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]
 *  Good Job ** ** 5/5pts  **


 * 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.

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'. (Taken from [] on Dec 27th, 2008)
 * Using deductive reasoning in hypothesis testing**
 * 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.

**II. Assignment** 1. Check the following links and explain what deductive reasoning is and inductive reasoning is. http://en.wikipedia.org/wiki/Deductive_reasoning __ Deductive reasoning __ is a logical deduction which provides the evidence that can validate or invalidate the hypothesis. This hypothesis is true if all arguments are valid, but if one of the arguments is invalid is false ** Good ** [] __Inductive reasoning__ is __an induction logical__ ** logical inductions ** which are strong or weak and that predict a theory to some future event. These arguments go from the specific facts toward the generalization, obtaining this way a general conclusion. ** Good **

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. [|Geometrical proportions of the Egyptian Pyramids.doc]

1. ** It **  Is **__possible__** to tell, that people aspired to cipher knowledge of world around in the created objects of human culture for what used proportional parities of a heptagon which expressed absolute knowledge. 2. Many researchers of the Pyramid of Cheops **__assume__**, that to builders (architects) of the Egyptian Pyramids knew the number of golden section and number "Pi" but actually in this knowledge there is no necessity, though it is obvious that builders of pyramids knew about "golden numbers" which are ciphered in pyramids. // 3. // 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. // 4. // 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. //5//. If exact geometrical calculations are not required, then it is **__possible__** to count that approximately the cubit is equal to the side of a correct diheptagon which is entered within the framework of a correct circle. The words in **boldface** and __underlined__ are those that allowed me to notice that was a hypothesis. ** Super **

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.

"It was one of the most surprising discoveries of the Pythagorean School of Greek mathematicians that there are [|irrational numbers.]According to Courant and Robbins in [|"What is Mathematics":]//This revelation was a scientific event of the highest importance. Quite possibly it marked the origin of what we consider the specifically Greek contribution to rigorous procedure in mathematics. Certainly it has profoundly affected mathematics and philosophy from the time of the Greeks to the present day.// Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational! The following proof is a classic example of a //proof by contradiction:// We want to show that A is true, so we assume it's not, and come to contradiction. Thus A must be true since there are no contradictions in mathematics! ".... taken of: http://www.math.utah.edu/~alfeld/math/q1.html

In this theorem it is shown that if in a square in that each side measures 1 want to obtain a diagonal for the theorem of Pythagoras we obtain that the result is equal to the square root of 2. I think that this hypothesis is __a__ ** obtained by using ** deductive reasoning because it comes from a series of ideas that prove __formulates__ ** __???__  ** a theory; this hypothesis is explained with the mathematical induction. ** Good **