Re: [lace] Lace and maths

[Sharon Ghamari-Tabrizi]

Dear Arachnites,
if you are at ease with computers, it would be helpful to post a URL link
to an image of the lace they have in mind when arguing for the mathematical
precision of a lace design.
For example, it would clarify the drift of the conversation for me if
Kathleen and Devon, say, would post the URL of an images of a pattern or
lace close-up and show us what makes something "intensely mathematical".


On Sun, May 20, 2018 at 10:33 AM, Devon Thein  wrote:

> Kathleen writes:  I wonder if it is simply that bobbin lace appeals
> particularly to scientists and especially mathematicians. Moving on
> from this, is it the more “regular” laces which appeal, I.e. Torchon,
> Bucks and Flanders, rather than Bedfordshire for instance?
>
> Actually, I have always thought that Bedfordshire was intensely
> mathematical. Isn't Bedfordshire a lace where you are presented with a
> design that has acanthus leaves strewn all over it, in different
> orientations, all basically the same shape, but you work each one
> differently as you have to keep the weaving line perpendicular to the
> edge? Similarly, laces such as Milanese and Duchesse present you with
> the mathematical challenge of making each stitch of linen stitch
> appear at a perfect right angle like a weave, while the tape or flower
> curls around. One time a museum colleague, looking at a Duchesse piece
> said, "It is like an Escher". I think that it is like the Escher that
> has all the stairs going hither and yon, always looking very
> straightforward and mathematical and yet not being that way at all.
>
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Re: [lace] Lace and maths

[Devon Thein]

Kathleen writes:  I wonder if it is simply that bobbin lace appeals
particularly to scientists and especially mathematicians. Moving on
from this, is it the more “regular” laces which appeal, I.e. Torchon,
Bucks and Flanders, rather than Bedfordshire for instance?

Actually, I have always thought that Bedfordshire was intensely
mathematical. Isn't Bedfordshire a lace where you are presented with a
design that has acanthus leaves strewn all over it, in different
orientations, all basically the same shape, but you work each one
differently as you have to keep the weaving line perpendicular to the
edge? Similarly, laces such as Milanese and Duchesse present you with
the mathematical challenge of making each stitch of linen stitch
appear at a perfect right angle like a weave, while the tape or flower
curls around. One time a museum colleague, looking at a Duchesse piece
said, "It is like an Escher". I think that it is like the Escher that
has all the stairs going hither and yon, always looking very
straightforward and mathematical and yet not being that way at all.

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Re: [lace] Lace and maths

[Sue Duckles]

Or... is it that one style appeals whilst another doesn't? By that I mean the 
finished piece... A bit like art really. And nothing to do with mathematics or 
science... 

Sue in East Yorkshire UK

Sent from my iPhone

> On 20 May 2018, at 07:55, Kathleen Harris  wrote:
> 
> I wonder if it is simply that bobbin lace appeals particularly to scientists 
> and especially mathematicians. Moving on from this, is it the more “regular” 
> laces which appeal, I.e. Torchon, Bucks and Flanders, rather than 
> Bedfordshire for instance?

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RE: [lace] Lace and maths

[Susan@]

I'm a Maths graduate (Leeds, 1987), I taught myself Torchon in the early 1980s 
while still at school.  I think the connection isn't Maths as such but some of 
the things Maths, Science, Computing, psychology teaches you namely logic, 
analytic thought, sequences, patterns and coding/representation.  But to be a 
good lacemaker you also need creativity.  I remember struggling reconciling the 
academic and creative sides of me when I was younger but later reconciled this 
as what I called "logical creativity".  The laces I now choose to work are the 
complex Belgian laces such as Binche and Flanders that use coloured technical 
drawings (essentially a form of coding but a form that anyone who understands 
the coding can understand regardless of their spoken language).  One really 
interesting thing we have done in classes in Brugge (particularly as a 
lacemaking teacher for my understanding of how others understand lace 
structures) is to take an enlarged copy of an old lace and try to w!
 ork out how it has been worked.  It is fascinating to watch others working on 
the task, while most people are quite happy with cloth stitch and can quite 
happily think of two horizonal lines being a worker it is fascinating watching 
them with half stitch and struggling with the working path (in Binche the 
working path could be either horizontal, diagonal or a combination of the two). 
 

In terms of Kathleen's question about laces that appeal, for me it is the laces 
which have grids in/behind them, and I class the Belgian laces and Honiton as 
geometric because of the grounds. 

Kind Regards
Susan
Website: www.susanroberts.info
e-mail address: su...@susanroberts.info
YouTube: https://www.youtube.com/channel/UCTWfnh8ulGj3pS1V0f6O1jQ

-Original Message-
From: owner-l...@arachne.com <owner-l...@arachne.com> On Behalf Of Kathleen 
Harris
Sent: 20 May 2018 07:56
To: lace@arachne.com
Subject: [lace] Lace and maths

I wonder if it is simply that bobbin lace appeals particularly to scientists 
and especially mathematicians. Moving on from this, is it the more “regular” 
laces which appeal, I.e. Torchon, Bucks and Flanders, rather than Bedfordshire 
for instance?

Sent from my iPad

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[lace] Lace and maths

[Kathleen Harris]

I wonder if it is simply that bobbin lace appeals particularly to scientists 
and especially mathematicians. Moving on from this, is it the more “regular” 
laces which appeal, I.e. Torchon, Bucks and Flanders, rather than Bedfordshire 
for instance?

Sent from my iPad

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Re: [lace] Lace and maths

[David C COLLYER]

Dear Nancy,

Because of these two observations, I've always thought that people who are
good at bobbin lace would make good software engineers, whether they know it
or not, and whether they are good at arithmetic or not. This is the other way
around from some of the observations that have been made, but related I think.


Whilst I have always been a natural mathematician, it was when I did 
the super-dooper psychiatric tests in the army and they made me an 
interpreter that I was told it's not just maths that I'm good at, 
it's the part of the brain that deals with code-breaking!


And that includes all those things such as: mathematics; reading and 
creating music; languages; Braille; typing, and not doubt many more.


Just food for thought
David in Ballarat, AUS

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Re: [lace] Lace and maths

[Nancy Neff]

Dear spiders,
 
I'm not sure where I fall in this debate but I have a couple
of observations to offer. They may be food for thought, or they may deserve to
be ignored--I hope the former.
 
I wonder if 'maths' is the right term or not.
Just for some context, let me note that I like precision and 'correctness' but
I prefer to make floral varieties of lace and have been told by one author and
teacher that I am a natural at Binche. I always scored very high on the math
section of standardized tests (99th percentile) but have never liked math or
felt any good at it. I can add and divide and all that but am much more
reliable with a calculator, and I was not any good at calculus.
 
What I am,
however, is a software engineer and I love designing and coding software
programs. The observations I offer are: 1) there is no addition etc. form of
maths in software development. Instead there is logical thinking and being
able to analyze the sequence of actions necessary to produce the desired
result. This is a type of 'maths' that seems to me necessary to do bobbin lace
at all, regardless of the creativity side of it.
 
2) My second observation
is very subjective, but one I have found fascinating. When I do a complicated
bit of bobbin lace, it FEELS in my head the same as when I'm doing software
design and coding. I get the same positive feeling FROM doing both bobbin lace
and software development, yes, but more than that: it feels the same WHEN I'm
doing it, like I'm doing basically the same thing. Like I said--subjective!
 
Because of these two observations, I've always thought that people who are
good at bobbin lace would make good software engineers, whether they know it
or not, and whether they are good at arithmetic or not. This is the other way
around from some of the observations that have been made, but related I think.
I believe that the same analytical and logical skills are required in both,
and also creativity to think of novel and more effective ways to do something.
 
So maybe both 'sides' in this debate are right but talking past each other?
Just a suggestion.
 
Nancy
from Connecticut, USA, but currently in Bruges,
Belgium :-) with an appointment to see some old Binche lace in the museums'
collections tomorrow and to photograph lace from a private collection this
afternoon :-))
 


 From: Maureen
maur...@roger.karoo.co.uk
To: alexstillw...@talktalk.net
alexstillw...@talktalk.net 
Cc: Arachne reply lace@arachne.com; Clay
Blackwell clayblackw...@comcast.net 
Sent: Sunday, July 7, 2013 3:18 PM
Subject: Re: [lace] Lace and maths
  
Hi all

As a non mathematical
person I feel I must comment from those of us who are mathematically
challenged.  I like to think I am a reasonable lacemaker, I can draw out
patterns on graph paper and use a lace design programme and I teach students
how to draw out patterns to help understand the working of lace.  But I cannot
add up for toffee and some maths completely confuses me.  I admit I am better
with floral type laces, Bucks, Honiton etc but I don't like to make mistakes
and teach accordingly.  Please give consideration to non mathematical
Lacemakers as well.  There is a place for us all.

Regards Maureen

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[lace] Lace and maths

[Kathleen Harris]

Could I suggest that many lace makers are problem solvers. This would
include mathematicians, and many scientists. I love puzzles of any kind but
especially logic problems, and when I am making lace, I can see a
problem-solving element in the process, even in a simple piece of Torchon. I
can also see a connection between this and design - where should I place
this element of my design? - whether it is lace, any other textile, or
something more solid which requires engineering skills as well.

 

But, as in every other field, not every lace maker is a mathematician or a
puzzler, and not every mathematician or puzzler makes lace, though it might
give them a head start if they wanted to learn.

 

Kathleen

In Berkshire, where it is too hot to make lace at the moment, but I hesitate
to complain!

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[lace] Lace and maths

[Jean Nathan]

I don't think it's maths in particular, but we all know that ALL, absolutely 
ALL women are totally and absolutely logical in their thinking and there's 
logic to where the threads move next. The majority of lacemakers are women 
so the men who make lace are obviously demonstrating their feminine side.


And before anyone shoots me down, you can't hear the grin in my voice.

Jean in Poole, Dorset, UK 


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RE: Re: [lace] Lace and maths

[Maureen]

Dear Lynn, et al

Thank you for your email.I was not suggesting that there is not  a 
mathematical aspect to making lace, only the following comment is, I think 
unfair.

'The best lacemakers are computer programmers, maths graduates and architects 
and anything that develops judgement of space and line is bound to help.'

Lyn wrote:
There is, I think you will agree, a mathematical aspect to lace.  Doesn't mean 
you have to be a math expert to do it.  Your drawing on graph paper, and using 
a computer program for lace design can be considered mathematical.  One learns 
a lot of things making lace, from the proper winding of bobbins to solving the 
puzzle of why there is an extra pair where it doesn't belong.  I suspect that 
some of these skills require the same brain functions as math.  Especially 
things like topology, logic. Being able to visualize the flow of threads in a 
Flanders or Torchon pattern. I think of these as included in math skills.  I 
don't think a lot of people realize that.  Einstein's theory of relativity 
doesn't involve numbers until it is applied.  I think.  Not sure about that, 
but I think so.  


I agree that maths logic helps the lacemaker to work out where the threads go, 
which part of the pattern to work next etc.,  but it also takes skill to 
visualise the lace whilst designing it and although maths and drawing helps 
with the skill of designing a piece of lace, the designer  needs to have the 
insight to envisage what the lace will look like once made.  The skills of 
drafting out a lace pattern was taught to me fairly early on in my lacemaking 
life and I teach it to students so that they can understand the direction that 
the threads should go into. Practice in working lace helps the 
understanding and also goes a long way to make a good lacemaker.

Maureen wrote:
As a non mathematical person I feel I must comment from those of us who are 
mathematically challenged.  I like to think I am a reasonable lacemaker, I 
can draw out patterns on graph paper and use a lace design programme and I 
teach students how to draw out patterns to help understand the working of 
lace.  But I cannot add up for toffee and some maths completely confuses me.  
I admit I am better with floral type laces, Bucks, Honiton etc but I don't 
like to make mistakes and teach accordingly.  Please give consideration to 
non mathematical Lacemakers as well.  There is a place for us all.


So as someone said later, there is a place for everyone with all level of 
skill.I just would not like to see someone discouraged and made to feel  
that they are not good enough because they are not a  maths grad, architect or 
computer programmer and  then give up.   Although hopefully there is no one on 
this list who would feel that way.

Maureen
E Yorks UK

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Re: [lace] Lace and maths

[Maureen]

Dear Jean

Agreed 


 I don't think it's maths in particular, but we all know that ALL, absolutely 
 ALL women are totally and absolutely logical in their thinking and there's 
 logic to where the threads move next. The majority of lacemakers are women so 
 the men who make lace are obviously demonstrating their feminine side.
 
 
Maureen
E Yorks

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Re: [lace] Lace and maths

[Lyn Bailey]

Dear Nancy,
You have given a wonderful response.  Ability to analyze and logical 
thinking.  I think you are right there.  And not limited to the realm of 
mathematics, but a way to think.  Your observation on feeling similarly when 
you make a computer program and making computer software is compelling. 
Until we become more familiar with the brain, with new technology, it is the 
best analysis of the thought processes that can be used in lace making. 
Except that lace is visual, and computer software design probably is not, 
although that may not be so, if you see it in your head.


I bet problem solving could also be included in the skills which can be 
developed with bobbin lace.  Which involves a lot of analysis.  Or maybe 
problem solving is a combination of other skills.  In any event, these 
skills are valuable for students to learn, and having this information could 
be very helpful in getting schools to allow lace classes, either on campus 
or off.


And you may be correct that 'math' is not the correct term, especially if it 
is associated only with those pesky numbers.  It is the other things 
involved in math, and, as you rightly say, other areas as well, that I was 
looking for, and these are more elusive.


And I don't think there really are two sides to this discussion.  I am being 
criticized for something I didn't say, and don't believe.  What I was trying 
to say is that lace making involves mental skills that would be useful to 
school children, and this could be an argument presented to schools to 
permit a club or advertising a group.  I associate those skills with math, 
although I use them in the practice of law, and in literary analysis, and my 
father and daughter use(d) them in engineering.  I believe I use these 
skills in lacemaking.  Whether my lace is good or poor is immaterial.


Lyn in Lancaster, Pennsylvania, USA

Nancy wrote:
I wonder if 'maths' is the right term or not.
Just for some context, let me note that I like precision and 'correctness' 
but
I prefer to make floral varieties of lace and have been told by one author 
and

teacher that I am a natural at Binche. I always scored very high on the math
section of standardized tests (99th percentile) but have never liked math or
felt any good at it. I can add and divide and all that but am much more
reliable with a calculator, and I was not any good at calculus.

What I am,
however, is a software engineer and I love designing and coding software
programs. The observations I offer are: 1) there is no addition etc. form of
maths in software development. Instead there is logical thinking and being
able to analyze the sequence of actions necessary to produce the desired
result. This is a type of 'maths' that seems to me necessary to do bobbin 
lace

at all, regardless of the creativity side of it.

2) My second observation
is very subjective, but one I have found fascinating. When I do a 
complicated

bit of bobbin lace, it FEELS in my head the same as when I'm doing software
design and coding. I get the same positive feeling FROM doing both bobbin 
lace
and software development, yes, but more than that: it feels the same WHEN 
I'm

doing it, like I'm doing basically the same thing. Like I said--subjective!

Because of these two observations, I've always thought that people who are
good at bobbin lace would make good software engineers, whether they know it
or not, and whether they are good at arithmetic or not. This is the other 
way
around from some of the observations that have been made, but related I 
think.

I believe that the same analytical and logical skills are required in both,
and also creativity to think of novel and more effective ways to do 
something.


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Re: [lace] Lace and maths

[Bronwen of Hindscroft]

I think many people are concentrating on just the bobbin laces here, when
they talk about lacemakers being good at maths or spatial reasoning or
whatever.

Because, as a needle lace maker, I'm not having to use maths so much.  Even
when I design my own piece, instead of trying to recreate a 1500s pattern,
it's more make the cartoon, couch down the lines, and fill in the spaces
with whatever looks good (or is what I can see they did from the blurry
pictures I have).

Yes, there is *some* maths.  But for me it's more how big is this cuff's
grid, how big should the grid lines be for this to look good, what kind of
detail can I put in with a 35/2 thread vs a 90/2 thread.  Maybe it's
because I'm so bad at maths, I do a lot of experimenting first.

I know there is math for knitting and crochet, but again, from what I
recall from when I knitted or crochet mumblemany years ago, not a lot.

And as to the spatial thing -- I'm TERRIBLE at it.  I have a friend and
sewing mentor that can draft out her own patterns, lay them down on checked
fabric, and have it all come together perfectly (all the lines and squares
meet up).  I, on the other hand, need an already made pattern, and need a
fabric that has no geometric designs or nap.  Then I *might* be able to
make something I'm not ashamed to wear!

Bronwen,
in sunny Colorado Springs, where the temperature is expected to get into
the 90s Fahrenheit, or mid 30s Celsius

On Mon, Jul 8, 2013 at 2:36 AM, Kathleen Harris ec...@cix.co.uk wrote:


 But, as in every other field, not every lace maker is a mathematician or a
 puzzler, and not every mathematician or puzzler makes lace, though it might
 give them a head start if they wanted to learn.

 Kathleen


-- 

Out of clutter, find Simplicity. From discord, find Harmony. In the middle
of difficulty lies opportunity. - Albert Einstein

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[lace] Lace and Maths

[Alan Sheila Brown]

This discussion has been very interesting, however for those of us who 
came to lace in the middle '70s there were not many 'textbooks' around, 
certainly in English.
My introduction  to lace was a Council evening class with Tordis Berndt 
as our tutor -20+ of us in September 1976..  The only literature/books 
available were the series from the Lace Guild, Magaret Maidment from 
approx. 1910.  and a few other booklets. Tordis also had her university 
notes , 2 Swedish booklets  which the number  of bobbins required , 
photos etc. but no prickings.
I think the need to work these out onto graph paper , whether one was 
maths inclined or not  did not come into it, it had to be done.But, one 
learnt how important it was to be able to follow the thread pairs 
through the design.  This then  leads one to the use of colours for 
different stitches  before the international colour code came into being.
Certainly I have found those 2 early years as having laid a good 
foundation  for the years ahead.It has also probably helped when one 
passed on to designing, not just  in geometric but in the 'free' laces 
so many of us now do.


Sheila in Sawbo, who's head is spinning round. with Murray's win and the 
good weather.


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Re: [lace] Lace and Maths - Sheila Brown's Contributions to Lace

[Jeriames]

Before the 20th century few lacemakers anywhere were educated,  and most 
could not even read.  However, they were able to produce  laces we admire and 
avidly collect today.
 

Please consider how little was available to anyone who wanted to  learn 
about lace after the two 20th C. World Wars.   No matter which nation.  We have 
had some powerful role models, and it  is doubtful they thought math and 
related school subjects were especially  important to their lacemaking success.
 
As to her comments (below my signature), Sheila Brown had, by 1990, written 
 a 96-page hardback book published by Batsford - Free Lace  Patterns.  
Lace Guild libraries will have it.  
 
Further, between 2000 and 2002 Sheila and her late husband Alan  Brown 
published reprints of four 19th C. government surveys by  Alan Cole, reporting 
on the conditions under which lacemakers worked in England  and Ireland.   
Making these easily available provided numerous  lace book authors with 
verifiable documentation of a period in history when  lacemaking was most 
important to the survival of many people.  (Alan Cole  was the youngest son of 
Sir 
Henry Cole, credited with being the  creator of the Victoria and Albert 
Museum.  Search Henry Cole in  Arachne archives for more information.)
 
Thank you for your devotion to lace, Sheila!
 
Jeri Ames in Maine USA
Lace and Embroidery Resource Center  

 
In a message dated 7/8/2013 
This discussion has been very interesting, however for those of us  who 
came to lace in the middle '70s there were not many 'textbooks' around,  
certainly in English.
My introduction  to lace was a Council evening  class with Tordis Berndt 
as our tutor - 20+ of us, in September 1976..   The only literature/books 
available were the series from the Lace Guild,  Margaret Maidment from 
approx. 1910, and a few other booklets. Tordis  also had her university 
notes , 2 Swedish booklets with the  number  of bobbins required, 
photos etc. but no prickings.
I think  the need to work these out onto graph paper, whether one was 
maths inclined  or not did not come into it, it had to be done.  But, one 
learnt  how important it was to be able to follow the thread pairs 
through the  design.  This then leads one to the use of colours for 
different  stitches before the international colour code came into being.
Certainly  I have found those 2 early years as having laid a good 
foundation for  the years ahead.  It has also probably helped when one 
passed on to  designing, not just  in geometric but in the 'free' laces 
so many of us  now do.  Sheila

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[lace] Lace and maths

[alexstillwell]

Hi Clay

In my experience those with a maths bias tend to be more accurate and can
understand how the threads work. In the many years I have been teaching I have
come across many who show this ability and who should have been good at maths,
but sadly for some reason or other it did not happen. Starting my career
teaching maths/science I have always been interested to find out why not.
Surprisingly sometimes it was as simple as returning to school after an
illness to find the subject had moved on and they feeling they could not catch
up assumed they could not do it. Just because a person thinks she cannot do
maths does not mean that the ability to think logically and ‘see’ straight
lines is not there.

Being mathematical is not at the expense of being creative. You can be both,
although there are some who require perfection and making lace that is
geometrically accurate is essential. These lacemakers prefer the geometrical
laces and find it very hard to make floral Bucks and the Lester type Beds in
which judgement is frequently made between two techniques, neither of which
will give a perfect result. Fortunately there are so many different forms of
lacemaking that we can all find plenty to satisfy our individual needs.

Happy lacemaking whichever type you make and whether you can do maths or not.

Alex

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Re: [lace] Lace and maths

[Maureen]

Hi all

As a non mathematical person I feel I must comment from those of us who are 
mathematically challenged.  I like to think I am a reasonable lacemaker, I can 
draw out patterns on graph paper and use a lace design programme and I teach 
students how to draw out patterns to help understand the working of lace.  But 
I cannot add up for toffee and some maths completely confuses me.  I admit I am 
better with floral type laces, Bucks, Honiton etc but I don't like to make 
mistakes and teach accordingly.  Please give consideration to non mathematical 
Lacemakers as well.  There is a place for us all.

Regards Maureen


On 7 Jul 2013, at 17:53, alexstillw...@talktalk.net wrote:

 Hi Clay
 
 In my experience those with a maths bias tend to be more accurate and can
 understand how the threads work. In the many years I have been teaching I have
 come across many who show this ability and who should have been good at maths,
 but sadly for some reason or other it did not happen. Starting my career
 teaching maths/science I have always been interested to find out why not.
 Surprisingly sometimes it was as simple as returning to school after an
 illness to find the subject had moved on and they feeling they could not catch
 up assumed they could not do it. Just because a person thinks she cannot do
 maths does not mean that the ability to think logically and ‘see’ straight
 lines is not there.
 
 Being mathematical is not at the expense of being creative. You can be both,
 although there are some who require perfection and making lace that is
 geometrically accurate is essential. These lacemakers prefer the geometrical
 laces and find it very hard to make floral Bucks and the Lester type Beds in
 which judgement is frequently made between two techniques, neither of which
 will give a perfect result. Fortunately there are so many different forms of
 lacemaking that we can all find plenty to satisfy our individual needs.
 
 Happy lacemaking whichever type you make and whether you can do maths or not.
 
 Alex
 
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Fw: Re: [lace] Lace and maths

[lynrbailey]

Dear Maureen, et al,
I can't add, subtract, multiply and divide worth anything. I can do it, but I 
don't like to.  I thank God for calculators. In my opinion they spoil math by 
putting numbers in.  But it does seem to me that there are a lot of math types 
making lace.  Whether their lace is better or worse due to their skill in math 
is an open question, in my opinion, yet they are drawn to lace.  It draws us 
for all sorts of reasons. There is room at the lace pillow for all types. 

There is, I think you will agree, a mathematical aspect to lace.  Doesn't mean 
you have to be a math expert to do it.  Your drawing on graph paper, and using 
a computer program for lace design can be considered mathematical.  One learns 
a lot of things making lace, from the proper winding of bobbins to solving the 
puzzle of why there is an extra pair where it doesn't belong.  I suspect that 
some of these skills require the same brain functions as math.  Especially 
things like topology, logic. Being able to visualize the flow of threads in a 
Flanders or Torchon pattern. I think of these as included in math skills.  I 
don't think a lot of people realize that.  Einstein's theory of relativity 
doesn't involve numbers until it is applied.  I think.  Not sure about that, 
but I think so.  

In another discussion a couple years ago, someone mentioned the lack of 
Alzheimers in lacemakers.  Personally I believe that is so for the same reason 
that there are very few people who work on crossword puzzles with Alzheimers.  
We exercise our brain solving the puzzles and problems related to lace.   

Maureen wrote:
As a non mathematical person I feel I must comment from those of us who are 
mathematically challenged.  I like to think I am a reasonable lacemaker, I 
can draw out patterns on graph paper and use a lace design programme and I 
teach students how to draw out patterns to help understand the working of 
lace.  But I cannot add up for toffee and some maths completely confuses me.  
I admit I am better with floral type laces, Bucks, Honiton etc but I don't 
like to make mistakes and teach accordingly.  Please give consideration to 
non mathematical Lacemakers as well.  There is a place for us all.

Regards Maureen



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