Hypotheses

I. Hypotheses **
 * Super Good ** **5pts **[[image:dancingpucca.gif]]

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.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Science is based on //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">inductive reasoning //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> : hypotheses are strengthened or rejected based on an accumulation of experimental evidence.

1. Check the following links and explain what deductive reasoning is and what inductive reasoning is. [] []
 * <span style="color: #e00b0b; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">II. Assignment **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">

<span style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: #ebeff9 none repeat scroll 0% 0%; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Deductive reasoning evaluates deductive arguments, which are either valid or invalid and draws conclusions from them. **<span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">It goes from general to specific ** <span style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: #ebeff9 none repeat scroll 0% 0%; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Inductive reasoning takes a certain set of facts and they take a general conclusion .**<span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">It goes from specific to general ** <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 2. Please visit the following page and read the text **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">"Geometrical proportions of the Egyptian Pyramids" **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 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] //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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). // <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Inductive reasoning. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 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="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Deductive reasoning. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Deductive reasoning. //
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Good **
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Good **

//<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Deductive reasoning. //
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Good **

//<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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. // //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Deductive reasoning. //
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Good **

//<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">I found the hypotheses in the text by the words stress //**<span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">ed **//<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> t__hat I put.**omit**__ //
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Good **

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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. <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">Explain whether the hypothesis you are explaining is deductive or inductive and give reasons to your explanation.

Riemann hypothesis

<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">In mathematics, the **Riemann hypothesis**, proposed by [|Bernhard Riemann] ([|1859]), is a [|conjecture] about the distribution of the [|zeros] of the [|Riemann zeta-function] which states that all [|non-trivial] zeros of the Riemann [|zeta function] have real part 1/2. The name is also used for some closely related analogues, such as the [|Riemann hypothesis for curves over finite fields]. The Riemann hypothesis implies results about the distribution of [|prime numbers] that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in [|pure mathematics] ([|Bombieri 2000]). The Riemann zeta-function ζ(//s//) is defined for all [|complex numbers] //s// ≠ 1. It has zeros at the negative even integers (i.e. at //s// = −2, //s// = −4, //s// = −6, ...). These are called the **trivial zeros**. The Riemann hypothesis is concerned with the non-trivial zeros, and states that: The real part of any non-trivial zero of the Riemann zeta function is ½. Thus the non-trivial zeros should lie on the so-called **critical line**, ½ + //it//, where //t// is a [|real number] and //i// is the [|imaginary unit]. The Riemann hypothesis is part of [|Problem 8], along with the [|Goldbach conjecture], in [|Hilbert]'s list of [|23 unsolved problems], and is also one of the [|Clay Mathematics Institute] [|Millennium Prize Problems]. Since it was formulated, it has withstood concentrated efforts from many outstanding mathematicians. In 1973, [|Pierre Deligne] proved that the Riemann hypothesis held true over finite fields. The full version of the hypothesis remains unsolved, although modern computer calculations have shown that the first 10 trillion zeros lie on the critical line. There are several popular books on the Riemann hypothesis, such as [|Derbyshire (2003)], [|Rockmore (2005)], [|Sabbagh (2003)], [|du Sautoy (2003)]. The books [|Edwards (1974)], [|Patterson (1988)] and [|Borwein et al. (2008)] give mathematical introductions, while [|Titchmarsh (1986)] is an advanced [|monograph].

It is inductive reasoning because Riemann takes a set of facts as the distribution of prime numbers and other mathematical facts <span style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: #ebeff9 none repeat scroll 0% 0%; font-family: 'Arial','sans-serif'; font-size: 10pt;">to get to make his hypothesis.
 * <span style="color: #09c309; font-family: Georgia,serif; font-size: 10pt;">Very Good **

<span style="font-family: 'Calibri','sans-serif'; font-size: 11pt; line-height: 115%;"> Taken from: []