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# Mathematics Knowledge and Teaching Techniques Essay

## The New Material Learned from the Readings

After having read the two articles listed on a reference page, I have learned that although irrational numbers are hard to be written in decimal equivalent, they are easy to visualize using a proper drawing technique. One does not necessarily need to do exact measurements when attempting to draw a line having a length of √2 inches, for example. If the Pythagorean theorem is used, the line can be drawn with no serious calculations applied. For that purpose one simply needs to use a right triangle with both feet being 1 inch long. The hypotenuse of the triangle will be exactly √2 inches in length. It is known, that for an irrational number to be written correctly a long list of figures is required: √17 = 4.123105625617661. However, if a right triangle is drawn and both legs are measured carefully, the hypotenuse will match a required number (Lewis, 2007).

Another peculiar fact I have known about is that when one uses the hypotenuse as afoot for a new right triangle with the length of its second foot corresponding to that of a previous triangle, the wheel of Theodorus starts to occur. The more triangles one draws with the help of this concept, the more a picture reminds a wheel. The author uses this method of visualization when explaining his students the principles of implementation of the Pythagorean theorem to irrational numbers. Each time a new triangle is added to the picture the hypotenuse becomes longer. Though its exact length is hard to measure using a straight scale, one does not need to bother with that kind of a task since the line is already drawn owing to the data of a previous figure.