Magical Math Sticks and Cover Case
This
one is for my father, who still uses a slide rule.
William Oughtred, an English mathematician,
invented the slide rule using Napier’s theory.
In 1614, John Napier, a Scottish mathematician,
invented logarithms to simplified complicated multiplication and division calculations.
He used wooden sticks (called Napier's Bones or Rods) to show the multiplication tables 1 through 9.
He used wooden sticks (called Napier's Bones or Rods) to show the multiplication tables 1 through 9.
These Magical Math Sticks are a crocheted version
of Napier’s Bones.
This pattern is fairly easy.
The paired-stitches create a clear hole to
embroider the numbers on both sides.
And there is a colorful edging around the sticks.
There are 11 Bones (each with 2 sides), so the
project can be a bit time consuming.
But sometimes repetition can be soothing.
And in the end, I think it is worth it.
There are many web sites about Napier’s Theory that
can be explored.
Here is a quick explanation of the Bones:
Note:
There
is a reason that I did not become a teacher so bear with me.
There
is a Guide Stick with Numbers 1 through 9.
On
the other sticks, a slanted line separates the tens digit on the left from the
units digit on the right.
To
multiply:
Place the Guide Stick
to the left,
and the number stick you want to multiply, to the
right of it.
Example:
6 x 7:
If
you read across from the number on the Guide Stick
(which is #6), you see that the #7 stick has a 4 in the ten’s place and a 2 in
the one’s place. (6 x 7 Answer: 42).
Use
the bones to multiply 9 x 82:
Place
the #8 and #2 sticks to the right of
the Guide Stick.
Read
across from the Guide number (which is #9).
[Numbers
that are contained in the parallel diagonals are added together. Here the 2 and the 1 are in the ten’s place.]
The answer will read across: [7 hundred’s] [2
+ 1 = 3 Ten’s] [8 One’s] So the answer
is 738.
The Bones can be used to do much more complicated
multiplication and division.
And there are many web sited that can explain it
much better than I can.
Like I said….. “Not a teacher.”
Abbreviations:
~ = Approximately
Beg = Beginning
Ch(s) = Chain(s)
Dec = 2 stitches worked
together
FO = Fasten Off
Lp(s) = Loop(s)
Sc = Single Crochet
Ss = Slip Stitch
St(s) = Stitch(es)
US Terminology
Materials:
* Crochet Thread: size #10 (at least 2 different colors)
Main Base Color: ~360 yds. of Cream (or any light color)
Note: ~16 yds. for each panel side (22 sides needed)
Note: ~16 yds. for each panel side (22 sides needed)
Numbers: ~44 yds. of
Black (or a dark color)
Note: ~2 yds. for each panel side
(If you wish,
Edging and Embroidered Numbers can all be done in the same color.
And instead of
Crochet thread #10, you could use DMC Floss.)
Edging: ~55 yds.
Note: ~5 yds. for each stick
Can be all the same color or 11 different shades.
For one set, I used Lt Blue, Pink, Purple, Turquoise, Yellow, Green, Red, Brown,
* 1.50 mm steel hook (~ US size 8)
* A
Small Embroidery Needle for the Crochet Thread (used for numbers and weaving in
ends)
* Plastic Canvas (7 holes to the inch): Cut
to the dimensions of the panel-side.
I used 42 holes long and 4 holes wide for each
panel for (~ 6.5” x .5”)
The plastic canvas size could be different, if you
crochet tighter or looser, or if you use a different size hook or thread.
When you complete Rows 1–57, be sure to measure, before you cut the canvas.
What do they say? “Measure twice, cut once”. Better
to be a bit big, than too short.
You will need to cut 11 plastic canvas sticks.
Gauge: 9 sc and 9 Rnds = ~1” Not crucial.
Finished Size: ~ 6 ½” Long and 1” Wide (16.5cm x 2.5cm)
Pattern Notes:
I used crochet thread because it rendered a nice
size stick to hold in your hands.
If you wanted
larger sticks, I suppose you could use just about any type of yarn or hook.
I used a plastic canvas sheet because it was
relatively strong and flexible.
However, you
could use cut plastic, such as Costco packaging.
Just measure the panel size before cutting the
plastic insert.
Round the edges slightly, so it will not be sharp
at the corners.
And make sure it is smooth on the sides, to easily
slip in between the panels.
Use a light color for the panels so the numbers
will stand out.
If you prefer, you can make the Guide Stick panel
in a different (light) color.
I used cream color for 10 sticks (20 panels) and a yellow
or for the Guide (2 panels).
The paired single-crochet stitch creates a clear
hole to embroider the numbers.
If you wish,
you can simply crochet 57 rows of plain single crochets.
I did try
that, but embroidering the numbers was a bit more difficult and took longer.
Regarding
copyright:
This is a
free pattern for your personal use.
You are
welcome to sell any items that you make.
But please, do not
sell the pattern or reproduce the text without permission.
Panel: (Note:
22 panels are needed for 11 sticks)
Row
1: Ch 8, Sc in the back ridge-bump of 2nd ch from the hook, and each ch across. Turn.
(7)
Row
2: Ch 1.
First Paired Stitch:
Insert hook into first st, YO, pull up a loop (2
lps on the hook now)
Insert hook in next st, YO and pull up a loop (now
there should be 3 lps on the hook).
YO and pull thru all 3 loops.
Note: The
paired SC stitch is basically a Sc decrease.
Next Paired Sts:
* Sc-Dec by pulling up a loop from
the same as the last st and the next st.*
Repeat from * to * 4 more times.
Sc in the same as the last st (to keep an even count). Turn. (6 paired + 1 sc = 7 sts)
Rows
3 - 56: Repeat Row 2.
Row
57: Ch 1, Sc across. FO.
(7)
Embroider Numbers:
The
Guide Stick can have the numbers 1 -
9 embroidered on just the front side.
Or both
sides, if you prefer.
The
Main Sticks have counterpart Front and Back sides.
Two sticks will have a “0” on one side with a “9”
on the opposite side.
Similarly,
there will be two sticks for the 1 and 8, 2 and 7, 3 and 6, and the 4 and 5.
Graph
You
will note that there are 9 horizontal lines and 8 diagonal lines across each of
the main 10 sticks.
The
Guide Stick just has 9 horizontal lines.
There
are 7 single crochets across the crocheted panels.
The
chain-1-turns produce an added segment that counts as the eighth square in the
graph.
Follow the graph-chart, and backstitch the black numbers and lines on each
panel.
The
red lines just show the outer-edge dimensions of each panel.
You
will need to make two of each number-panel.
Weave
in ends when finished.
Side Note: If you want, you can slant the diagonal lines in
the opposite direction (to the left).
But be sure to make all 20 diagonal-panels in a set
consistently the same.
Edging Notes:
The Guide
Stick should have an edging that stands out: like Black or Variegated.
Start
by Matching the embroidered-number
panels:
You can make the two matching sticks the same color
(to identify them easier).
Possible colors:
0 and 9 = Red
1 and 8 = Blue
2 and 7 = Yellow
3 and 6 = Green
4 and 5 = Orange
Hold
two corresponding panels (i.e. 0 and 9) with wrong sides together. The numbers
sides should be facing out on both.
Stitch
the 0 as the right side (with the 9 as the back side) of one stick.
And
the 9 as the right side (with the 0 as the back side) of the second stick.
Continue
with the rest of the sticks, so each of the 10 numbers will have a right side.
If you prefer, you can use a reverse-sc stitch for the edgings.
Periodically
keep track of back side to make sure that you have not missed a stitch or gone
off track.
The
horizontal lines should meet on both front and back sides.
There
should be 5 stitches between each horizontal line.
Be
especially careful on the row back up the 2nd long side. The back part tends to shift up a bit.
Also
note, you will be single crocheting completely over the 7 stitches of the first
and last rows (the short ends). This
produces a thicker top and bottom to compensate for the added plastic insert.
Edging: Now….Keeping the two aligned:
3 Sc through both layers, in the right-corner-stitch on
the bottom.
Sc up the panel (54 sts) and 3 Sc in the next corner st.
Sc across the top next 5 sts with 3 Sc in the next corner.
Continue to Sc down the other side about 20 to 30 sts.
Then insert
the plastic canvas between the two panels.
Continue to Sc to the bottom with 3 Sc in the final corner.
Sc across the bottom last 5 stitches. Join to the
first sc with a ss.
FO and weave in.
© 2013
P Perkins
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Holding Case:
Materials:
Caron
Simply Soft (WW Med yarn):
Can be made in
Various colors
I used: ~ 60 yds of Red for the
cover
~ 55” of Black for the letters
E / 3.5 mm
Rounded yarn needle to sew letters
Gauge: 9 sc and 10
Rnds = ~ 2” Not crucial.
Round 2 should = ~ 3 ½” x 1 ¼”
Note: Adjust hook size, for a larger or smaller
one.
Finished Size: Height
~6”
Width ~3”
Depth ~1 ¼”
Abbreviations:
~
= Approximately
BLO = Back Loop Only
Ch(s)= Chain(s)
FO = Fasten Off
Hdc = Half Double Crochet
Rnd(s) = Round(s)
Sc = Single Crochet
Sc-Inc = 2 single
crochets in one stitch
Ss = Slip Stitch
St(s) – Stitch(es)
US Terminology
Regarding copyright:
This
is a free pattern for your personal use.
You
are welcome to sell any items that you make.
But
please, do not sell the pattern or reproduce the text without permission.
Rnd 1: Ch 15.
3
Hdc in 3rd ch, [Mark first
hdc]
Hdc
in next 11, 5 Hdc in last ch.
Working
other side of ch:
Hdc
in next 11, 2 Hdc in same as first-3-hdc’s.
Join
to first (marked) st with a ss. (32)
Rnd 2: Ch 1,
Sc
in same as the joined st and the next st,
Sc-Inc in
next, Sc in next 11 sts,
Sc-Inc in
next, Sc in next 3, Sc-Inc in
next,
Sc
in 11, Sc-Inc,
Sc in last st and join to the first st. (36)
Note:
Now work in a spiral.
Do not join or ch 1.
Mark beg of rnds.
Rnd 3: Sc in BLO of each st around. (36)
Now work in a spiral.
Do not join or ch 1.
Mark beg of rnds.
Rnd 3: Sc in BLO of each st around. (36)
After
Rnd 6, check to make sure that the bones will fit.
Rnds 4 – 30: Sc in the 1st
st and around. (36)
At the end of rnd 30, ss in the next 2 sts, FO and weave
in.
Lettering:
Put the bones in the case and
mark where the front edges are, so lettering will be even on front.
Then, remove the bones and
start about 6 rows down from the top edge, and very close to the left side (marked)
edge with the capital “N”. I used about 54”
of Black yarn for the Letters.
I made the “N” over 3 rows
and the “APIER’S” over 2 rows.
The “B” should begin 2 rows
down and start under the “A”.
Note: You could leave the case blank, or add a name,
if you prefer.
2013
P Perkins
