The picture is Very Wrong™ (but the area formula is correct)
The lengths of the not-horizontal lines are interchanged.
And it looks distorted but that’s not too bad.
And then it should be r =. sideOfUnitHexagon
which is obviously due to the same confusion
as the mislabelled lines.
Just think of the hexagon cut into six triangles.
They’ll be regular as well, so radius = side.
Another way to see this is to remember you can
construct a regular hex by taking a circle and
repeatedly go around that circle finding
intersections at one radius distance.
Am 08.02.21 um 06:30 schrieb Devon McCormick:
> This scales the hexagon to have unit area.
> hexagonArea=: 3 : '3*y*(-:y)*%:3' NB. Where y is side length
> sideOfUnitHexagon=: 0.6204032394013997
> hexagonArea sideOfUnitHexagon
> 1
> ]r=. sideOfUnitHexagon*-:%:3
> 0.537285
> 'title Regular Hexagons Centered at Origin;type line;pensize 2; aspect
> 0.866' plot (],.{."1) (r,1)*"(0 1) (_1^1r3)^i.6
>
> See
> https://code.jsoftware.com/wiki/NYCJUG/2021-02-09#Corners_of_Unit_Hexagon_Centered_at_Origin
> for a diagram illustrating why we use the square root of 3.
>
> On Sun, Feb 7, 2021 at 4:00 PM Hauke Rehr <[email protected]> wrote:
>
>> I wonder about that scaling factor in
>>
>> */ , 5e_7 > | hexCorners - 0.537285 * +. (_1^1r3)^i.6
>>
>> Is there anything special about it?
>>
>>
>> Am 07.02.21 um 21:28 schrieb Devon McCormick:
>>> I'm trying to draw a unit hexagon centered at the origin with the
>>> horizontal sides parallel to the X-axis. I've come up with these
>>> co-ordinates for the corners but when I plot them, the drawing looks a
>>> little too wide:
>>>
>>> hexCorners=. _2]\,0.537285 0 0.268642 0.465302 _0.268642 0.465302
>>> _0.537285 0 _0.268642 _0.465302 0.268642 _0.465302
>>> 'title Regular Unit Hexagon Centered at Origin;type line;pensize 2'
>> plot
>>> (],{.) j./"1 hexCorners
>>>
>>> I can use my paint program to distort a picture of this plot until it
>> looks
>>> like it has a square aspect ratio (roughly, width height * 0.92 1.06) but
>>> how can I plot this with the correct aspect ratio in the first place?
>>>
>>
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>
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