Introduction to Mary Everest Boole
Mary Everest Boole was a self-taught mathematician born on March 11, 1832 in Wickwar, Gloucestershire. Her uncle, George Everest is the surveyor and geographer, after whom Mount Everest is named. Her husband, George Boole, seventeen years her senior, was a fellow mathematician who published work on differential equations and the algebra of logic a forerunner of Boolean logic.
In her own words, “… the needle and thread has many advantages over the implements in more ordinary use for curve drawing. Among them are these: --
It enables the child to get a perfectly uniform line long before he would be able to keep a ruler straight or a pencil sharp; to make a thicker line at pleasure; and to keep parts of a diagram separate by the varying of colour, without the risk of smudging involved in the use of coloured inks of the clumsiness of chalk points.
“ Preface by M.E. Boole, A Rhythmic Approach to Mathematics, Edith L. Somervell, National Council of Teachers of Mathematics, 1975 reprint of 1906 edition.
Mary Everest
Boole was a proponent of hands-on, discovery learning at a time when rote
learning was the norm. She thought that
a needle and thread could be useful
tools in a child’s discovery of what they would later come to learn were
principles of geometry and algebra. She
adapted sewing cards that were a child’s plaything in her youth into teaching
and self discovery tools that were used in schools throughout the early
1900’s.
The
first set of cards that young children worked with were simple shapes. The
parabola was the first curve that was introduced.
Children weren’t given instructions about how to stitch through the holes in the cards but rather were encouraged to explore and create patterns. Eventually they would find that curves could be created using only straight stitches to form a simple parabola shape.
A parabola is defined as a curve where any point is at an equal distance from: 1. a fixed point (the focus), and 2. a fixed straight line (the directrix)
This could also be done on a right angle in one corner, opposing corners or all four corners. The stitching could be done with one colour, two colours, or four colours.
Drawing and Measuring for a Parabola Pattern (video)
For our
purposes, we are going to use numbers to begin to see the pattern of curve
stitching. Using the dotted square pattern you will find below (you may want to
make a photocopy in the size you wish), place your pattern over a piece of
cardstock, tape lightly in place with removeable masking tape and poke through
the holes with a paper piercer (This can be a push pin, needle, awl, or
anything that will make a hole large enough for your needle to go through
without being too large.) . You may want
to just do two sides for your practice piece.
*Make sure they are connected sides and form a right angle.
Number the
holes just as you see in the diagram in the top right. The numbers will be on the back of your
piece. Notice how the numbers run around
the square. 1 always follows the last number, which means that sometimes you
are writing the numbers in what appears to be a reverse order. This is important. It will make things
easier in the beginning if you do this.
Once you are familiar with the pattern you won’t have to number
everything.
Stitching the Parabola Curve (video)
To start,
- bring your thread (I typically use one strand of embroidery floss because I work on 3.5” square pieces) up through hole number 1 from the back and go down through hole number 1 that is on the line perpendicular to it.
- From the back move the short distance to the number 2 hole and come up through it and down through the number 2 hole on the original line.( you can tie off your thread now or use a bit of masking tape temporarily and glue the thread tails down at the end).
- From the back move the short distance to the number 3 hole on the original line and come up through that hole and go to the number 3 hole on the other line.
- You are going to keep going back and forth between the two lines, moving a short distance on the back with the longer stitches on top.
- You will be matching the same numbered holes for your stitches.. Keep going until you reach the end of the line. Your parabola is now done and should look like the diagram above.
- You will probably have to add thread at some point in your design. Attach the thread at the back of the work in whatever way works best for you. A single strand of floss does not leave a big knot but I also use temporary tape and then glue all threads at then end.
Try stitching in opposite corners, then try an example stitching in all corners. Try changing colours, using two colours or four colours.
This cross grid can be used inside the square for four parabolas going from the centre out in one colour, two colours, or multi-coloured.
There are
more variations on the square – you may have discovered them for yourself.
This grid
can be used to create several designs. Parabolas
can be stitched in the centre corners and outer corners or on either side or
the outer edges of the cross. You will
get a different pattern each way. If you
put the crossed lines on the diagonal, you’ll get different patterns again.
To keep your
designs easy to stitch, you want to have the same number of holes on each side
of your parabola. Keep that in mind when
creating your square and dividing it into sections.
 |
Free images from
Sparklingbuds.com Some have been
modified |
This is two of the above grids overlaying each other at a 45 ̊ angle. Just imagine the variations you can come up with for this one.
Some Stitched Examples (video)
I found the following useful. I either created them or found them as free templates or graphics on the internet.
The full
protractor with proportional scale lines is a very useful tool when figuring
out where you want holes in circles of different sizes. You can resize this to
be larger or smaller, whatever is most useful for the size you want to work
with.
A square
with regularly spaced holes is useful for doing parabola work.
The following is a link for grid paper for making your own templates. It can be found here:
Useful
Links
Curves of Pursuit 1 -YouTube multiple polygon shapes –
good video
Mathsand Art Collide = Parabolic curves - Mum In The Madhouse free parabolic worksheets
Home (maths-pro.com) many useful worksheets. The graph paper at the
end of your handout came from that webpage.
Tutorial– Stitches for prick and stitch cards – Form-A-Lines stitching tutorials from an embroidered card
vendor. Some free patterns available.
curve stitching - YouTube great examples of curve stitching
PrintableCircle Divider | Setting Circle Templates (blocklayer.com) lets you create printable circles in
the size you want with the number of increments you want. Where was this when I was starting out!!!!!****
usasef2018-hexagon.pdf (ams.org) numbered
hexagon
usasef2018-circle.pdf (ams.org) large 36
point circle
usasef2018-square.pdf (ams.org) square all sides numbered
usasef2018-parabola-1.pdf (ams.org) right angle numbered
for pdf (woollythoughts.com) curve
of pursuit knitting spiral who knew?
ParabolicCurve Art Embroidery : 8 Steps (with Pictures) - Instructables multiple curves of pursuit
Curves of Pursuit 1 -YouTube multiple polygon shapes – good video
How to Draw Parabolic CurvesUsing Straight Lines | Geometric Tutorial - YouTube creating advanced parabolic curve designs
(you may want to turn the sound off – no commentary but loud music)
How To Draw Square FractalPattern With Parabolic Lines | Geometric Tutorial - YouTube another design by the same creator
21 Weird Drawing Tricks ForBoring Days - YouTube only some
of the designs will be interesting for mathematical (curve) stitching; some
will be more suited to zentangles and some may not relate to anything.
13 Weird Drawing Tricks ForBoring Days - YouTube again, only
some of the designs will be interesting for mathematical stitching.
Free Patterns to Download site is in Hungarian but can be translated
Segments(xtec.cat) program lets you look at the effect of changing the length of chords on a circle and changing the multiplier – S and M values in Segments and Circumference ie. creating cardioids, nephroids, etc.
A Geometric "Love" Story - How to draw hearts with circles A tutorial on string art hearts that can be adapted to create an embroidered "mathematical" stitched heart for a Valentine's Day card
Heart Curve interesting information about Heart curves (the math behind the embroidered heart above)
Grid paper for making your own designs. It can be found here:
PDFViewer - Printable Dot Paper (stemsheets.com)
Learnto pin stitch (pin embroidery, paper piercing) part 1 - YouTube
Pin stitch tutorial part 3 - YouTube
Pinstitch embroidery part 4 - YouTube
Pinstitch tutorial part 5 - YouTube
6SINGLE PATTERN DESIGN IN A TRIANGLE | GEOMETRIC DESIGN |RAINBOW ART - YouTube
HOWTO DRAW DESIGN 6 / RAINBOW ART BY RADHAPADA MANNA -YouTube
HOW TODRAW GEOMETRIC DESIGN 5 | RAINBOW ART - YouTube
HOW TO DRAW DESIGN 4/ SIMPLE GEOMETRIC DESIGN/ RAINBOW ART BY RADHAPADA - YouTube
