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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2012-06-23 03:07:41

Hi Agnishom;

Yes, follow the link that Bob has provided for the rigorous proof.

Let's see if geogebra can give us a clue.

Remember that line in post #1. That is one of the uses of software and computers. All in all, geogebra did well don't you think. Also, it was fun! Try it, it might even make you change your signature...

bob bundy
2012-06-23 02:17:54
bobbym
2012-06-23 01:40:49

Hi Agnishom;

Yes, for a rigorous proof you would use traditional methods. But for finding things to apply the traditional methods to, you might try the ideas presented here.

I know that you have only been exposed to the methods of traditional or classical mathematics. This training is geared toward the teaching of the calculus or continuous mathematics.

As you progress you will come into contact with the new "Discrete Mathematics." The methods I am playing with will then be more relevant to you.

anonimnystefy
2012-06-23 01:38:17

Actually, it was only with the use of a computer that the conjecture about there being 24 4 dimensional spheres tangent to one 4D sphere.

Computers were also used to prove that a valid sudoku grid must have at least 17 clues given at the beginning.

Agnishom
2012-06-23 01:29:10

But only the traditional methods can really prove
What can be done with softwares is just illustrations of examples.

bobbym
2012-05-24 04:06:03

Hi Agnishom;

The purpose of this thread is to use the techniques and software of experimental mathematics to find and soft - prove conjectures. Traditional and rigorous methods that you seek are handled in the other thread.

Agnishom
2012-05-24 00:24:02

Hi Bobbym;

Will you give me the mathematical reason why this happens?
I mean how do you come to know that: BCD + BAD = 180

bobbym
2012-05-23 23:32:33

Hi;

This problem came up:

In the adjoining figure, Find angle BCD

http://www.mathisfunforum.com/showimage.php?pid=220409&filename=Circle.png

Let's see if geogebra can give us a clue.

1) Create points A(0,0) and B(5,0).

2) Use the angle with a given size tool and click B and then click A. In the input box enter 30. Point B' will be created.

3) Draw a line between A and B'.

4) Use the angle with a given size tool and click A and then B' and enter 80

5) Point A' will be created.

6) Hide point B and draw a line from B' to A'.

7) Get the intersection of the new line and the x axis.

8) Point C will be created. Hide line AB' and B'C.

9) Use the circle through 3 point tool on A, B' and C.

10) Create a polygon with A, B' and C as vertices.

11) Create a point anywhere on the bottom half of the circle's circumference. Call it D.

12) Use the polygon tool on A,C and D. Color the polygon a different color from the top one.

13) Use the angle measure tool to measure angle ADC. What do you get for the angle? Move point D around and observe the angle.

Here is what your picture should look like:

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