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Divide a surface into equal sized areas

SOLVED
Peridot

Divide a surface into equal sized areas

Puzzle only to fun. Question graphs are made by using Mathcad programing.

Divide a surface into two equal sized areas by using matchsticks.

1. With using two matchsticks.

2. With using three matchsticks.

3. With using n>3 matchsticks.

puzzle-6.png

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Divide a surface into equal sized areas

Ttokoro, it seems like this ? :

Quarter_Volume.PNG

Quarter_Volume (2).PNG

 

Regards.

   Loi

View solution in original post

22 REPLIES 22

Re: Divide a surface into equal sized areas

That's a no-brainer. I have very large match-sticks, so I can divide the triangle into two pieces of equal size with a single match-stick, using a variety of positions of the stick.

And if it can be done with one, it can be done with any number of match-sticks.

But I think that's not what you're after, and you implicitly assume some rules that you have not explained.

 

Luc

Re: Divide a surface into equal sized areas

Assuming that only match-sticks with length 1 may be used, and they must be only inside the triangle, here is a solution for 2 match-sticks.

LM_20180905_Triangle1.png
LM_20180905_Triangle2.png


Luc

Re: Divide a surface into equal sized areas

Here's a second solution using two match sticks:

B.png

An additional puzzle: Using four matchsticks divide the triangle area in three areas of equal size.

Re: Divide a surface into equal sized areas

Good answers!

Both of you using Mathcad and it will be help for Machcad usage for the users. 

Match stick puzzle usually use unit length 1 and it put on dot points on the figure of the stick top or bottom.

Or the position can be fixed by using match sticks. 

If you got two and three stick answers, you can arrange them any number of this problem.

 

Then, using 12 all sticks in my picture and move two or more sticks to reduce the area size from 4*3/2=6 to 5, 4,3 and 2. I don't know the answer the area size is 1. Of course the minimum movement number of the sticks are the good answers.   

 Tokoro.

Re: Divide a surface into equal sized areas

image.pngimage.png

The one of 3D.

Tags (1)

Re: Divide a surface into equal sized areas

Ttokoro, It seems something like this :Half_Vulume.PNG

Best Regards.

   Loi.

Tags (1)

Re: Divide a surface into equal sized areas

And It seems to be as half-volume, too. ?

Half_Vulume.PNG

Regards.

  Loi.

Re: Divide a surface into equal sized areas

image.pngimage.png

1/4th.

Tags (1)

Re: Divide a surface into equal sized areas

Ttokoro, it seems like this ? :

Quarter_Volume.PNG

Quarter_Volume (2).PNG

 

Regards.

   Loi

View solution in original post

Re: Divide a surface into equal sized areas

One more third divide by a plane would output a 1/8 V.

Eighth_Volume.PNG
Regards.
Loi.

Re: Divide a surface into equal sized areas

image.png

Tags (1)

Re: Divide a surface into equal sized areas

Thanks for your hint, Tokoro. And it seems this is half-volume of "frame".

#10.PNG

Regards.

Loi.

Re: Divide a surface into equal sized areas

image.png

Nice Job! Oden for kudos.

Tags (1)

Re: Divide a surface into equal sized areas

image.pngimage.png

image.png

Tags (2)

Re: Divide a surface into equal sized areas

Regular Icosahedron.PNG

Re: Divide a surface into equal sized areas

image.png

Tags (1)

Re: Divide a surface into equal sized areas

1.png

2.png

Re: Divide a surface into equal sized areas

image.png

Tags (1)

Re: Divide a surface into equal sized areas

It seems this is last surface patch that I have known about that rotation. (And It seems to divide a surface of regular dodecahedron into equal sized area.) 

Rotate.PNG

(a).PNG

b.png

Best Regards.

Loi.

Re: Divide a surface into equal sized areas

I.png

II.png

Re: Divide a surface into equal sized areas

Rotation and divide a surface into equal sized areas. (divide by 6 sticks) 

A.png

B.png

Regards.
Loi.

Re: Divide a surface into equal sized areas

Tokoro, there are two more other planes that divide a surface into equal sized areas :

 (1).png

(2).png

 

Best Regards.

Loi.

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