Hypotheses

**I. Hypotheses**
 * Good ** 3pts

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.

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. [] []

__DEDUCTIVE REASONING__: IT Is a ** type of **reasoning in which from two or more premises __to__ ** you can **reach a conclusion. __th__is may be true or false depending on the value of true of the premises.

__INDUCTIVE REASONING__: IT Is a common ** type of **reasoning in which from specific observations __to__ ** you can **reach a general conclusion. this conclusion only can be considered probable.

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) Or 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) In different sources of the information there are different data on size of the Egyptian cubit, __but I think that__ the size of the Egyptian cubit is equal to 466 millimeters that is taken from sources of the information which the authentic from my point of view, as it is anthropometrical size of a human "elbow" (forearm + palm + fingers). //

3) 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.

//__4) Probably__, the concrete ratio of diameters of a living circle in the geometrical drawing of the Cheops' pyramid has other sizes about which I can not tell anything certain as more exact calculations are necessary for this purpose. //

// __5) It is possible to assum__e, 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. //

// I recognized the hypothesis for the presence of modal verbs in the text. these are key words for recognizing the hypothesis. // Good

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.

== Axiom of induction == where //P// is any proposition and //k// and //n// are both [|natural numbers]. In other words, the basis //P//(0) being true along with the inductive case ("//P//(//k//) is true implies //P//(//k// + 1) is true" for all natural //k//) being true together imply that //P//(//n//) is true for any natural number //n//. A proof by induction is then a proof that these two conditions hold, thus implying the required conclusion. This works because //k// is used to represent an //arbitrary// natural number. Then, using the inductive hypothesis, i.e. that //P//(//k//) is true, show //P//(//k// + 1) is also true. This allows us to "carry" the fact that //P//(0) is true to the fact that //P//(1) is also true, and carry //P//(1) to //P//(2), etc., thus proving //P//(//n//) holds for every natural number //n//. ([])

I think that axiom of induction __is a inductive reasoning__ because from of two premises or inductive __hipotesis__ ( P is true for n=1 and P is true for n=k so P is true for n=k+1) to reach a conclusion.