Geogebra Help

Agnishom · 2014-03-30 01:34:02

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

phrontister · 2014-03-30 03:03:11

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.

phrontister · 2014-03-30 03:33:49

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.

phrontister · 2014-03-30 03:57:27

...and here's my Geogebra drawing:

Agnishom · 2014-03-30 03:58:46

Is there no simpler way?

bobbym · 2014-03-30 04:03:26

Hi;

Or

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

g = 2.126037602964608

phrontister · 2014-03-30 04:13:25

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)

bobbym · 2014-03-30 04:16:32

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.

phrontister · 2014-03-30 04:38:12

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!

bobbym · 2014-03-30 04:41:09

Hi;

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

ElainaVW · 2014-03-30 05:14:20

It raises two more difficult questions.

Did I guess the two questions?

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

bobbym · 2014-03-30 05:16:50

Hi;

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

ElainaVW · 2014-03-30 05:18:49

I think I have stepped on it as Agnishom did.

bobbym · 2014-03-30 05:21:03

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

phrontister · 2014-03-30 10:45:20

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.

Agnishom · 2014-03-30 14:23:30

bobbym wrote:

Hi;
Or
2*IntegralBetween[sqrt(49 - x²), 7, x(E), 0]
g = 2.126037602964608

What is this?

ElainaVW · 2014-03-30 14:44:16

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)

bobbym · 2014-03-30 14:57:25

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?

Agnishom · 2014-03-30 15:03:02

It is not a picture.

Is it M code or G?

bobbym · 2014-03-30 15:05:51

It is not a picture.

It is most certainly a picture.

It is Geogebra code.

phrontister · 2014-03-31 00:07:13

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:

bobbym · 2014-03-31 00:10:27

Hi;

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

phrontister · 2014-03-31 01:21:44

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.

bobbym · 2014-03-31 01:26:36

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

phrontister · 2014-03-31 01:31:59

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

Math Is Fun Forum

#1 2014-03-30 01:34:02

Geogebra Help

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