Hypotheses

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 Hypotheses    [|…]

  Taken from: https://msmchenrysclass.wikispaces.com/Period+7+Sir+Issac+Newton?f=print  **I. Hypotheses**

 When hypothesizing you are giving a possible solution to a problem or situation. Please visit the following link so that you can learn how to write hypotheses and when to use them.  [|http://www.accessexcellence.org/LC/TL/filson/writhypo.php]

 ** As you could see in the link above, hypotheses are written using modal verbs, like may, could, should. would, and if conditional structures. They can also be written using expresions (__key words__) as probably, possibly, and verbs such as: think, assume, hypothesize, imagine, suppose, guess, believe, among others. When reading a text, the indicators of hypotheses are the previously mentioned grammatical structures and key words. **

 **Read the following information extracted from the web page**: [] on Dec 27th, 2008  **Hypotheses and mathematics**

 So where does mathematics enter into this picture? In many ways, both obvious and subtle: Very often, the situation under analysis will appear to be complicated and unclear. Part of the mathematics of the task will be to impose a clear structure on the problem. The clarity of thought required will actively be developed through more abstract mathematical study. Those without sufficient general mathematical skill will be unable to perform an appropriate logical analysis.  (Taken from [] on Dec 27th, 2008)
 * A good hypothesis needs to be clear, precisely stated and testable in some way. Creation of these clear hypotheses requires clear general mathematical thinking.
 * The data from experiments must be carefully analysed in relation to the original hypothesis. This requires the data to be structured, operated upon, prepared and displayed in appropriate ways. The levels of this process can range from simple to exceedingly complex.

 **Using deductive reasoning in hypothesis testing**  There is often confusion between the ideas surrounding proof, which is mathematics, and making and testing an experimental hypothesis, which is science. The difference is rather simple: Of course, to be good at science, you need to be good at deductive reasoning, although experts at deductive reasoning need not be mathematicians. Detectives, such as Sherlock Holmes and Hercule Poirot, are such experts: they collect evidence from a crime scene and then draw logical conclusions from the evidence to support the hypothesis that, for example, Person M. committed the crime. They use this evidence to create sufficiently compelling deductions to support their hypotheses //beyond reasonable doubt//. The key word here is 'reasonable'. There is always the possibility of creating an exceedingly outlandish scenario to explain away any hypothesis of a detective or prosecution lawyer, but judges and juries in courts eventually make the decision that the probability of such eventualities are 'small' and the chance of the hypothesis being correct 'high'. <span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> (Taken from [] on Dec 27th, 2008)
 * Mathematics is based on //deductive reasoning// : a proof is a logical deduction from a set of clear inputs.
 * Science is based on //inductive reasoning// : hypotheses are strengthened or rejected based on an accumulation of experimental evidence.

<span style="background-color: #ffffff; color: #e00b0b; display: block; font-family: Arial,Helvetica,sans-serif;"> **II. Assignment** <span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> 1. Check the following links and explain what deductive reasoning is and inductive reasoning is. <span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> [] <span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> []

<span style="background-color: #ffffff; color: #008080; display: block; font-family: Arial,Helvetica,sans-serif;"> -The inductive reasoning is a type of logical and probabilistic reasoning that consist in to formulate general results from concrete facts, with some degree of probability. In this type of reasoning the hypotheses are considered either strong or weak, according to how likely it is that the conclusion is true. The result can be true of false independently of the validity of the hypotheses.

<span style="background-color: #ffffff; color: #008080; display: block; font-family: Arial,Helvetica,sans-serif;"> -The deductive reasoning is a process of reasoning which, starting from a set of general premises reaches a logical conclusion. If all hypotheses are true, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

<span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> 2. Please visit the following page and read the text **"Geometrical proportions of the Egyptian Pyramids"** then find and extract the hypotheses in it. There are 6 hypotheses in the text extract 5 and explain how you found them. <span style="background-color: #f3f3f3; display: block; font-family: Arial,Helvetica,sans-serif;">
 * [|Details]
 * [[file:englishformath2/Geometrical proportions of the Egyptian Pyramids.doc|Download]]
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<span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> The hypotheses were identified because they assumed overall results based in experimental data.

<span style="background-color: #ffffff; color: #008000; display: block; font-family: Arial,Helvetica,sans-serif;"> -The analysis of geometrical proportions of other Egyptian Pyramids can be made in comparison with pyramid of Cheops <span style="background-color: #ffffff; color: #008000; display: block; font-family: Arial,Helvetica,sans-serif;"> -The size of the Egyptian cubit is equal to 466 millimeters <span style="background-color: #ffffff; color: #008000; display: block; font-family: Arial,Helvetica,sans-serif;"> -It is possible to assume, that the ratio of diameters of a living circle in the geometrical drawing of the Cheops' pyramid turns out as a result of transformation of the living circle when size of the line TA is precisely equal to size of lines CE, DF, LJ, MK. <span style="background-color: #ffffff; color: #008000; display: block; font-family: Arial,Helvetica,sans-serif;"> -It is possible to speak that magnitudes of the Egyptian Pyramids have fixed sizes of measurements which allow to understand structure of world around, and allow to apply "Great Egyptian Measures" to designing environmental space and for an arrangement of the objects of the human world created by people. <span style="background-color: #ffffff; color: #008000; display: block; font-family: Arial,Helvetica,sans-serif;"> -There is hypothesis that the found 22 arcane became the reason of an esoteric legend that predictive cards of Tarot have the Egyptian origin.

<span style="background-color: #ffffff; display: block; font-family: Arial,Helvetica,sans-serif;"> 3. Look for any mathematical hypothesis and put it in your wiki. Please make sure you cite the source properly so that you do not commit plagiarism. Explain whether the hypothesis you are explaining is deductive or inductive and give reasons to your explanation.

Hypothesis: All natural numbers are interesting. Demonstration: Starting with the deductive reasoning. This is a deductive process because we build the overall result by means of a recurrent sequence of logical deductions which cover all possibilities

Suppose that there are numbers that are not interesting. Then we can make a partition of natural numbers into two subsets, firstly interesting numbers and otherwise boring numbers. However, as in any subset of natural numbers there is always one that is smaller than all the others, the subset of the boring have a number that is the smallest of this group, but for that reason, that number becomes an interesting number: it is indeed the smallest of the numbers boring. This forces us to get him out of this group and place it in the group of interesting numbers, but now a new number in the subset of the of boring numbers will be the smallest and for the same reason we must move it to the subset of interesting numbers and so on until only a single number remains in the group. Now this last number has the interesting property of being the only number not interesting and with this him will also be transferred to the group of interesting. So we have to conclude that there are no boring numbers.

Source: http://es.wikipedia.org/wiki/Paradoja_de_los_n%C3%BAmeros_interesantes