I came across a very interesting problem – one that seems to involve math tricks of some sort.  Or is it magic?  Whatever it is, it is certainly a math brain teaser!  Anyway, here is the graphic that had me scratching my head:

So what’s the deal here??  Where did the hole come from?  Please post your answers  :)

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Tags: brain teaser, math brain teaser, Math Tricks

So you have seen already a few posts about the golden ratio, which is approximately equal to 1.618. Are there math tricks that will allow you to determine the value for the golden ratio?  Well, since the title of this post is “The Golden Ratio and the Fibonacci Sequence”, then you might have guessed that there is a way to determine the golden ratio with the Fibonacci Sequence.

What the heck is the Fibonacci Sequence?  True, I have not written a post on it yet – but you just wait because there is a LOT to say about it later on – a LOT!!  But for now, let me just give you the sequence:

0,1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …

Do you see the pattern?  Each value, starting with the second “1″ in the sequence, is simply the sum of the preceding two values.  The general formuls for the Fibonacci sequence is:

F(n) = F(n – 1) + F(n – 2)

So how does this interesting sequence of numbers relate to the golden ratio?  Take any value in the sequence and divide it by the preceding value – what do you get?

For example:

34/21 = 1.619

Looks familiar, eh?

Try it again for a pair farther down the sequence:

233/144 = 1.61806

In fact, this manipulation of the Fibonacci series converges to the golden ratio.

Also, you can perform this manipulation using an “out of frame” Fibonacci series – that is, choose any two consecutive numbers, apply the general formula F(n) = F(n – 1) + F(n – 2) to get a new sequence, and then from the new sequence you will be able to determine an approximation for the golden ratio by following the same procedure as outlined above.  For example, starting with 887 and 888, we get the series:

887, 888, 1775, 2663, 4438, 7101, 11539, 18640, 30179 ,48819, 78998, 127817, 206815, 334632

Notice here that you do not get a very good approximation if you divide 888 by 887.  But as you move down the sequence, the value you obtain gets closer and closer to the golden ratio:

334632/206815 = 1.6180258

A superb example of math tricks in nature!

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Tags: 1.618, 1.61803399, fibonacci numbers, Fibonacci Sequence, fibonacci series, golden ratio, Math Tricks

Math Tricks – How to Remember Pi

What is pi?  Can’t remember pi beyond 3.14?  That’s OK. because there are math tricks to help you remember.  My favorite is this mnemonic:

“How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”

Each word contains the number of letters for the digit that belongs in that word’s place.  For instance, replace “How” with “3″, “I” with “1″, etc.

Using this math trick, we get:

3.14159265358979

Of course, you can make up your own mnemonic; if you do, please post your ideas here!

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Tags: Math Tricks, Remember Numbers

There are a few basic properties of numbers, and, no, giving throbbing headaches is NOT one of them.  The three basic (and my three favorite) properties of numbers are:

1: The Associative Property

2: The Commutative Property

3: The Distributive Property

If you spend the time to study the basic properties of numbers, you will grasp a deeper understanding of why you are able to manipulate algebraic equations – throw out your algebra book, because you will gain a natural ability to rearrange and simplify equations!  (Well – just in case, DON’T throw out your algebra book!)

Here I will discuss the Distributive Property of numbers and why I should be uttering such things on a web site about math tricks!

Let’s start out with a general formula which demonstrates the distributive property of numbers:

a(b + c) = ab + ac

The way to remember this property is to think of the number outside of the parentheses as “distributing itself” among the values being added within the parentheses.

So what does this have to do with math tricks?  Fair question – let me give you an example of why understanding this property is useful for performing fast mental multiplication.  Let’s say we want to multiply 8 x 1531.  Sure, it looks imposing, but remember that we can break down the number 1531 to:

1000 + 500 + 30 + 1

Now we can perform the multiplication in this fashion:

8(1000 + 500 + 30 + 1)

From the distributive property, we know that:

8(1000 + 500 + 30 + 1) = (8 x 1000) + (8 x 500) + (8 x 30) + (8 x 1)

Now the problem is in a form that we can easily solve mentally by first multiplying left to right:

8000 + 4000 + 240 + 8

And then performing the simple addition step to arrive at the answer, 12248!

So there you have it, the secret to how multiplication math magic works – Shhhh . . . . .

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Tags: distributive property, Math Tricks, multiplication math tricks, Multiplication Tricks, properties of numbers