Nobody downloaded yet

Theorem of Pythagoras in Mathematics - Math Problem Example

Comments (0) Cite this document
The philosophy of mathematics begins with Pythagoras, who later developed Pythagoras Theorem. While believing that mathematics gave us the key to understand reality he proved that mathematics is known a priori that is, without appeal to sense experience. He started talking to a slave boy, and by a series of questions elicited from him a method of constructing a line, using a special case of Pythagoras' theorem.
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER97.5% of users find it useful
Theorem of Pythagoras in Mathematics
Read TextPreview

Extract of sample
"Theorem of Pythagoras in Mathematics"

Download file to see previous pages When I talk about the diagonal of the square, or the nine-point circle, or the Euler line, I am not talking about the often rather sketchy and highly imperfect drawing on the blackboard, but about something which underlies all particular exemplifications of squares and diagonals, nine-point circles, or Euler lines, and is independent of each of them" 2. The very fact that we use the definite article, and talk of the square, the nine-point circle, etc., bears witness to this; and by the same token, it would be absurd to ask where the square was, or to ask when the nine-point center came to be on the Euler line, or to suggest that Pythagoras' theorem might hold for you but not for me. So Plato's answer to the question "What is mathematics about" is that it is about something timeless, spaceless and objective 3.
Among the five postulates which Euclid wanted us to grant the fifth one is "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles. ...
aight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles. "These were generally taken to express self-evident truths. This is somewhat surprising, in that the first three are not really propositions at all, but instructions expressed in the infinitive, and the last too complex to be self-evident no finite man can see it to be true, because no finite man can see indefinitely far to make sure that the two lines actually do meet in every case. Many other formulations of the fifth postulate have been offered, both in the ancient and in the modern world, in the hope of their being more self-evidently true"4 . Among them the most notable was "In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides" 5.

Fig 1.1 6

The alternative formulations of the fifth postulate of the theorem are less cumbersome and may be more acceptable than Euclid's own version, but none of them are so self-evident that they cannot be questioned. The importance of Pythagoras proposed theorem can be seen from the fact that Pythagoras' theorem is far from being obviously true, something that should be granted without more ado, it does not need any further justifications. "In fact, none of the other alternative formulations was felt to be completely obvious, and they all seemed in need of some kind of further justification. The philosophers Wallis and Saccheri in search of a better justification, devoted years to trying to prove the fifth postulate by a reductio ad absurdum, assuming it to be false and trying to derive a contradiction. The attempt failed, but in the course of it he unwittingly discovered ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
(“Theorem of Pythagoras in Mathematics Math Problem”, n.d.)
Retrieved from
(Theorem of Pythagoras in Mathematics Math Problem)
“Theorem of Pythagoras in Mathematics Math Problem”, n.d.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document
...and therefore, it is important to realize as what is it that is integrated or summed up. It is essentially the product of the dependent variable (y) and infinitesimally small increment in the independent variable or ?x which is continuously summed up. If we know from which point to which point this summation is to be done, then we get a definite answer and this integral is known as definite integral. Mathematically it is expressed by indicating the limits or boundaries of integration as shown below. This is a definite integral with integration being carried out between ‘a’ and ‘b’ (a < b) for y, which is a function of x. This definite integral gives many useful parameters like area under curve, area of a curved surface,...
10 Pages(2500 words)Essay
The Pythagorean Theorem
...THE PYTHAGOREAN THEOREM [Source: http] April 30, 2008 The Pythagorean Theorem In mathematics, the Pythagorean Theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras who lived in the 6th century B.C. The theorem is as follows: "In any right angle triangle, the area of the square of the side opposite the right angle i.e. whose side is the hypotenuse is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs" In other words The square on the hypotenuse is equal to the sum of the squares on the other two sides Geometric... ...
14 Pages(3500 words)Essay
...Instructions: Independent study. Choose a topic within algebra for independent study. Your topic should be mathematics that you have not studied before or that goes beyond what you have studied. For example, you may use this topic on"Nuclear salvation or nuclear folly" by R.E Lapp. Do not think about developing a lesson plan, or to teach your topic to children. A little story of mathematics is welcome, but that should not be the main theme of your paper. The objective is to describe some mathematics that you have learned. Include a summary of why you selected your topic, and what you learned about it from each resource that you used. Also include some questions provoked by what you...
4 Pages(1000 words)Article
...Waring’s Problem and Goldbach’s Conjecture 20-2008 Waring’s Problem Lagrange’s 4 square theorem s that every number can be written as the sumof four integer squares. Waring proposed a generalisation of this theorem in 1770, stating that every natural number is the sum of a fixed number g(k) of kth power integers, where k is any given positive integer and g(k) depends only on k. In this paper, we will investigate what is currently known about this problem. Warings Problem was proven for all k by Hilbert in 1909 (Ellison 1971), with the Hilbert-Waring Theorem. Prior to that, the problem was solved in the affirmative for specific ks, especially for small k. If we let "s" stand for the...
6 Pages(1500 words)Essay
...1. An instance in my daily life where I rely on the skills of rounding and estimating is when I do the grocery shopping. In order to get a fair estimate of what my bill is up to, I roughly calculate the value of each shopping item by rounding to the closest whole number. An occupation such as a shop teller would need to have sound multiplication and division skills because their job requires them to give and receive the right amount of change. 2. The concept of negative numbers is harder to grasp because there cannot be anything less than nothing, which is what zero is. An example of where it is important to understand integers in the financial world is with banking (Glydon). If someone spends more than they have available... An instance in...
1 Pages(250 words)Essay
Pythagorean Theorem
...Pythagorean Theorem (Add (Add (Add Pythagorean Theorem Introduction Evidences show that Pythagorean Theorem was popular even among ancient civilizations. This famous theorem was developed by the Greek mathematician and philosopher Pythagoras. Historical writings argue that though Babylonian mathematicians had knowledge in the theorem, they could not develop it into a mathematical framework. Unlike any other mathematical...
3 Pages(750 words)Essay
Coase Theorem
...Coase Theorem Coase Theorem Coase theorem targets economic efficiency that is attributed to economic allocation and outcome when externalities are present. The theory stipulates that if trade is possible in the presence of an externality when transaction costs are significantly low, the end result will be an efficient outcome when initial allocation of property is not considered. The major obstacles to Coasian bargaining emerge when property rights have been defined poorly (Buchanan, 2005). This paper will discuss Coase theorem as an alternative to government regulation in terms of facilitating for the provision of goods and services. Ronald Coase stipulated that...
2 Pages(500 words)Essay
...Mathematics: Open/Closing Credit The credit card will largely depend on the credit card holder purchasing behavior. Your current card charges 16.5% annually. Therefore, interest charges on a balance of $5,000 will be given by: This is the interest charged on your current card, regardless of the duration. On the other hand Visa Student Card charges a lower annual percentage of 10.8% after a 6 month 0% interest period. On a balance of $5,000, the interest will be; Obviously, the student card charges a lower interest compared to your current card and even offers a grace period of 6 months interest free which makes it an attractive option. However, since you usually have a large outstanding balance, chances of defaulting or exceeding...
1 Pages(250 words)Speech or Presentation
Bayes' Theorem
...Bayesian Theorem Introduction Reverend Thomas Bayes developed Bayes’ theorem of probability. The theorem provides understanding about the how the probability of a theorem is affected by a new set of evidence. It is applied to in a variety of context to explore a relationship between theory and evidence. Contemporary, the theorem’s application is broad, ranging from mathematics to the field of science. It explains the relations between two theories and evidences. It allows the researcher to determine the relation between current beliefs with respect to previous beliefs and evidences. Simon Jackman (2009) defines Bayes’...
15 Pages(3750 words)Essay
The Pythagorean Theorem
...The Pythagorean Theorem The Pythagorean Theorem The Pythagorean Theorem is used to determine the areal distance of a right angled road trip. Through determining the length of each road and applying the Pythagorean formula [c= √(a2+b2)], the areal distance is determined (Kramer, 2011). Pythagorean Theorem is highly effective and easy to use as compared to the other mathematical tools. For measuring the length of each road, the odometer tool of car or other motor are used. For determining the distance, no other geometrical tool is required. Moreover, for resolving such kind of issues Global Positioning System (GPS) navigation is used in the modern day. This...
1 Pages(250 words)Coursework
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Let us find you another Math Problem on topic Theorem of Pythagoras in Mathematics for FREE!
logo footer
Contact us:
Contact Us Now
FREE Mobile Apps:
  • StudentShare App Store
  • StudentShare Google play
  • About StudentShare
  • Testimonials
  • FAQ
  • Blog
  • Free Essays
  • New Essays
  • Essays
  • Miscellaneous
  • The Newest Essay Topics
  • Index samples by all dates
Join us:
Contact Us