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Pythagoras and his contribution to mathematics
Pythagoras and his contribution to mathematics
Pythagoras and his contribution to mathematics
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Investigating Pythagoras
Introduction
============
[IMAGE]For this piece of work I am investigating Pythagoras.
Pythagoras was a Greek mathematician. Pythagoras lived on the island
of Samos and was born around 569BC. He did not write anything but he
is regarded as one of the world's most important characters in maths.
His most famous theorem is named after him and is called the
Pythagoras Theorem. It is basically a²+b²=c². This is what the
coursework is based on.
I am going to look at the patterns, which surround this theorem and
look at the different sequences that can be formed.
The coursework
The numbers 3, 4 and 5 satisfy the condition 3²+4²=5² because
3²=3x3=9
4²=4x4=16
5²=5x5=25
And so
3²+4²=9+16=25=5²
I will now check that the following sets of numbers also satisfy the
similar condition of (smallest number) ²+(middle number) ²=(largest
number) ²
a) 5, 12, 13
5²=5x5=25
12²=12x12=144
25+144=169
√169 = 13
This satisfies the condition as
5²+12²=25+144=169=13²
b) 7, 24, 25
7²=7x7=49
24²=24x24=576
49+576=625
√625=25
This satisfies the condition as
7²+24²=49+576=625=25²
The numbers 3,4 and 5 can be the lengths - in appropriate units - of
the side of a right-angled triangle.
[IMAGE]
5
3
[IMAGE]
The perimeter and area of this triangle are:
Perimeter = 3+4+5=12 units
Area = ½x3x4=6 units ²
[IMAGE]
The numbers 5,12,13 can also be the lengths - in appropriate units -
of a right-angled triangle.
[IMAGE]
Perimeter = 5+12+13=30
Area=½x5x12=30
[IMAGE] This is also true for the numbers 7,24,25
[IMAGE]
Perimeter = 7+24+25=56
Area=½x7x24=84
I have put these results into a table to see if I can work out any
patterns.
Length of shortest side
Length of middle side
Length of longest side
Perimeter
The results of this experiment are shown in the compiled student data in Table 1 below.
2. Width of the base which divided to 3 groups: 1: More than 5 mm; 2: between 3-5 mm; less than 3 mm.
This shows that there is a difference of 2cm between A and B, and B
Above is my original data. In the graph, it can be seen that there are
9) Collect all heart rates and arrange the results in a table.
Using a square, both the length & the width are equal. I am using a
0.000 7 63 106 55 74.7 1.245 9 70 135 90 98.3 1.638 11 85 135 70 96.8 1.613 [ IMAGE ] [ IMAGE ] Conclusion = = = =
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.
· When I have collected my results I will place them in a table like
Euclid and Archimedes are two of the most important scientists and mathematicians of all time. Their achievements and discoveries play a pivotal role in today’s mathematics and sciences. A lot of the very basic principles and core subjects of mathematics, physics, engineering, inventing, and astronomy came from the innovations, inventions, and discoveries that were made by both Euclid and Archimedes.
Pythagoras was one of the first true mathematicians who was not only known for the famous Pythagorean theorem. His father was from Tyre while his mother was from Samos but when Pythagoras was born and growing up he spent most of his time in Samos but as he grew he began to spend a lot of time with his father. His father was a merchant and so Pythagoras travelled extensively with him to many places. He learned things as he went along with his father but the primary teacher known to be in his life was Pherekydes. Thales was also a teacher for himself and he learned some from him but he mainly inspired him. Thales was old when Pythagoras was 20 and so Thales told him to go to Egypt and learn more about the subjects he enjoyed which were cosmology and geometry. In Egypt most of the temples where the learning took place refused him entry and the only one that would was called Diospolis. He was then accepted into the priesthood and because of the discussions between the priests he learned more and more about geome...
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
Both graphs and data tables show that no anomalous results were present. This is evident within the data as no one point cause a major shift in the trend of the results.
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.