Thursday, October 8, 2026

Mathematical (Curve) Stitching 2026 - Lesson 2

Using Parabolas with Circles

Lesson 2 Presentation

Parabolas can be used with divided circles to create interesting designs as well.

These can later be combined with the use of chords to create more complex designs.

The full protractor template that was given with the first handout will be useful here.  So will the site where you can create your own circles.

 Printable Circle Divider | Setting Circle Templates (blocklayer.com)

 

  Chart

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Don't Eat the Paste: Curve stitching templates (donteatthepaste.com)

These patterns can be used with the stitching pattern for parabolas to create interesting designs.  Experiment with using the curved areas as well.

 Try stitching parabolas in the following areas of the circle. 


 




 

 

 

 






  



 

 

 



 

 

 





























Make sure you have the same number of holes across the top of the segment (arc) as you do down the side (radius).




Polygons

Interesting designs can be created with other polygons.  Mary Everest Boole. Introduced her students to the equilateral triangle (all sides the same length and all angles the same  60 ̊), the pentagon, hexagon, octagon and more.

Just as with the circle, the polygons can be divided into sections and parabolas can be sewn in the outer angles, the inner angles and combinations of the two.    

A hexagon can become a cube with the addition of some interior lines and if the parabolas are stitched in two colours to help show dimension.


 


 

 

Shape

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Try dividing the triangle from the angle vertices to the center point,  Divide the lines you’ve created into equal sections ( adding up to the same number as along the side of the triangle) and use those new lines to create parabola like stitching.

Note:  my diagrams may not always have the correct number of dots (I have trouble drawing diagonal dotted lines and getting the number of dots that I want in this drawing program – so it’s do as I say and not as I do in those cases – making templates by hand is much easier)

 

 



 

 

                                             

 

 



  

 

 

 

 

 

















What other designs can you create?

 

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Apply the same idea to an octagon or hexagon.

 A picture containing sky, line, several, day

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Wednesday, September 23, 2026

Mathematical (Curve) Stitching 2026 : Lesson 1

 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)     

Making the Holes (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)


 Useful Templates to Have

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:

Grid Paper


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:

Grid Paper Maker

 Videos you might find interesting:

Learnto pin stitch (pin embroidery, paper piercing) part 1 - YouTube

Pinstitch part 2 dealing with squares, free pin stitch patterns we will do overthese tutorials. - YouTube

Pin stitch tutorial part 3 - YouTube

Pinstitch embroidery part 4 - YouTube

Pinstitch tutorial part 5 - YouTube

Pin stitch tutorial part 6 -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 





Tuesday, August 4, 2026

Mathematical (Curve) Stitching: Overview



In the course of these six classes, we will be looking at how stitching straight stitches in various geometric shapes will give the
illusion of curves. The title Mathematical (curve) Stitching comes from the fact that many of the shapes produced are in fact mathematical constructs and derived from the results of algebraic functions.  The math is incidental to our purposes and is more of a point of interest rather than a necessary piece of knowledge needed to create the design.  If you were worried about the word

Mathematics in the title, don’t be.  We don’t need to know the math, it’s just interesting that some of things that we are going to be stitching have connections in the realm of math and physics and we could have stumbled onto them purely by chance.

The class format will be Zoom and a link will be sent to you a few days before each class. If you don’t receive one by the Tuesday morning before your class, check your junk or spam folder and then let me know by email.  Sometimes with a large group,  some email filters get picky and think I’m sending spam when I send all the emails at once.  I will present information through presentations, demonstrations and videos. 

I will be supplying handouts for each class so you will have a set of notes on the topic I plan to discuss for that class.  They will also be posted on the blog,  In MyWorkroom.  Each lesson, complete with accompanying videos and relevant links will be posted there after each class.  I will send the link to the lesson page in a follow up email after the class.  You will be able to go back to any lesson by clicking on Mathematical (Curve) Stitching on the top right hand side of the navigation bar on the page.

Class time and dates: Thursday, 7 - 9 pm  6 classes: Sept. 24,  Oct. 8,  Oct. 22, Nov. 12, Nov. 26, Dec.10  

Any questions about the class can be emailed to me.

Supplies to Gather

You will want to have on hand:


Paper  (heavy) -             I’ve been working with black Artist’s Tile Set, Acid Free tiles, 300 gsm, 3.5” square. Peter Pauper Press.  (I had them from another project)  I also used blank playing cards (they are at least 300 gsm) by various companies in various sizes and polygon shapes – square, circle, hexagon and classic card size. You can use whatever size you feel comfortable with.

                                       Any reasonably heavyweight paper that can stand up to thread tension without bending, will work.  Colour choice is up to you.  You’ll want to make a nice contrast with your threads.

              (light) -              Paper to make patterns. Copy paper weight is fine.  Patterns can be designed on graph paper .

 

Thread  --                       I’ve used single strand embroidery floss.  Since I work with black and white, bright colours work best for me.

                                       Button and Craft thread – this is a type of thread that is quite strong and a little thicker than ordinary thread.  It does not come in a wide range of colours but the red is nice and I use a lot of red.


 Needles –                      Whatever you’re most comfortable with, Sharp, Chenille, Quilting.  You don’t want the eye of the needle to be much larger than the rest of the needle and enlarge the hole.


Measuring tools -            Ruler, protractor (a full protractor is great – I’m sending a paper one),pencil.  *I found an incredible webpage for creating circles that will take most of the work out if it for you.  I wish I'd known about it when I was starting this project. I'll give you the link at the first lesson and demonstrate how to use it when we get to circles; you'll love it


Misc.                               Paper piercer* (very important) – it can be an awl, pin vise with needle inserted, anything that will pierce paper and leave a hole about the size of your needle

                                        A piece of craft foam or cardboard or something soft to put under your cardstock when you are piercing your holes.

                                        Repositionable tape is handy to hold down thread ends until you can tie them off or glue them down.

                                        Scissors to cut threads, scissors to cut down paper if necessary

                                       Graph paper will be handy when creating your own designs (look for graph paper divided into small sections ). I will also give a link to a webpage for creating custom size graph paper as well as send a sample with your first lesson handout.


Tuesday, December 9, 2025

Paper, Paint, Stitch and More ...

Ephemera - Paper based

Paper Embellishments

Paper embellishing paper is not as boring as it sounds.  We aren’t simply talking about adding another layer of paper to your piece but manipulating paper into something more dimensional and creative and adding the resulting decorative item to your work in progress.

One simple form of paper embellishment can be the use of paper die cuts. These can be purchased pre-punched and coloured, homemade from purchased metal dies,  or purchased hand punches, and designed and cut using innovative technology such as electronic cutting machines.  In fact, the term “die cut” has been expanded to cover most extras that are pre-cut from cardstock or paper included tags, dimensional stickers and chipboard elements.

 

Manipulating Paper

Paper can also be manipulated to make embellishments.  As mentioned in an earlier class, weaving paper can be done on a large scale to make a background or as a way of making layers, but it can also be done as a form of embellishment.  Partially weaving into a piece can enhance your artwork.  A smaller, woven item can be used as an embellishment.

Paper, in the form of cord or string, can be knitted, to create an interesting texture.  This can be firm in its own right if the paper cord/rope is thick, but it can also be made firm by using a textile stiffener if that is what your piece requires.

In addition to paper, cardboard, particularly corrugated cardboard, can provide texture and dimension to paper art.  The top layer of the cardboard can be torn or cut away revealing the corrugation beneath. This provides interesting opportunities for stitch.

Tips for Exposing Corrugation

 

Paper Beads

In addition to die cuts, there are other categories of paper elements that can be added to your work.  One such element is a paper bead. Paper beads can be made out of a wide variety of papers in an equally wide variety of shapes and sizes.  Templates for various bead shapes are easily available.

 



The thickness of the paper and the length and width of the template will determine the size of the bead.

The following video covers just about anything you would ever want to know about making paper beads – it’s long but good.  She has also put time codes in the description so you can go to the sections you are interested in without watching the entire video. (though it is well done and easy to watch)

{MASSIVE} Fancy Paper Beads Tutorial - YouTube

This next video shows some wire wrapped beads made out of book pages.  I included this video because the book page beads are long, have quite a different feel to the regular paper bead and include glass bead/pearls as well as wire.  They would give a distinctive look to your piece.

How to Make BOOK PAPER BEADS for Junk Journals! Ep: 74 Step By Step Tutorial Paper Outpost! :) - YouTube

 

Paper casting

Paper casting is the forming of paper from fibre or pulp using a dimensional mold. The experimenting we are going to be doing will be with recycled paper or with layers of napkin or toilet paper.  Typically, the paper would be soaked overnight or longer if you have the patience (this is definitely needed for recycled paper) to break down the fibres into pulp. .  Heating the water can also help break down the fibres.

It helps if the soaked paper can be blended using a household blender or immersion blender to further break down the fibres. It is appropriate at this time to add a binder to the pulp.  A bit of watered down PVA or methyl cellulose or wheat or rice starch paste can be added. A lot is not needed. The finer the pulp, the smoother the cast paper

DO NOT throw the excess slurry water down a household drain when you are finished – it will cause problems – the bits of fibre still in the water will harden when they dry. Dispose of it outside or let it evaporate and save any dried fibre for next time.

You can use almost anything as a mold.  I have used deep cut rubber stamps.  Carved wooden blocks have been used, clay cookie stamps have been used. Silicone molds, chocolate molds, and molds for polymer clay are just a few other examples. Anything that has depressions in it can be used.  If it is a rubber or plastic surface, the paper won’t stick but it might to a porous surface so in that case it is wise to spray the mold with a release agent – like a silicon release or a cooking spray.

Scoop some of the pulp and pat it into the mold.  It is good to protect your work surface because you will be removing the excess water and the surface could get wet.  Put enough pulp into the mold to fill it and press down to compact the pulp and more if necessary.  You need to press the pulp into all the depressions. You don’t want any air bubbles. When the pulp fills the mold, you can use a sponge or soft cloths to press down on the surface of the pulp to continue to compress it and to help remove some of the excess water. When you have removed as much excess as possible, leave the pulp to dry in the mold, naturally, in a warm place.  Use the point of a knife to gently release the paper from the mold when dry.

Any excess pulp can be put in an air-tight container and frozen until you want to use it again.

Using pulp is the best way to do paper casting but there is a quick a dirty way that doesn’t involve the fuss and mess or making the pulp but still gives satisfactory results. This involves using layers of toilet paper or the extra plies of napkins.  Yes, that’s right, toilet paper.  These casting are a little more delicate than the pulp variety and you have to take a bit more care to bond the layers together, but you do get reliable results.

You need to have some watered down PVA, or PVA/methylcellulose mix ready in a small container because you are going to use this will a small, stiff paint brush to tamp the layers of paper together to bond them.  When your mold is ready, tear a piece of toilet paper or napkin and  lay it at the bottom of the mold.  Dip your paint brush into the glue/water mixture and tap the paper into the crevices of the mold. Lay the next piece of paper into place and repeat the process. Keep adding paper and using the glue/water mixture on the paint brush to tamp the layers together. The first layers will seem to dissolve because the paper is so fragile, but gradually you will begin to see the layers begin to build up.  This is something to do while you are listening to music or watching TV.  It is much slower than using the pulp, but it doesn’t require the advance preparation, and you don’t have to guess at how much pulp you are going to need to make.  

Once the mold is full, you will use the sponge or cloth to press down on the paper to remove any excess water from the paper. When it is as compressed and dry as possible, leave it to dry completely in the mold and then remove carefully.  If the layers have been completely saturated with the glue mixture, they should be bonded.  The one weakness of this method is that if not completely bonded, the layers can separate if handled too much. That is not a problem if the piece is mounted and does not experience too much handling.

3D Embellishments from Toilet Paper and Glue - YouTube

TOILET PAPER EMBELLISHMENTS | JUNK JOURNAL DECORATIONS - YouTube

My Attempts at Paper Casting

 

 Paper Clay

You can create your own dimensional embellishments using paper clay.  This is also readily available from most craft and art supply stores.  Paper clay is an air-dry product that does not need any special tools or equipment to produce your embellishments.  You need to protect your work surface – I use my Teflon mat which wipes down easily.  I use a piece or plastic/acrylic tube as a roller to roll it out flat and you can use anything to make a mark or impression.  I used the same molds that I had for paper casting as molds for paper clay. My molds are flexible, so it is easy to get the dried clay out without damaging either mold or clay.  In fact, it was possible to remove the damp clay from the molds. The dried clay can be painted and sealed.  If you are planning to stitch your embellishment onto your piece, don’t forget to make the stitching holes before it dries – that’s why I tried removing the clay from the molds while damp.  ¼” is a good thickness for flat pieces.

There are recipes on the internet for making your own paper clay.

Paper Mache Clay Recipe - The Easy Original Recipe - YouTube

New Smoother Air Dry Clay Recipe - YouTube

Note:  You can’t use DAP brand joint compound in these recipes – that brand doesn’t work for some reason.

 

Paper Pulp

A bit like paper mache but more liquid, paper pulp is what handmade paper (and paper clay) is made from.  In this case we are talking about recycled paper that has been torn into small pieces and has been soaked in water, blended with a machine, had the bulk of the water removed, and PVA glue and possibly other ingredients (cornstarch, vinegar and glycerin added).  Colour may also be added in a variety of ways.  When the desired consistency has been reached for the purposed desired (there are a number of ways to use paper pulp), you squeeze, pour, press or mold the pulp into the desired shape.

Pulp can be placed in squeeze bottles and then used like a thick paint to create a drawing or outline on a fine mesh or screen.  This needs to be left to dry for several days and then can be removing by releasing it from the screen/mesh.  This must be done carefully because the paper pulp, though dry, will be somewhat fragile.  A palette knife or thin blade inserted between the paper and the mesh to release the edge of the paper will aid the process.

 

Quilling

Paper quilling is the rolling, pinching and gluing of thin paper strips into shapes and designs.  It is also known as paper filigree. It is believed to have originated in the Renaissance period in Europe as a form of religious decoration and in the 18th century become a pastime for gentlewomen. It has experienced a resurgence of popularity in the 21th century in both traditional and modern design applications.

Beginners can start with little investment in tools – a few toothpicks, scissors, some strips of paper, and glue are all you really need to get started.  Wax paper to cover your work area will prevent your work from sticking to your pattern.  Typically, the strips of paper are 1/8” to ¼ “ wide (you decide what width you are comfortable working with unless you are creating from a pattern that specifies).

You can purchase the paper in precut strips or cut your own.  There are many places online that will sell it. (just search quilling strips)

 

Basic Shapes

 

Twelve basic quilling shapes

Image from : Basics of Quilling - Decorative Crafts - Aunt Annie's Crafts  Use this link for directions on how to make each of the shapes shown.  There is also a cutting guide for make your paper strips. Quilling strip cutting guide - 1/4 inch     Quilling strip cutting guide - 1/8 inch

Aunt Annie’s Crafts also provides a Snowflake template:  Basics of Quilling Project Sheet - Snowflakes   Even though it says it is done with 1/8” wide strips, it can be done with ¼” wide strips just the same. 

 

 

Artist Links

Kelly High School Art

Jennifer Davies

Stitched Paper Society Instagram of group that follows stitched paper artists

Yulia Brodskaya

Phillipa Reid

Griffin Carrick

Kukhwa Studio

Paperpan

 

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