You are watching: Different shapes with the same perimeter

First I thought that having the same perimeter length and same surface ar would be enough, but I experienced on that link that it is not correct hypothesis.

If ns take as added condition that the two shapes have the same variety of segments, would it be enough? Or else how deserve to I check that?

The trouble is because that each detail, castle can gain rotation, or symmetry.

**Edit :**

Thanks for her answers, i finally uncovered a method to settle the problem (answer below)

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edited Jul 26 "19 at 12:31

Siegfried.V

request Jul 25 "19 at 5:35

Siegfried.VSiegfried.V

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In the soul of the no-words answer come the connected question:

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edited Jul 30 "19 in ~ 18:29

Andrew Stacey

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answered Jul 25 "19 at 5:56

Hagen von EitzenHagen von Eitzen

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Inspired by Hagen von Eitzen"s answer, a details pair of tetrominoes furnishes another counterexample (minimal among polyominoes):

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answer Jul 26 "19 at 14:57

Travis WillseTravis Willse

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No, it is still not enough. Also for quadrilaterals the is no enough. Take it a kite with sides $1,1,3,3$ and the angle between the two $1$s a appropriate angle. The perimeter is $8$ and the area is $frac 12(1+sqrt17)$. Currently take a rhombus through sides that $8$. It also has a perimeter that $8$ and you can pick the edge to do the areas match. It is even worse for more sides. The area and also perimeter are simply two constraints, if there are lots of levels of freedom.

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reply Jul 25 "19 in ~ 5:47

Ross MillikanRoss Millikan

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Possibly the most basic counterexample: form two sides of a triangle v line segments of uneven length. In one version, mirror it. In the other, rotate it 180°.

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answered Jul 28 "19 at 2:13

GnubieGnubie

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Well, ns finally managed to execute that, yet it was much longer than expected :

My form is identified by a perform of contour element, edge is defined by 2 points and also a radius.If this is a segment climate radius=0, if this is one arc, radius is confident if I rotate in trigonometric direction, an adverse if the opposite side).

I make a an initial check, check if areas are equal(just come identify much faster if shapes are equal or not).

For each shape, i browse each segment(or one arc) ClockWise direction and also I return 3 outcomes :

List the the lengths of segments(just Pythagoras, don"t check radiuses)List of radiuses of every segment/arcList of angles between each segment and consecutive segmentI then can compare lock (let"s take in account that I begin from the same allude on each figure). In C# I just made a loop trying to begin from different points.

If every 3 lists room equals, this method the shapes are equal and without rotation.

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Then for symmetry trouble I simply will recalculate 3 over lists for second shape, yet browsing border in the contrary direction, if the results are equal(angles and radiuses simply will it is in opposite sign), so that is the same shape with symmetry.