# Dw i eisiau hecsagon du a gwyn.

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Dw i eisiau hecsagon du a gwyn.

The above sentence is in the Welsh language.

The sentence translates into English as follows.

I want a black and white hexagon.

I am learning some Welsh.

There is a free course.

Anyway, the sentence arose in an exercise about colours.

So, having finished the exercise, I wondered, how exactly would one have a black and white hexagon.

Some readers may remember the image in the following post.

That image has a source file with square5.afdesign as its file name.

So I made a copy as hexagon1.afdesign and then deleted the image, yet kept the background.

So it is 1641 pixels square.

So, start with a hexagon, produced using the Polygon Tool with the keyboard shift key depressed, with a zero-width stroke.

Ah, the bounding box is square.

The Transform panel has the excellent faciiity that one can have the X and Y coordinates of an image about any one of nine places and one can change that as one proceeds if one chooses to do so.

So, with X and Y measured about the centre of the image, set (X, Y) = (820, 820) and the width and height of the bounding box both to 1000 pixels.

Colour the hexagon white.

Now, convert to curves.

Please note that the size of the bounding box changes.

Copy the hexagon, paste a copy, colour the copy black, and use the node tool to delete two nodes and save.

Here is a png 547 pixels square.

Yet there are many possible black and white hexagons.

Here are a few more images that I have produced. Each of these images with the extra conditions that the area of black is the same as the area of white, and that the shapes of the black areas are the same as the shapes of the white areas.

One or more of those conditions need not necessarily apply to all black and white hexagons, but both of those two conditions do apply to each of these four images.

The technique that I used was to copy a shape, delete a node or nodes and then position the shape precisely by entering numbers into the Transform Panel, typically 820 for each of X and Y having chosen the option of from about which point to measure X and Y as seemed was needed for the particular shape positioning.

William

Until December 2022, using a Lenovo laptop running Windows 10 in England. From January 2023, using an HP laptop running Windows 11 in England.

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In this image, the black hexagon is a copy of the original white hexagon that has had its height and width each multiplied by 0.7071, which is the square root of 2 divided by 2.

So is the area of white that is displayed in the image the same as the area of black that is displayed in the image?

William

Until December 2022, using a Lenovo laptop running Windows 10 in England. From January 2023, using an HP laptop running Windows 11 in England.

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For completeness.

William

Until December 2022, using a Lenovo laptop running Windows 10 in England. From January 2023, using an HP laptop running Windows 11 in England.

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This seventh image was produced by starting with a copy of the source file of the fifth image.

In fact, this image is made up of two complete white hexagons, and two black half hexagons, all upon a grey background.

Grey, white, black, white, black.

William

Until December 2022, using a Lenovo laptop running Windows 10 in England. From January 2023, using an HP laptop running Windows 11 in England.

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William

Until December 2022, using a Lenovo laptop running Windows 10 in England. From January 2023, using an HP laptop running Windows 11 in England.

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