By Arthur T. Benjamin

Approximately This Course

24 lectures | half-hour in keeping with lecture

Ready to workout these mind cells? people were enjoying arithmetic for millions of years. alongside the way in which, they have stumbled on the fantastic software of this field—in technology, engineering, finance, video games of probability, and plenty of different features of existence. This process 24 30 minutes lectures celebrates the sheer pleasure of arithmetic, taught by means of a mathematician who's actually a magician with numbers. Professor Arthur T. Benjamin of Harvey Mudd collage is popular for his feats of psychological calculation played ahead of audiences at colleges, theaters, museums, meetings, and different venues.

Although racing a calculator to resolve a tricky challenge could appear like a superhuman success, Professor Benjamin exhibits that there are easy tips that permit somebody to appear like a math magician. Professor Benjamin has one other objective during this path: all through those lectures, he exhibits how every thing in arithmetic is connected—how the attractive and sometimes enforcing edifice that has given us algebra, geometry, trigonometry, calculus, chance, and rather a lot else is predicated on not anything greater than being silly with numbers.

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**Example text**

The formula is F1 + F3 + F5 + … + F2 n 1 = F2n. Let’s now look at a different pattern. Which Fibonacci numbers are even? According to the data, every third Fibonacci number appears to be even. Will this pattern continue? Think about the fact that the Fibonacci numbers start off as odd, odd, even. When we add an odd number to an even number, we get an odd number. Then, when we add the even number to the next odd number, we get another odd number. When we add that odd number to the next odd number, we get an even number, and we’re back to where we started: odd, odd, even.

This works for multiplying two numbers that are close together. We’ll start with 106 u 109. The ¿rst number, 106, is 6 away from 100; the second number, 109, is 9 away from 100. Now, we add 106 + 9 or 109 + 6, which is 115. Next, This equation can we multiply 115 by our easy number, 100: 115 u 100 = 11,500. Then, multiply 6 u 9 and add help you learn to that result to 11,500 for a total of 11,554. square numbers in Lecture 7: The Joy of Higher Algebra your head faster than you ever thought possible.

Instead of intercepting the x-axis and y-axis one away from the origin, suppose we intercept them r away from the origin; the equation then is x2 + y2 = r2. Here’s another example: x2 + y2 = 102, or 100, would be a circle of radius 10. If we shift that circle two units to the right, the equation would be (x í 2)2 + y2 = 102. If we then pushed it up by one unit, the equation would be (x í 2)2 + (y í 1)2 = 102. In this lecture, we’ve seen polynomials and how to graph them. We’ve also talked about the fundamental theorem of algebra and about negative and fractional exponents.