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How do I get the area of DEC that is within the square?

'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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Agnishom,

Deducting the areas of triangle ABE and the Circular Sectors AED and BCE from square ABCD should work. I got approx 2.126.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

You'll need to use the Circular Sector tool and the Polygon tool to draw the three shapes. Their areas display automatically in the Algebra column.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

...and here's my Geogebra drawing:

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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Is there no simpler way?

'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: 86,257

Hi;

Or

2*IntegralBetween[sqrt(49 - x²), 7, x(E), 0]

g = 2.126037602964608

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

It had to be simple for me to be able to understand it, so I think that may be about as simple as it can get! I don't know of any other way, but someone else might...

The arithmetic is taken care of automatically, too, just by entering "poly1-poly2-g-h" into the Input bar, the result of which shows up in the Algebra column for 'i'.

Btw, I erred with the triangle notation in the text bar below the drawing: it should read ABE, not ADE.

PS...I see bobbym's just posted a 'simpler' way!

*Last edited by phrontister (2014-03-30 04:15:40)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Hi phrontister;

A great feature about G is that it will shade the area it is integrating, that way you can not make a mistake.

It is not really simpler and anyway simpler is an undefined term. It raises two more difficult questions.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Yes, the more I use G the more I'm impressed with it...in so many ways! And I've only just started to scratch the surface of its abilities!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Hi;

I do not think I will ever be able to get out of the rank of beginner using it.

**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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

It raises two more difficult questions.

Did I guess the two questions?

*Last edited by ElainaVW (2014-03-30 05:14:59)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Hi;

Yes, you did. Do you hear the grasshopper at your feet?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

I think I have stepped on it as Agnishom did.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

I never did hear that little bug down there. A triumph of experimental mathematics which is just seconds from ruling the world!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi ElainaVW,

Nice! Not that I have any clues as to how you got those.

I suppose I could cheat and work backwards to the second one (which is E's height above the x-axis) by using Geogebra's area of ΔABE and the base length, but I wouldn't know how to use that in shape DEC's area calculation.

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bobbym wrote:

Hi;

Or

2*IntegralBetween[sqrt(49 - x²), 7, x(E), 0]

g = 2.126037602964608

What is this?

'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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Hello:

phrontister wrote:

I suppose I could cheat and work backwards to the second one (which is E's height above the x-axis) by using Geogebra's area of ΔABE and the base length, but I wouldn't know how to use that in shape DEC's area calculation.

I am pleased to meet you. You do not have to limit yourself to the use of Geogebra, you are M capable too.

Agnishom wrote:

What is this?

It looks like the right answer.

*Last edited by ElainaVW (2014-03-30 14:44:59)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Hi;

phrontister meet ElainaVW, she used M to get those answers.

What is this?

They say a picture is worth a thousand words. Did you try it?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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It is not a picture.

Is it M code or G?

'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: 86,257

It is not a picture.

It is most certainly a picture.

It is Geogebra code.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

ElainaVW wrote:

You do not have to limit yourself to the use of Geogebra, you are M capable too.

I did this in M with G's area of ΔABE to get E's height above the square's base:

RootApproximant[2*21.2176223927/7] // FullSimplify, resulting in:

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Hi;

You do not have to limit the construction. It might be easier to create 2 circles rather than 2 arcs.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Sorry, I'm not getting the picture re the 2 circles instead of the 2 circular sectors.

I find my method of {Square - Triangle - 2 Circular Sectors} to be quick and easy. In fact, I just drew it up in G from scratch and found the decimal approximation of the shape's area in just under 2 minutes.

I suppose that it can be done quicker in M, but I'd struggle all day (minimum) to get the same result! But it's all a matter of knowing, I know, and I just don't know enough to know how to obtain the solution differently.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,257

Okay, if you feel comfortable with it then do it that way.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

I'm happy with it, but I'll keep watching the thread to find out which method will make Agnishom happy.

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