By Steven G. Krantz

An Episodic historical past of Mathematics gives you a sequence of snapshots of the historical past of arithmetic from precedent days to the 20 th century. The cause isn't really to be an encyclopedic heritage of arithmetic, yet to offer the reader a feeling of mathematical tradition and heritage. The e-book abounds with tales, and personalities play a powerful position. The ebook will introduce readers to a couple of the genesis of mathematical rules. Mathematical historical past is fascinating and profitable, and is an important slice of the highbrow pie. an exceptional schooling comprises studying various equipment of discourse, and positively arithmetic is likely one of the such a lot well-developed and critical modes of discourse that we've got. the focal point during this textual content is on getting concerned with arithmetic and fixing difficulties. each bankruptcy ends with a close challenge set that would give you the pupil with many avenues for exploration and lots of new entrees into the topic.

Show description

Read Online or Download An Episodic History of Mathematics: Mathematical Culture through Problem Solving PDF

Similar science & mathematics books

1+1=10: Mathematik für Höhlenmenschen

Mehr als die einfache Logik eines Frühmenschen brauchen Sie nicht, um die Grundzüge der Mathematik zu verstehen. Denn Sie treffen in diesem Buch viele einfache, quickly gefühlsmäßig zu erfassende mathematische Prinzipien des täglichen Lebens. Deswegen kann der Autor bei seinem Versuch, die Mathematik „begreiflich“ zu machen, in die Steinzeit zurückgehen – genauer gesagt: etwa in die Jungsteinzeit, 10.

Solid-Phase Peptide Synthesis

The significantly acclaimed laboratory common for greater than 40 years, tools in Enzymology is among the so much hugely revered courses within the box of biochemistry. in view that 1955, every one volumehas been eagerly awaited, usually consulted, and praised via researchers and reviewers alike. greater than 275 volumes were released (all of them nonetheless in print) and lots more and plenty of the cloth is appropriate even today-truly a necessary book for researchers in all fields of lifestyles sciences.

Schöne Sätze der Mathematik. Ein Überblick mit kurzen Beweisen

In diesem Buch finden Sie Perlen der Mathematik aus 2500 Jahren, beginnend mit Pythagoras und Euklid über Euler und Gauß bis hin zu Poincaré und Erdös. Sie erhalten einen Überblick über schöne und zentrale mathematische Sätze aus neun unterschiedlichen Gebieten und einen Einblick in große elementare Vermutungen.

Extra resources for An Episodic History of Mathematics: Mathematical Culture through Problem Solving

Sample text

17). 18). Notice that each of the central angles of each of the triangles must have measure 360◦ /6 = 60◦ . Since the sum of the angles in a triangle is 180◦ , and since each of these triangles certainly has two equal sides and hence two equal angles, we may now conclude that all the angles in each triangle have measure 60◦ . 19. But now we may use the Pythagorean theorem to analyze one of the triangles. 20. Thus the triangle is the union of two right triangles. 3 Archimedes 27 hexagon—is 1 and the base is 1/2.

Now we consider a regular 24-sided polygon (an icositetragon). As before, we construct this new polygon by erecting a small triangle over each side of the dodecagon. 27. 28 √ decagon. We first solve the right triangle with base 2 − 3/2 and hypotenuse 1—using the Pythagorean theorem, of course—to find that √ it has height 2 + 3/2. Then we see that the smaller right trian√ √ gle has base 1 − 2 + 3/2 and height 2 − 3/2. Thus, again by the Pythagorean theorem, the hypotenuse of the small right triangle is √ 2 − 2 + 3.

So our approximation is quite crude. The way to improve the approximation is to increase the number of sides in the approximating polygon. In fact what we shall do is double the number of sides to 12. 22 shows how we turn one side into two sides; doing this six times creates a regular 12-sided polygon. Notice that we create the regular 12-sided polygon (a dodecagon) by adding small triangles to each of the edges of the hexagon. Our job now is to calculate the area of the twelve-sided polygon. Thus we need to calculate the lengths of the edges.

Download PDF sample

Rated 4.51 of 5 – based on 9 votes