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## #1 2012-03-15 23:59:12

bobbym
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### Largest equilateral triangle

What is the Area of the largest equilateral triangle that can inscribed in a 2 x 2 square?

How can geogebra answer the question for us?

1)Place point A at (0,0)

2)Place point B at (0,2)

3)Draw a slider with MIn = 0, Max = 2 and Inc = .001. Call it b.

4)Place point C at (2,2).

5)Draw a line segment BC. Color it red. Draw point (2,0) and label it D. Draw line segment CD and color it red. This represents our square.

6)Place a point at (b,2).
This is done by entering P = (b,2).

7)Use the regular polygon tool and select P then A and in the input box enter 3 and equilateral triangle APE is created.

8)Draw a line through E and perpendicular to the x axis.

9)Get the insection of this line and the x axis by using the intersect 2 objects tool. It will be labelled F.

10)You can hide E and now highlight the slider point called b and use the arrow keys and and shift arrow keys until F is as close to (2,0) as is possible. I set the rounding option to 15 digits for this.

11)After doing that I was able to get F = (2.000000807568878, 0). Now just read off poly1 = 1.856407210140189. That is the largest area based on the accuracy of our drawing.

Read off d = 2.070552778849165 as the sides of that triangle.

12)Put a point G on the bottom of the triangle and measure GAF. I get

14.999956829241965°

Check to see how this compares to the math solution at http://www.mathisfunforum.com/viewtopic … 92#p204492

where the answer given is 15°  for the angle and

for the sides. Pretty good accuracy from geogebra!

Here is the drawing

Uploaded Images

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #2 2012-04-06 00:23:54

anonimnystefy
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### Re: Largest equilateral triangle

hi bobbym

What would be the non-computational way of doing this?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #3 2012-04-06 00:27:12

bobbym
Administrator

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### Re: Largest equilateral triangle

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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