Hypotheses


 * 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.

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.


 * ANSWERS:**

1.
 * Deductive Reasoning:** Is an attempt or a way to show that a conclusion is based on previous premises.
 * Inductive Reasoning:** It is what we usually call an educated guess, because it makes a statement or concluion, from some information (not solid).

2.
 * 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) - 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.
 * 3) - 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.
 * 4) - There is hypothesis that the found 22 arcane became the reason of an esoteric legend that predictive cards of Tarot have the Egyptian origin.
 * 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.

3. First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial [|Riemann zeta function zeros], i.e., the values of other than ,, , ... such that (where is the [|Riemann zeta function] ) all lie on the "[|critical line] " (where  denotes the <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|real part] of ). A more general statement known as the <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|generalized Riemann hypothesis] conjectures that neither the <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|Riemann zeta function] nor any <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|Dirichlet L-series] has a zero with <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|real part] larger than 1/2.
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline1.gif height="14" caption="s"]] ||
 * s ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline2.gif height="14" caption="-2"]] ||
 * -2 ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline3.gif height="14" caption="-4"]] ||
 * -4 ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline4.gif height="14" caption="-6"]] ||
 * -6 ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline5.gif height="14" caption="zeta(s)=0"]] ||
 * zeta(s)=0 ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline6.gif height="14" caption="zeta(s)"]] ||
 * zeta(s) ||
 * [[image:http://mathworld.wolfram.com/images/equations/RiemannHypothesis/Inline9.gif height="14" caption="s"]] ||
 * s ||


 * Site: <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[] **

It is a deductive argument because it uses premises to build up a conclusion.