My Math Genius

Inverse's inverse.

2010-07-25T08:51:00.000-07:00

I have forgotten where the subject came from, but thinking about some sort of paradoxical function that's its own inverse is really a neat idea. So here's what I have come up with:

Is there a function that's its own inverse?

Yes!

As a matter of fact, I have found 2, {(1/x) and x/(x-1)}, just thinking about it.

However, if you're in a bind to find as many as you can anything with points that stick to y = 1/x will work. (because basically that's what the definition of an inverse is)

If anyone can think of another function that is it's own inverse, please post it if you can!

-Mr.Mathematic

*Robert also noted that y = x is the trivial case for an inverse, making 3. Thanks Robert!

The infinitly interesting interests of infinity.

2009-08-10T07:49:00.000-07:00

Everyone seems to know that crazy little sideways eight we all call "infinity" if not it looks like this: ∞

So what about it?

Its flaws:

1) how can 1 number represent every other number?

2) if ∞ does equal every number such as 1, 2, 3, .... then 1*0, 2*0, 3*0.... = 0 yet ∞*0 = ∞ (See August Brain Buster and its solution)

3) ∞/∞ Should = 1, but in reality it could equal any number so it equals ∞

4) Basically ∞ seems to break all of the rules in mathematics, so it seems to be a bad choice for a number.

The Good:

1) Although a major pain to work with in any equation, it can be used quite well in limit problems.

2) It's a concept that is very interesting to think about, but can never actually be reached on a number line.

Any More?
Email MrMathematic@gmail.com to see it on the list.

Did YOU know that....

2009-08-09T14:58:00.000-07:00

=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ...
A sphere has two sides. However, there are one-sided surfaces.
There are shapes of constant width other than the circle. One can even drill square holes.
There are just five regular polyhedra
In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
Everything you can do with a ruler and a compass you can do with the compass alone
Among all shapes with the same perimeter a circle has the largest area.
There are curves that fill a plane without holes
Much as with people, there are irrational, perfect, complex numbers
As in philosophy, there are transcendental numbers
As in the art, there are imaginary and surreal numbers
A straight line has dimension 1, a plane - 2. Fractals have mostly fractional dimension
You are wrong if you think Mathematics is not fun
Mathematics studies neighborhoods, groups and free groups, rings, ideals, holes, poles removable poles, trees, growth ... and
Mathematics also studies models, shapes, curves, cardinals, similarity, consistency, completeness, space ...
Among objects of mathematical study are heredity, continuity, jumps, infinity, infinitesimals, paradoxes...
Last but not the least, Mathematics studies stability, projections and values, values are often absolute but may also be extreme, local or global.
Trigonometry aside, Mathematics comprises fields like Game Theory, Braids Theory, Knot Theory and more
One is morally obligated not to do anything impossible
Some numbers are square, yet others are triangular
The next sentence is true but you must not believe it
The previous sentence was false
12+3-4+5+67+8+9=100 and there exists at least one other representation of 100 with 9 digits in the right order and math operations in between
One can cut a pie into 8 pieces with three movements
Program=Algorithms+Data Structures
There is something the dead eat but if the living eat it, they die.
A clock never showing right time might be preferable to the one showing right time twice a day
Among all shapes with the same area circle has the shortest perimeter

Funny Math (1=2) Brain teaser

2009-08-05T15:22:00.000-07:00

Let's say that a = a

So it's obvious that a*a = a*a

And a^2 - a^2 = a^2 - a^2

Difference in Squares says that a(a - a) = (a-a)*(a+a)
Divide by (a-a)

And you get a = a+a

Which means the same as a = 2a
Divide both sides by a

And 1 = 2

Tada!

Do you see the problem?
Email your answer to MrMathematic@gmail.com

Mathematics is...

2009-08-03T21:57:00.000-07:00

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” -- Bertrand Russell

“Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.”

“Mathematics is the art of giving the same name to different things.” -- J. H. Poincare

“Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.”

"Mathematics is a game played according to certain simple rules with meaningless marks on paper." -- David Hilbert

"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

"A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.”

“Mathematics is like love; a simple idea, but it can get complicated.”

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

“Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.” -- Plato

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder

"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent." -- Raoul Bott

"Obvious is the most dangerous word in mathematics." -- E.T. Bell

"Arithmetic is being able to count up to twenty without taking off your shoes." -- Mickey Mouse

"The greatest unsolved theorem in mathematics is why some people are better at it than others." -- Adrian Mathesis

"Mathematics is not a deductive science – that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." -- Paul Halmos

“The different branches of Arithmetic are Ambition, Distraction, Uglification, and Derision.” – Lewis Caroll

"Mathematics is written for mathematicians." – Copernicus

"Mathematics should be fun." -- Peter J. Hilton

"Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."

"But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer." -- Tom Lehrer

Brain Buster for August

2009-08-02T23:00:00.000-07:00

If 1/∞ =0 and 1/0 = ∞

then what does 0 * ∞ = ?

Email your Answer to MrMathematic@gmail.com

Pythagorean Theorem Proof

2009-08-01T12:15:00.000-07:00

Everyone of course knows of the Pythagorean Theorem, but where did it come from?

How did our good friend Pythagoras know that

Well this is how, First he took a square and put another one inside of that so you could have 4 triangles like so:

Then as you can see he just compared the areas and whaaalaa! The Pythagorean Theorem!

-Mr.Mathematic

Derivative Proof

2009-07-29T21:34:00.000-07:00

So here is the equation for the derivative:

Now if you are like me I bet you are wondering how in the world did that become the finial answer?

Well here is how:

I will assume by now you know what the slope is, if not here is a picture of the slope equation:

Now this is the same as saying

Now let's say that Y = f(x) and imagine pluging it in up there.
and we get: (f(x2)-f(x1))/Δx or basically Δf(x)/Δx

So now look at Δx, it equals x2-x1 so solve for x2 you get Δx+ x1 =x2
So plug that in and you get f(x1+Δx)-f(x1) divided by Δx

At this point you probably notice that this look a lot like the derivative formula

Except without the limit and instead of Δx, the letter h was used (same basic thing)

Now what the limit say is that h approaches 0 which is what we are trying to do, if you need a better understanding look at "what is a derivative"

So now I hope you fully understand what the Derivative is and if you do then keep in mind I will most likely do an article on integration that will turn you Calculus world upside down.

See you next time!

-Mr.Mathematic

What is the derivative?

2009-07-29T21:26:00.000-07:00

Well besides being a major pain the (3 letter word for rump) of any Calculus student, the derivative is actually pretty useful. It's basically the slope of a tangent line like so:

you see?

Just like in calculus you study what happens to things as you get them really really small, or really really big, in this case it's letting the delta x (or change in x approach 0)

Now if you are of those people that like equations and proof (Me, but the graph is good too) There is also one on that named "Derivative Proof"

Zeno's Paradox

2009-07-27T21:55:00.002-07:00

Zeno, a Greek man around the time of 500 B.C., decided to take a runner

This runner is racing a turtle and for every 10 ft the turtle goes the runner goes 100 ft. but Zeno gives the turtle a 300 ft head start. So now for the as the race starts the runner has to go 300 ft to catch up, but by the time this happens the turtle goes 30 ft. Then the runner goes 30 ft and the turtle goes 3ft this continues for infinity.
So who wins?

The Turtle! (after an infinite amount of years)

It's all about Pi.

2009-07-27T21:55:00.001-07:00

Historians estimate that by 2000 B.C. humans had noticed that the ratio of circumference to diameter was the same for all circles. This discovery hinged on the idea of proportion - in this case humans noticed that if you double the distance "across" a circle, then you double the distance "around" it. As of today this is the formula:

where Pi was constant. (It wasn't until 1706 that this notation, using the Greek letter seen in the above equation - often written Pi and pronounced like the English 'pie' - was introduced by William Jones).

But one problem remained - what is the numerical value of Pi?

let's take a look!

Person/People	Year	Value
Babylonians	~2000 B.C.	3 1/8
Egyptians	~2000 B.C.	(16/9)^2= 3.1605
Chinese	~1200 B.C.	3
Old Testament	~550 B.C.	3
Archimedes	~300 B.C.	proves 3 10/71<3 67441="">
Ptolemy	~200 A.D.	377/120=3.14166...
Chung Huing	~300 A.D.	sqrt(10)=3.16...
Wang Fau	263 A.D.	157/50=3.14
Tsu Chung-Chi	~500 A.D.	proves 3.1415926<3.1415929
Aryabhatta	~500	3.1416
Brahmagupta	~600	sqrt(10)
Fibonacci	1220	3.141818
Ludolph van Ceulen	1596	Calculates Pi to 35 decimal places
Machin	1706	100 decimal places
Lambert	1766	Proves Pi is irrational
Richter	1855	500 decimal places
Lindeman	1882	Proves Pi is transcendental
Ferguson	1947	808 decimal places
Pegasus Computer	1957	7,840 decimal places
IBM 7090	1961	100,000 decimal places
CDC 6600	1967	500,000 decimal places

Contact Me

2009-07-27T21:54:00.000-07:00

You can email your questions or ideas to MrMathematic@gmail.com I am happy to help out, especially if it helps you out. If you want more than free email support, instantaneous help is available here where you can reserve an hour or more. Or you can email me and set up a time when you are able.

Check out any of the next 3 dots for more info. . . .

-Mr.Mathematic

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2001-07-24T23:53:00.000-07:00

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2001-07-24T13:20:00.000-07:00

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