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#1 2012-03-15 00:59:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

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

View Image: 2012-03-15_062232.gif

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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#2 2012-04-05 02:23:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,809

Re: Largest equilateral triangle

hi bobbym

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2012-04-05 02:27:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

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.

Offline

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