Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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Bobbym had told me that it is not an inspirational essay.. It's only his thoughts and feelings on the field.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Nope, the front part is the definition!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

Agnishom wrote:

We have used this property in lower grades to mark irrational numbers like sqrt(2) on the real number line.

Long, long ago, when I was doing O level Technical drawing, we used it to construct (compass, set square and straight edge only) a square equal in area to a given rectangle.

We also learnt how to use construction techniques to do:

n sided polygon ---> equal area n-1 sided polygon

triangle ---> equal area rectangle

Thus you can convert any polygon to an equal area square.

But not a circle

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

bob bundy wrote:

See diagram below.

Your diagram is a special case where ADB is a diameter. => chord CE is bisected by ADB so CE = DE.

b

How do you write out the notation like this? I think I have another solution that works.

*Last edited by PatternMan (2014-04-24 10:40:37)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

Where did you draw this also?

*Last edited by PatternMan (2014-04-25 04:12:54)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

It is hard to write the solution here so I'll just explain.

Area of the biggest semi circle minus the area of the two smaller semicircles. Once you cancell down you get 1/4 pi AD times DB

Then:

You have now have a right angled triangle by the inscribed angle rule. You can now apply pythagorus theorem.

AB^2 = AC^2 + CB^2 Now AC is the hypotenuse of triangle ACD

CB is the hypotenuse of triangle CDB

So AB^2 = AD^2 + CD^2 + CD^2 + DB^2

AB^2= AD^2 + 2CD^2 + DB^2

bla bla bla

2AD x DB = 2CD^2

AD x DB = CD^2

so replace AD x DB by CD^2

*Last edited by PatternMan (2014-04-25 04:21:21)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi Patternman,

Where did you draw this also?

You should be able to see a diagram in post 5. If you meant 'what software am I using?' it's called Geometers Sketchpad. You can also use Geogebra which is a free download.

The notation is done using Latex. If you click on some, you'll get a window showing the actual code. You enclose it in square brackets math /math to switch in the Latex handling program.

There's a tutorial at

http://www.mathisfunforum.com/viewtopic.php?id=4397

and you and set up code using the editor at

http://latex.codecogs.com/eqneditor/editor.php

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

A friend sent the question to me so I don't know how it was made. I just drew the right angle triangle in ms paint.

*Last edited by PatternMan (2014-04-25 05:58:58)*

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You can also use Geogebra which is a free download.

Also, it is mostly free software. Parts of GPL and CC BY-SA.

The freedom of commercially using the modified code is prohibited, though.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Geometer's sketchpad is nice too, for drawing and getting results quickly.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Georgie Gebra is the man. If he can not do it nobody can! Georgie Gebra!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Well, of course Geometer's sketchpad is not nearly as powerful as Geogebra, but it is nice for quick things - especially at Patternman's level.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

I would imagine they would both be very useful to him. Georgie makes it so easy to develop the art of creative guessing...

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

ShivamS wrote:

Geometer's sketchpad is nice too, for drawing and getting results quickly.

Richard Stallman wrote:

Proprietary software is itself an injustice.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Stallman's full of sheep dip or maybe even kaboobly doo.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Most people use the program rather than changing it.

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