PROBLEMS WITH BRAILLE CIRCLES
By: Lena and Richard Hinkle
Design is 23 rows, 30 cells.
Note: Full size pictures are the last full pages of this document.
It is imperative that you take the time to draw the drawing before you read the remainder of this work as we discuss the problems of drawing circles and refer to the drawing at the end of this document.
Begin Design:
Row 1: space 1 time, A [1], space 3 times, B [12], space 4 times, C [14], space 4 times, D [145], space 4 times, E [15], space 5 times, F [124].
Row 2: space 1 time, dot 3, space 3 times, hyphen [36], space 4 times, A [1], space 3 times, dot 2, A [1], EN [26].
Row 3: A [1], K [13], A [1], space 1 time, B [12], U [136], B [12], space 1 time, dot 4, space 1 time, A [1], dot 4, space 1 time, dots 46, space 1 time, A [1], dots 46, space 3 times, dot 4, space 5 times, dot 5.
Row 4: space 10 times, A [1], space 4 times, C [14].
Row 5: space 1 time, G [1245], space 3 times, H [125], space 4 times, I [24], space 4 times, J [245], space 4 times, K [13], space 5 times, L [123].
Row 6: space 1 time, dot 3, space 3 times, hyphen [36], space 4 times, dot 2, space 3 times, dot 3, colon [25], dot 3, space 2 times, dot 2, A [1], dot 2, space 2 times, dot 6, dot 2, C [14], EN [26].
Row 7: dot 2 three times, space 1 time, L [123], dot 2, L [123], space 1 time, dot 5, space 1 time, dot 2, dot 5, space 1 time, dots 56, space 1 time, dot 2, dots 45, space 1 time, dot 2, space 1 time, dot 2, space 1 time, dot 2, space 1 time, L [123], space 1 time, dot 2, space 1 time, L [123].
Row 8: space 1 time, A [1], space 3 times, C [14], space 4 times, dot 2, space 3 times, A [1], colon [25], A [1], space 2 times, dot 2, dot 3, dot 2, space 2 times, dot 4, dot 2, hyphen [36], dots 24.
Row 9: space 1 time, M [134], space 3 times, N [1345], space 3 times, O [135], space 4 times, P [1234], space 5 times, Q [12345], space 5 times, R [1235].
Row 10: space 5 times, hyphen [36], space 3 times, hyphen [36], space 3 times, dot 3, colon [25], dot 6, space 2 times, dot 6, dot 2, C [14], dot 5, dot 3, space 1 time, dot 6, dot 2, C [14], dot 5, dot 3.
Row 11: dot 5, X [1346], dot 2, space 1 time, K [13], space 1 time, dots 46, space 1 time, dots 456, space 1 time, L [123], space 1 time, dot 5, space 3 times, dot 2, space 1 time, dot 2, space 3 times, dot 4, space 1 time, K [13], space 3 times, dots 46.
Row 12: space 5 times, C [14], space 3 times, C [14], space 3 times, A [1], colon [25], dot 4, space 2 times, dot 4, dot 2, hyphen [36], dot 4, A [1], space 1 time, dot 4, dot 2, hyphen [36], dot 5, dot 1.
Row 13: S [234], space 3 times, T [2345], space 4 times, U [136], space 4 times, V [1236], space 5 times, W [2456], space 5 times, X [1346].
Row 14: space 4 times, dot 6, dot 3, space 3 times, dot 6, dot 3, space 2 times, dot 6, dot 5, dot 2, dot 3, space 2 times, IN [35], dot 4, A [1], EN [26].
Row 15: OW [246], O [135], space 1 time, dots 46, space 2 times, K [13], space 1 time, OW [246], space 2 times, O [135], space 1 time, K [13], space 2 times, dots 46, space 1 time, dots 46, space 4 times, K [13].
Row 16: space 4 times, dot 4, A [1], space 3 times, dot 4, A [1], space 2 times, dot 4, dot 5, dot 2, A [1], space 2 times, E [15], dot 6, dot 3, I [24].
Row 17: A [1] two times, space 1 time, A [1], B [12], space 2 times, A [1], C [14], space 3 times, A [1], D [145], space 5 times, A [1], E [15].
Row 18: space 1 time, hyphen [36], space 1 time, dot 6, colon [25], dot 3, space 1 time, IN [35], C [14], EN [26], space 2 times, dot 6, colon [25], dot 3, space 3 times, dot 6, space 1 time, C [14], space 1 time, dot 3.
Row 19: space 1 time, C [14], space 1 time, dot 4, colon [25], A [1], space 1 time, E [15], hyphen [36], I [24], space 1 time, ST [34], space 3 times, CH [16], space 1 time, dot 6, space 5 times, dot 3, space 2 times, A [1], I [24].
Row 20: A [1], F [124], space 1 time, A [1] G [1245], space 2 times, A [1], H [125], space 2 times, CH [16], space 3 times, ST [34], space 1 time, dot 4, space 5 times, A [1], space 1 time, IN [35], dot 4, A [1], EN [26].
Row 21: dot 6, dot 3, space 1 time, IN [35], EN [26], space 1 time, dot 6, dot 4, A [1], dot 3, space 2 times, dot 4, colon [25], A [1], space 3 times, dot 4, space 1 time, hyphen [36], space 1 time, A [1], space 1 time, ST [34], space 4 times, CH [16].
Row 22: dot 4, A [1], space 1 time, E [15], I [24], space 1 time, dot 4, dot 6, dot 3, A [1], space 14 times, CH [16], space 4 times, ST [34].
Row 23: space 25 times, E [15], dot 6, dot 3, I [24].
End Design:
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Circles are defined by Wikipedia as:
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
It is this constant that is the inherent problem with drawing in braille.
Circle A:
The center of this circle is the A [1] in cell two of row three. The radius going left and right is 2 dots and one space. The space going to the top of the page is larger than those between cells, so only one dot is used in row 1. Going down the page, we use dot 3 because there is no way to add a dot in the space between row two and row three and going to row four is too long. What we have looks and feels more like a cross than a circle.
If we remove the dot 1 in cell two, row three, we get a different feel. Now, we feel a diamond shape, though we could draw an imaginary circle around the four remaining dots—an impossibility with braille.
Circle B:
This is the circle defined by the A [1] in cell six of row three. This is an attempt to add more dots to define the outer edge of circle A. Remove the center dot and now the design looks and feels more like a square, though not a good one.
Circle C:
The center of this circle is the A [1] in cell eleven of row three. The radius going up and down is 3 dots and one space. The radius going left and right is also 3 dots and a space. You think this would look and feel great. However, at this size, four dots does not a circle make. This circle has the same problems as circle A, only in a larger size.
Circle D:
The center of this circle is the A [1] in cell sixteen of row three. Additional dots have been added around the perimeter to attempt to fill in the outer boundary and give it the feel of a circle.
However, we still do not have a circle. The bottom is too flat. Visually, there are too many dots on the right side of center and not enough dots on the left side of center to look appealing. To have a good feeling and looking circle it needs to be symmetrical top to bottom or side to side. A perfect circle is symmetrical to each of the four quadrants.
Circle E:
The center of this circle is the A [1] in cell twenty-one of row three. The outer diameter of the circle is up to you to draw, however, remember that there is only three rows in which to work.
Circle F:
The center of this circle is the A [1] in cell twenty-one of row three. This center is for you to have another chance to draw that circle of your design.
Moving the center point to dot 4, dot 3, or dot 6 produces all the same problems, just in slightly different formats.
In order to further illustrate the problem, the next six circles all have the center as dot 2 on row five. (Note that our perimeters begin to feel circular in J, K, and L. At Six Dots Art, we require our drawings to be visually and tactually appealing, and this further complicates circles, squares, and even sometimes straight lines.)
Circle G:
The center of this circle is the dot 2 in cell two of row seven. The radius going left and right is 2 dots and a space, the same as circle A. Going towards the top and bottom, the radius is also 2 dots and a space. The final item feels more like an oval as the space to the top and bottom is larger than going to the sides. Remove the center dot and the diamond look and feel is back.
Circle H:
The center of this circle is the dot 2 in cell six of row seven. Additional dots have been added around the perimeter to attempt to fill in the outer boundary and give it the feel of a circle. This made the circle worse, again more like a square as all the additional dots are in straight lines.
Circle I:
The center of this circle is the dot 2 in cell eleven of row seven. Three of the outside dots are almost perfect. Can you tell which dot is closer to the center than the rest? The radius going to the top and bottom is three dots and a space, the same as circle C. The radius to the left is three dots and two spaces. The radius to the right is three dots and one space to make the circle look and feel more uniform, although still shorter in length.
Circle A, circle C, circle G and circle I all have the same problem of feeling and looking like a diamond once the center dot is removed. Four points is just not enough information to portray a circle.
Circle J:
The center of this circle is the dot 2 in cell sixteen of row seven. Additional dots have been added around the perimeter to attempt to fill in the outer boundary and give it the feel of a circle. Again, the right side is not symmetrical to the left side which throws off the feel and look of the circle. Did you notice that circles I and J have the same radius layout as circles C and D?
Circle K:
The center of this circle is the dot 2 in cell twenty-one of row seven. The left and right dots are 4 dots and 2 spaces from center. The top and bottom dots are 4 dots and 1 space from center but are almost the same distance. By adding the four quadrant dots, this makes a nice circle.
Circle L:
The center of this circle is the dot 2 in cell twenty-seven of row seven. The left and right dots are 4 dots and 2 spaces from center. The top and bottom dots are 4 dots and 1 space from center but are almost the same distance. We have added more dots to our perimeter. To the sighted viewer, the sides are flat enough to be a distraction. But to the Braille reader, this is not a distraction and is considered to be a good circle.
Using dot 5 as the center inherits all the same problems as using dot 2, just in a different location. Can you achieve symmetry when any dot is your center? We don’t think so. The very layout of the braille cell and braille page restricts the ability to layout symmetrical dots when one of the dots is the center.
The next six circles are an attempt to make symmetrical circles. The true center of each is between dots 2 and 5 of the identified cell.
Circle M:
This circle is centered on cell two of row eleven. It is an attempt to make the smallest circle possible. Although it failed, this shape may be useful as something else.
Circle N:
This circle is centered on cell six of row eleven. The radius is approximately three dots and one space to the sides and two dots, one space going up and down. This is again because the space between rows is larger. The use of symmetrical dots left and right and top to bottom help the look and feel. Yet, to the braille reader, the shape is more rectangular than circular.
Circle O:
This circle is centered on cell ten of row eleven. Adding the dot 5 and dot 2 to the sides flattened the design and it now looks more like a football. I am not sure it really feels like anything but a box.
Circle P:
This circle is centered on cell fifteen of row eleven. The radius is one-half dot larger than circles C, D, I or J. The circle is also one-half dot smaller than circles K and L. This circle is symmetrical side to side or top to bottom. It is this layout that gives a good feel and look to this circle. Whether the braille reader touches just the perimeter or feels the entire shape all at once, there is no doubt that this is a circle.
Circle Q:
This circle is centered on cell twenty-one of row eleven. It is a full three vertical cells in diameter. Although drawn symmetrically, the spacing between rows and cells make this circle slightly oval in look.
Circle R:
This circle is centered on cell twenty-seven of row eleven. This is the same as circle Q with only a slight modification. Changing the sides to two dots instead of one helps to fill in the design and gives it a better look. Does it feel better to the fingers? Compare circles Q and R to circles K and L which are the same size and determine which one is best? How might you use one of these shapes in a picture?
The next six circles are a second attempt to make symmetrical circles. The true center of each is between dots 5 and 2 of adjoining cells. By moving the center to between cells it becomes much easier to create circles that are symmetrical side to side.
Circle S:
This circle is centered between cells one and two of row fifteen. It is a second attempt to make the smallest circle possible. Although it failed, this worked out to be nice lights on our CHRISTMAS TREES.
Circle T:
This circle is centered between cells five and six of row eleven. The radius is approximately three dots and one space to the sides and two dots and one space going up and down. This is the same size as circles G, H and N. The flatness of the adjoining dots gives this more the look and feel of a square.
Circle U:
This circle is centered between cells ten and eleven of row eleven. Adding the dot 2 and dot 5 to the sides flattened the design and it now looks more like a stubby, fat football.
Circle V:
This circle is centered between cells fifteen and sixteen of row eleven. The radius is the same as circle P. This circle is symmetrical side to side or top to bottom. It is this layout that gives a good feel and look to this circle. The two dots on the sides fit the radius well and do not flatten the sides visually or tactually.
Circle W:
This circle is centered between cells twenty-one and twenty-two of row eleven. It is a full three cells in diameter vertically, the same as circle Q and circle R. Although drawn symmetrically, the spacing between rows and cells make this circle slightly oval in look along the horizontal plane.
Circle X:
This circle would be centered between cells twenty-seven and twenty-eight of row eleven. Can you draw a circle using this imaginary point location?
The next six circles are centered between rows and dots 3 and 6. We are still searching for that perfect location to create symmetrical circles.
Circle AA:
This circle is centered below cell two between rows eighteen and nineteen. Like all the small circles, it looks and feels like a small rectangle.
Circle AB: This circle is centered below cell five and between rows eighteen and nineteen. Being two dots in diameter and centered between rows allows more dots and a symmetrical layout to be used. This is a very good-looking circle, and it feels good, too.
Circle AC: This circle is centered below cell nine and between rows eighteen and nineteen. Enlarged to three dots in diameter and centered between rows still allows more dots and a symmetrical layout to be used. This is also a very good-looking circle.
Circle AD:
This circle is centered below cell fourteen and between rows nineteen and twenty. Enlarged to two rows vertically, the use of dots 2,5 for the top and bottom gives a more circular looking dot pattern. Try drawing various dot patterns for the top and bottom rows of this circle and determine if you like any of them better.
Circle AE:
This circle is centered below cell twenty-one and between rows nineteen and twenty. It has been enlarged to the top of two rows vertically. The more dots you use, the less the outline retains its shape.
The last four circles to be discussed are centered both between the cells and between the rows. You might believe this would be the best location for drawing circles but you would be wrong. Just like all the other locations, certain sizes work well but others do not.
Circle AF:
This circle is centered between cells one and two and between rows twenty-one and twenty-two. It is the same size as circle AA and has the same problem, only wider. Yes, it feels and looks like a rectangle, not a circle.
Circle AG:
This circle is centered between cells four and five and between rows twenty-one and twenty-two. It is the same size as circle AB. Which one do you think makes a better circle? Used in a drawing, they both would appear as good circles.
Circle AH:
This circle is centered between cells eight and nine and between rows twenty-one and twenty-two. It is the same size as circle AC. There are not enough possible dot locations at this size to make this look like a circle. Are the dots too spaced out to convey the feel of a circle?
Circle AI:
This circle is centered between cells twenty-seven and twenty-eight and between rows twenty-one and twenty-two. It is the same size as circle AE. Alone, it appears slightly longer on the vertical plane but looks just fine when added within a drawing amongst other lines.
This brings me to the end of this discussion. While I could easily add a second page of circles and review each and every one, it would take all the “fun” out of trying to draw in Braille. See our page for other types of circles we have drawn. Explore on your own, after all, we have not discussed Lena’s favorite circle, which is the rear wheel of the FARM TRACTOR drawing.
Notes on the attached drawings:
The first drawing has all the circles, the dot pattern background and all the construction lines I use to draw circles. This should help you see which dots were picked and why. These construction lines also tend to override the true shape created by just the dots.
The second drawing does not have the construction lines. This is the normal style drawing that is attached to our other patterns. This allows the sighted artist to draw the pattern with precision not otherwise obtainable.
The third drawing has only the dots that the blind artist feels.
Want more circles?
