5

A figure consists of 5 equal squares in the form of a cross. show how to divide it by two straight cuts into 4 equal figures which will fit together to form a square. enter image description here

i cut the figure through 2 perpendicular straight lines through center as shown. is it correct? is there any other way to solve this question?

Ishita Hariramani
  • 323

2 Answers2

2

Hints: In this type of geometric dissection problem, "forming a square" generally means a solid square.

As a suggestion for solving your problem, find a way to tile the plane with your cross-shaped figures. The tiling has square symmetry; superimpose a (necessarily tilted) square grid in a way that each square contains a congruent collection of "pieces of cross". There is your dissection.

For further reading:

  • Chapter four of Knots and Borromean Rings, Rep-Tiles, and Eight Queens by Martin gardner, reprinted by the MAA and Cambridge University Press.

    This chapter contains a fairly extensive bibliography.

Spoiler

Andrew D. Hwang
  • 78,195
2

This is another way to cut the cross. enter image description here

Seyed
  • 8,933
  • 1
    Unless you came up with this yourself, you ought to cite the source. And in the 3rd figure, the four pieces aren't equal, and in the first figure, the square isn't solid. – Gerry Myerson Nov 05 '16 at 12:21
  • @GerryMyerson, that is correct, the four pieces in the third figure were not equal and i removed it. The question didn't ask for a solid square. – Seyed Nov 05 '16 at 12:27
  • No, but I bet that's what was meant, as it always is in these dissection puzzles. Anyway, your source? – Gerry Myerson Nov 05 '16 at 12:30
  • 2
    got it. if solid squares are not must, then even my way was correct. right? – Ishita Hariramani Nov 05 '16 at 12:37
  • @GerryMyerson, The question and its solution is very famous to those who are familiar with this kind of puzzles. – Seyed Nov 05 '16 at 13:08
  • 1
    @Seyed: I think you miss Gerry's point, which is that if you did not create these images yourself, then without citation of a source the images in your answer constitute plagiarism. – Andrew D. Hwang Nov 05 '16 at 16:10
  • @AndrewD.Hwang, Sorry i didn't know Gerry couldn't explain himself and he needed someone to do the job for him, but for your information I should say that I drew those images. – Seyed Nov 05 '16 at 18:12
  • @Seyed: Speaking for myself, thank you for the clarification. – Andrew D. Hwang Nov 05 '16 at 18:32