# The pond of symmetry

There is a $$4$$m by $$4$$m square pond. You have $$3$$ straight planks of wood, each exactly $$2$$m in length.

You need to place the planks so that they go from one corner of the pond to the diagonally opposite one. There is to be no plank overlapping.

The planks must be laid rotationally symmetric around the centre of the pond.

How do you do it, using only a water-compass? (i.e. no angle-ommeters!)

• What do you mean by "water-compass" exactly? – Deusovi May 24 '20 at 15:28
• @Deusovi; as in en.wikipedia.org/wiki/Straightedge_and_compass_construction, but for use in water. – JMP May 24 '20 at 15:31
• Do we also not have any form of straightedge? Can we assume that our weight is negligible in comparison to the weight of the planks of wood? (that is, that we can walk on the planks of wood without worrying about them tipping and falling in?) Can the compass be used on the planks of wood, separately from the water? – Deusovi May 24 '20 at 15:33
• walking around the pond isn't an option? – SteveV May 24 '20 at 15:37
• The planks are straight-edged. You only need to place the planks - you can swim in the pond if you want. – JMP May 24 '20 at 15:38

Of course, the compass can be set to a radius of 2m, using a plank. Similarly with 1m - if you disagree, use the compass to mark 1/2 of a plank.

First, to find the center,

Use a plank to find the midpoint of one side, and use the water compass to construct a line through that point and perpendicular to the side. Again using a plank of 2m gives the center. Use your watercolor pencil to mark it. Then, to position all three planks,

make circles of radius 2m around two opposing cornes, and a circle of radius 1m around the center: • "Watercolor pencil"! Always handy. – humn May 25 '20 at 6:47 Let's have a square pond where AB=AC=4. First we draw the diagonal AD. From point A we draw a circumference with R1=2. From the point where the circumference cuts the diagonal AD we draw a circle with R2=2. Finally, from the point D we draw another circle with R3=2. We set points where R1 cuts the diagonal AD and where the circles with R2 and R3 intersect. We set the planks between A and the first point, between the two points, and from the second point to D.