straight line drawn from one point of the circumference to another point of the circumference through the center point (Origin) .
Circumference:
Circumference is the curved line drawn from the origin of the Circle having equal radii.
It is evident that so many people from ancient period tried to understand the nature of a Circle.
They found the relationship between the Circumference and radius of the Circle.
Circumference increases with the increase in Radius or Diameter
Pi is the ratio of Circumference of the Circle to its Diameter .
The value of Pi (Its value is Constant) is very essential factor to know the Area of a Circle.
Finding the Value of Pi is not a simple thing because the measurement of the Circumference is not so easy.
So many people tried to know the value of Pi by
different mathematical methods.
It is believed that the Egyptians and...

...Before I talk about the history of Pi I want to explain what Pi is. Webster's Collegiate Dictionary defines Pi as "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265" A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behavior in different situations. In order to understand where Pi fits in to the world of mathematics, one must understand several of its properties pi is irrational and pi is transcendental.
A rational number is one that can be expressed as the fraction of two integers. Rational numbers converted into decimal notation always repeat themselves somewhere in their digits. For example, 3 is a rational number as it can be written as 3/1 and in decimal notation it is expressed with an infinite amount of zeros to the right of the decimal point. 1/7 is also a rational number. Its decimal notation is 0.142857142857…, a repetition of six digits. However, the square root of 2 cannot be written as the fraction of two integers and is therefore irrational.
For many centuries prior to the actual proof, mathematicians had thought that...