More handpicked essays just for you.
Pythagoras theorem and its invention
How did pythagoras create pythagorean theorem
Pythagoras theorem and its invention
Don’t take our word for it - see why 10 million students trust us with their essay needs.
Pythagoras' Theorem
I am going to study Pythagoras' theorem. Pythagoras Theorem is a2 + b2
= c2. 'a' being the shortest side, 'b' being the middle side and 'c'
being the longest side (hypotenuse) of a right angled triangle.
For example, I will use 32 x 42 = 52 . This is because:
32 = 3 x 3 = 9
42 = 4 x 4 = 16
52 = 5 x 5 = 25
So.. 9 +16 = 25
For this table, I am using the term a, b, b + 1
Triangle Number (n)
Length of shortest side
Length of middle side
Length of longest side
Perimeter
Area
1
3
4
5
12
6
2
5
12
13
30
30
3
7
24
25
56
84
4
9
40
41
90
180
5
11
60
61
132
330
6
13
84
85
183
546
7
15
112
113
240
840
8
17
144
145
296
1224
Formulas
========
Shortest side = 2n + 1, n being the triangle number
Middle side = 2n2 + 2n. This is because:
Triangle Number
1 = 2 x 2
2 = 3 x 4
3 = 4 x 6
4 = 5 x 8 = 2n2 + 2n
5 = 6 x 10
6 = 7 x 12
7 = 8 x 14
8 = 9 x 16
Longest side = 2n2 + 2n + 1
Perimeter = A + B + C
Area = A x B x 0.
In the story a stranger visits a family's home because he used to live there back in 1949 and wants to reminisce. While visiting he goes to what was room back in 1949. The son in the family is working on math work. The stranger notices this and shows him a drawing that represents infinity. The drawing consists of a square with triangles drawn within it that gradually get smaller. This is infinity that can’t be perceived due to the fact the triangles
Sum Law (the sum of the interior angles of a triangle must sum to 180
A triangle has certain properties such as all of the angles. add up to 180o and even if we have never thought about it before we clearly recognise these properties ‘whether we want to or not’. Cottingham. J. 1986). The 'Secondary' of the 'Se A triangle’s real meaning is independent of our mind, just as God’s existence is.
Step-Stair Investigation For my GCSE Maths coursework I was asked to investigate the relationship between the stair total and the position of the stair shape on the grid. Secondly I was asked to investigate the relationship further between the stair totals and the other step stairs on other number grids. The number grid below has two examples of 3-step stairs. I will use Algebra as a way to find the relationship between the stair total and the position of the stair on the grid.
Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, isosceles triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and Fig 1. Table 1 showing the areas for the different shapes formed by using the
Using a square, both the length & the width are equal. I am using a
Empedocles was born in Acragas, Sicily about 492 BCE to a distinguished and aristocratic family. His father, Meto, is believed to have been involved in overthrowing Thrasydaeus who was the tyrant of Agrigentum in the year 470 BCE. Empedocles is said to have been somewhat wealthy and was a popular politician and a champion of democracy and equality.
Text Box: In the square grids I shall call the sides N. I have colour coded which numbers should be multiplied by which. To work out the answer the calculation is: (2 x 3) – (1 x 4) = Answer Then if I simplify this: 6 - 4 = 2 Therefore: Answer = 2
Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...
Thucydides indicates that people are indiscriminate about the stories or accounts they are told. They do not put them to the test. This is the case even with accounts that deal with their own country. Thucydides uses the example of the murder of Hipparchus. The Athenians believe that Hipparchus was a tyrant and was the ruler when he was killed by Harmodius and Aristogeiton. The fact of the matter is, Thucydides says, that it was Hipparchus older brother Hippias who was in power, not Hipparchus. Hippias was the eldest son of Pisistratus, so he was the ruler of Athens, not Hippias, who was younger, and not Thessalus, the third son of Pisistratus, who was also younger than Hippias. As for Harmodius and Aristogeiton, they originally planned to assassinate Hippias. However, somehow Hippias found out about their plot. Knowing that they would soon be arrested, Harmodius and Aristogeiton steered clear of Hippias, knowing that he knew of their plot. The pair suspected their own accomplices of having disclosed the plot to Hippias. Harmodius and Aristogeiton, their scheme spoiled, were still determined to do something. That something soon presented itself when they came across Hipparchus by chance. They encountered him at the Leocorium, where he was organizing the Panathenaic Procession. Since he was Hippias's brother, they murdered him. These were the real facts of the case, yet, somehow, Athenians have swallowed a legend or myth which obscures and distorts the true facts. The illustration of Hipparchus's murder serves to prove Thucydides' point that "People take in reports about the past from each other all alike, without testing them- even reports about their own country" (Thucydides, 12). The inference is that Thucydides...
are how to follow lines of reasoning, how to say precisely what is intended, and
Euclidean Geometry is the study of plane and solid figures based on the axioms and theorems outlined by the Greek mathematician Euclid (c. 300 B.C.E.). It is this type of geometry that is widely taught in secondary schools. For much of modern history the word geometry was in fact synonymous with Euclidean geometry, as it was not until the late 19th century when mathematicians were attracted to the idea of non-Euclidean geometries. Euclid’s geometry embodies the most typical expression of general mathematical thinking. Rather than simply memorizing basic algorithms to solve equations by rote, it demands true insight into the subject, cleaver ideas for applying theorems in special situations, an ability to generalize from known facts, and an
Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears.
Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem.
The Golden Rectangle is a unique and important shape in mathematics. The Golden Rectangle appears in nature, music, and is often used in art and architecture. Some thing special about the golden rectangle is that the length to the width equals approximately 1.618……