The Cartesian coordinate system is a marvelous tool for plotting equations. The graph we obtain tell us a lot about the behavior of the function being graphed. The simplest equation we can graph is the equation of the straight line, but since it can assume many orientations, we call it a family of straight lines.
Straight lines are the simplest of all equation that an be graphed on the Cartesian coordinate plane. Straight lines are usually defined with two parameters only; the beginning and ending point, or by the slope (slope = inclination) and the intersection point with the Y-axis.
Small numbers are easy to read; for example, 456 is easily spelled as: four hundred and fifty-six. But confusion arises when we have billions, trillion, quadrillions, etc. Some numbers are so big that they don't have names at all, but only exclamation expressions. A Googol! is an exclamation expression for a big, big number. But what number is this and what is its relation with Google, the all familiar name of the search engine giant?
Google is the name of a search engine, Google Inc. is the corporation that specializes in internet services and products. Googol is the name of a very special number. So, Google is a misspelling of googol.
The tablet is a wonderful Internet browsing and computing device. So wonderful are the tablets that you can virtually browse the almost infinite Internet with one of them. Doesn't this remind you of the short story by Jorge Luis Borges' The Book of Sand?
The Book of Sand is an infinite book, it has no beginning and no end. The Book of Sand has no numbered pages, well its pages have numbers but not in numerical sequence. You can open this book at page n, but its next page is not n + 1.
So, tablets and the Internet are like The Book of Sand; there is no way to point at the next web page.
Today, almost every physics department in main universities has in its main building a Foucault pendulum in displays for the enjoyment of its students and for physics courses. Good pendulums are usually longer than 50 meters long, because the longer the wire holding the bob the easier to track its oscillations.
The pendulum is so a simple artifact that besides being used for wall clocks, or for hypnotizing people, few will notice that pendulums have a double movement. The first movement is the oscillatory movement we see at firs sight, the second movement –called the precession period– is a slow sideways movement that can take up to to a full day to complete.
In the English System of measures, weight is measured in pounds and abbreviated lb. Thus, we can buy 3 lb of fish, or 1 lb of ground coffee.
However, the numerical value of the weight of those two products in metric units is different. 3 lb of fish is 1.36078 Kg, while 1 lb of ground coffee is 0.453592 Kg.
We use to take the fractions for granted, we do not question the negative numbers. Even the irrational numbers seem "reasonable" for us. However, the sole mention of "imaginary numbers" appears to be a crazy idea.
Being afraid of working with imaginary numbers is natural. They are not part of the common natural numbers, they are not part of the real numbers, etc. However, we can have integer imaginary numbers, we can have imaginary fractions, and even we can have decimal imaginary numbers.
So, imagine the imaginary numbers and get related with them as soon as possible.