2) We looked at Triangle numbers in our last class (the sequ.docx

2) We looked at Triangle numbers in our last class (the
sequence 1, 3, 6, 10, ...) - each number is given by the
number of dots in a triangular array. By adding together
consecutive numbers you end up with this sequence of
numbers (i.e. 1, 1+2 = 3, 1+2+3 = 6, 1+2+3+4 = 10,
etc). Now we also know that adding together consecutive
odd numbers gives you the Square numbers (i.e. 1, 1+3 = 4,
1+3+5 = 9, 1+3+5+7 = 16, etc.) - we saw different proofs of
this result using the picture proofs in class. Using this same
approach, figure out what the Pentagonal numbers must be -
and make patterns of dots to show each of the first four
Pentagonal numbers (hint, sums such as 1+2+3+4+5 give
you Triangle numbers, sums where each term goes up by
two, such as 1+3+5+7 give Square numbers, so
for Pentagonal numbers consider numbers given by sums
where each term goes up by ...(?)).
3) Now I'd like you all to create another "proof by
picture". We'll do this one somewhat in reverse by working
out the formula first and then creating the picture. First find
the formula... consider the Triangle number sequence, 1, 3,
6, 10, 15, 21, 28,... Now take a look at the sum of any two
consecutive triangle numbers, for instance 3+6 or
10+15. What kind of number are you getting each time? Is
this a coincidence or is something going on - prove it by
creating your own proof by picture. Think back to what we
saw in class when we put together two identical triangle
numbers creating a rectangle N by N+1 (in the picture
example we saw, the rectangle was 6 by 7). Now consider
what happens to this picture if you combine
two consecutive triangle numbers instead... To turn in your
work on this problem show this picture result for several

distinct cases. Next follow this up by writing down an
algebraic proof of your result as well using the formula we
found in class for the nth triangle number.
4) Next, I mentioned an article that included a conversation
about definitions of geometric figures - we looked at an
example with trapezoids in class. Now please read the
article: Conversations in a Geometry Class - you'll notice
that we've already had two of the conversations in our class
(and we'll touch on the third a bit later on!) Afterwards,
please make a comment on our class discussion board
(linked under the "Discussions" tab on the left) about the
article, either something that resonated with you, something
that you'd like to try in your own geometry class (or better
yet, a comment after you've tried one of these conversations
in one of your classes!) Please feel free to reply back to
someone else's comment as well - and/or write about a
similar type of conversation that you've had with your
students at some point in one of your classes.
5) So far in class we worked through Props 1 and 9, so now
it's time to look at what came in between them! First, start by
looking at the inner workings of the mysterious Proposition
2. To remind you of the context for this proposition (and also
for proposition 3) - as I mentioned in our last class, Euclid
supposes that a compass can be used to draw a circle with a
given radius on a page, but that the compass cannot be then
be used to transfer distances to another location on the page
- with a Euclidean compass it was assumed that as soon as
a compass is lifted from the page the arms of the compass
became loose and the length of the radius is lost (this is
different from most modern compasses that have fixed arms
that stay in position until you resize them) Thus it is not

possible (using a “floppy” Euclidean compass) to draw two
circles that are exactly the same size - after you draw one
circle and lift up the compass from the page the size of the
first circle is lost - the compass collapses as soon as you lift
it up so it's not possible to draw another circle with the exact
same radius (just for now anyway – Propositions 2 and 3
show you that it can still be done, but boy is it tricky!).
So... now try your hand at the construction in Proposition 2
(but don't read it in Euclid yet!): Given a line segment BC,
and another point, A, located a short ways away from the
line segment, draw a line segment starting at point A that is
the same length as line segment BC (i.e. show how it's
possible to copy a line segment to another location).
Note that the whole challenge is to do this construction using
a "floppy compass" - i.e. one that cannot transfer
distances. Good luck - this is a pretty challenging
construction in my opinion - few people are able to get this to
work out on their own (but it is possible!) This construction
would be trivial if you could use a fixed arm compass to
transfer distances - then you'd just draw a random line
through point A, and measure off the distance of line
segment BC with your compass and mark that on the new
line starting at A... but you're not allowed to do that with
Euclid's "floppy" compass! Count the number of steps
required for your construction, then after you're finished, read
Proposition 2 in Euclid and count the number of steps he
took (remember that counting steps in a compass and
straightedge construction means that every time a circle or a
line is drawn counts as one step, but that locating random
points, or points that are the intersections of lines or circles
is "free" - they don't count as a step). If you get totally stuck
(again this one is quite hard!) then you can always check out
Euclid's construction, but really do try hard to do this on your

own first. Please turn in your final construction - if you're able
to do this without resorting to Euclid, fantastic! – you’ll get a
bonus point on the homework. Otherwise at the least,
please go through Euclid's construction in Prop. 2 carefully
recreating the steps used there. The result of this
proposition (and proposition 3) will be that it really doesn't
matter whether one has a Euclidean compass (a "floppy
compass") or a modern, rigid arm compass - all the
propositions from here on will be possible to construct using
either type of compass given the results of Props. 2 and 3.
Very mild hint for this problem (before you go to Euclid) note
that all that's been done before Proposition 2 is the creation
of an equilateral triangle in Proposition 1. So - at some point
to do Prop 2 it’s quite likely that you’ll want to consider
creating an equilateral triangle somewhere in your diagram,
and there are only so many line segments to try building one
on given you've only got three points at the start, A, B, and
C...
7) Next create a list that summarizes each proposition
(again, just for the first 12 props) - just a brief one line
summary is all that I’m looking for. For instance on your list
Prop 6 might read "If the base angles are equal then the
triangle is isosceles." To create this list you'll need to figure
out what each proposition actually does - some of the
wording for the propositions is quite flowery and hard to
decipher!
8) Counting construction steps: Now, again working with
just the first 12 propositions, count the number of
construction steps required in each proposition that
demonstrates a construction. Note that propositions 4
through 8 don't really involve constructions, so you can just

put down a zero for these non-construction propositions on
your list. If a proposition is used in a subsequent
proposition, then you should add its steps in to the total for
the proposition that uses it, considering it as including as
many steps as it did in the original construction - for
example in Prop 9, there is an equilateral triangle
construction (Prop 1), and this should show up as requiring
4 steps, not just 1, in the counting of construction steps,
given that Prop 1 takes 4 steps. Remember that a step is
anytime a new circle or a new line is created (important note
- extending an existing line does not count as a new step
and locating new intersection points also doesn't count –
points are free!).
Note that it is possible to come up with slightly different
answers for this question - the point is to try to be as
consistent as possible and to count as carefully as you're
able to. This is just one example of a way to study The
Elements - we won't be doing this for the rest of the
propositions, so don't worry about having to do this for all
48 propositions in Book One!
The Story of a Sweatshop Girl: Sadie Frowne
Independent, LIV (Sept 25, 1902), 2279 82.
My mother was a tall, handsome, dark complexioned woman
with red cheeks, large brown eyes and a great quantity of jet
black, wavy hair. She was well educated, being able to talk in
Russian, German, Polish and French, and even to read English
print, tho, of course, she did not know what it meant. She kept a
little grocer's shop in the little village where we lived at first.
That was in Poland, somewhere on the frontier, and mother had
charge of a gate between the countries, so that everyody who

came through the gate had to show her a pass. She was much
looked up to by the people, who used to come and ask her for
advice. Her word was like law among them.
She had a wagon in which she used to drive about the country,
selling her groceries, and sometimes she worked in the fields
with my father.
The grocer's shop was only one story high, and had one window,
with very small panes of glass. We had two rooms behind it, and
were happy while my father lived, altho we had to work very
hard. By the time I was six years of age I was able to wash
dishes and scrub floors, and by the time I was eight I attended
to the shop while my mother was away driving her wagon or
working in the fields with my father. She was strong and could
work like a man.
When I was a little more than ten years of age my father died
He was a good man and a steady worker, and we never knew
what it was to be hungry while he lived After he died troubles
began, for the rent of our shop was about $6 a month and then
there were food and clothes to provide. We needed little, it is
true, but even soup, black bread and onions we could not always
get.
We struggled along till I was nearly thirteen years of age and
quite handy at housework and shop keeping, so far as I could
learn them there. But we fell behind in the rent and mother kept
thinking more and more that we should have to leave Poland
and go across the sea to America where we heard it was much
easier to make money. Mother wrote to Aunt Fanny, who lived
in New York, and told her how hard it was to live in Poland,
and Aunt Fanny advised her to come and bring me. I was out at
service at this time and mother thought she would leave me as I
had a good place and come to this country alone, sending for me
afterward But Aunt Fanny would not hear of this. She said we
should both come at once, and she went around among our
relatives in New York and took up a subscription for our
passage.
We came by steerage on a steamship in a very dark place that

smelt dreadfully. There were hundreds of other people packed in
with us, men, women and children, and almost all of them were
sick It took us twelve days to cross the sea, and we thought we
should die, but at last the voyage was over, and we came up and
saw the beautiful bay and the big woman with the spikes on her
head and the lamp that is lighted at night in her hand (Goddess
of Liberty).
Aunt Fanny and her husband met us at the gate of this country
and were very good to us, and soon I had a place to live out
(domestic servant), while my mother got work in a factory
making white goods.
I was only a little over thirteen years of age and a greenhorn, so
I received $9 a month and board and lodging, which I thought
was doing well. Mother, who, as I have said, was very clever,
made $9 a week on white goods, which means all sorts of
underclothing, and is high class work
But mother had a very gay disposition. She liked to go around
and see everything, and friends took her about New York at
night and she caught a bad cold and coughed and coughed She
really had hasty consumption, but she didn't know it, and I
didn't know it, and she tried to keep on working, but it was no
use. She had not the strength Two doctors attended her, but they
could do nothing, and at last she died and I was left alone. I had
saved money while out at service, but mother's sickness and
funeral swept it all away and now I had to begin all over again.
Aunt Fanny had always been anxious for me to get an education,
as I did not know how to read or write, and she thought that was
wrong. Schools are different in Poland from what they are in
this country, and I was always too busy to learn to read and
write. So when mother died I thought I would try to learn a
trade and then I could go to school at night and learn to speak
the English language well.
So I went to work in Allen street (Manhattan) in what they call
a sweatshop, making skirts by machine. I was new at the work
and the foreman scolded me a great deal.
"Now, then," he would say, "this place is not for you to be

looking around in. Attend to your work. That is what you have
to do."
I did not know at first that you must not look around and talk,
and I made many mistakes with the sewing, so that I was often
called a "stupid animal." But I made $4 a week by working six
days in the week For there are two Sabbaths here our own
Sabbath, that comes on a Saturday, and the Christian Sabbath
that comes on Sunday. It is against our law to work on our own
Sabbath, so we work on their Sabbath.
In Poland I and my father and mother used to go to the
synagogue on the Sabbath, but here the women don't go to the
synagogue much, tho the men do. They are shut up working
hard all the week long and when the Sabbath comes they like to
sleep long in bed and afterward they must go out where they can
breathe the air. The rabbis are strict here, but not so strict as in
the old country.
I lived at this time with a girl named Ella, who worked in the
same factory and made $5 a week. We had the room all to
ourselves, paying $1.50 a week for it, and doing light
housekeeping. It was in Allen street, and the window looked out
of the back, which was good, because there was an elevated
railroad in front, and in summer time a great deal of dust and
dirt came in at the front windows. We were on the fourth story
and could see all that was going on in the back rooms of the
houses behind us, and early in the morning the sun used to come
in our window.
We did our cooking on an oil stove, and lived well, as this list
of our expenses for one week will show:
ELLA AND SADIE FOR FOOD (ONE WEEK)
Tea $0.06
Cocoa .10
Bread and rolls .40
Canned vegatables .20
Potatoes .10
Milk .21
Fruit .20

Butter .15
Meat .60
Fish .15
Laundry .25
Total $2.42
Add rent 1.50
Grand total $3.92
Of course, we could have lived cheaper, but we are both fond of
good things and felt that we could afford them.
We paid 18 cents for a half pound of tea so as to get it good,
and it lasted us three weeks, because we had cocoa for
breakfast. We paid 5 cents for six rolls and 5 cents a loaf for
bread, which was the best quality. Oatmeal cost us 10 cents for
three and one half pounds, and we often had it in the morning,
or Indian meal porridge in the place of it, costing about the
same. Half a dozen eggs cost about 13 cents on average, and we
could get all the meat we wanted for a good hearty meal for 20
cents two pounds of chops, or a steak, or a bit of veal, or a neck
of lamb something like that. Fish included butter fish, porgies,
codfish and smelts, averaging about 8 cents a pound.
Some people who buy at the last of the market, when the men
with the carts want to go home, can get things very cheap, but
they are likely to be stale, and we did not often do that with
fish, fresh vegetables, fruit, milk or meat Things that kept well
we did buy that way and got good bargains. I got thirty potatoes
for 10 cents one time, tho generally I could not get more than
15 of them for that amount. Tomatoes, onions and cabbages,
too, we bought that way and did well, and we found a factory
where we could buy the finest broken crackers for 3 cents a
pound, and another place where we got broken candy for 10
cents a pound. Our cooking was done on an oil stove, and the
oil for the stove and the lamp cost us 10 cents a week.
It cost me $2 a week to live, and I had a dollar a week to spend
on clothing and pleasure, and saved the other dollar. I went to
night school, but it was hard work learning at first as I did not
know much English.

Two years ago I came to this place, Brownsville, where so many
of my people are, and where I have friends. I got work in a
factory making underskirts all sorts of cheap underskirts, like
cotton and calico for the summer and woolen for the winter, but
never the silk, satin or velvet underskirts. I earned $4.50 a week
and lived on $2 a week, the same as before.
I got a room in the house of some friends who lived near the
factory. I pay $1 a week for the room and am allowed to do
light housekeepingthat is, cook my meals in it. I get my own
breakfast in the morning, just a cup of coffee and a roll, and at
noon time I come home to dinner and take a plate of soup and a
slice of bread with the lady of the house. My food for a week
costs a dollar, just as it did in Allen street, and I have the rest
of my money to do as I like with. I am earning $5.50 a week
now, and will probably get another increase soon.
It isn't piecework in our factory, but one is paid by the amount
of work done just the same. So it is like piecework. All the
hands get different amounts, some as low as $3.50 and some of
the men as high as $16 a week. The factory is in the third story
of a brick building. It is in a room twenty feet long and fourteen
broad There are fourteen machines in it. I and the daughter of
the people with whom I live work two of these machines. The
other operators are all men, some young and some old.
At first a few of the young men were rude. When they passed
me they would touch my hair and talk about my eyes and my red
cheeks, and make jokes. I cried and said that if they did not stop
I would leave the place. The boss said that that should not be,
that no one must annoy me. Some of the other men stood up for
me, too, especially Henry, who said two or three times that he
wanted to fight Now the men all treat me very nicely. It was
just that some of them did not know better, not being educated.
Henry is tall and dark, and he has a small mustache. His eyes
are brown and large. He is pale and much educated, having been
to school. He knows a great many things and has some money
saved I think nearly $400. He is not going to be in a sweatshop
all the time, but will soon be in the real estate business, for a

lawyer that knows him well has promised to open an office and
pay him to manage it.
Henry has seen me home every night for a long time and makes
love to me. He wants me to marry him, but I am not seventeen
yet, and I think that is too young. He is only nineteen, so we
can wait.
I have been to the fortune teller's three or four times, and she
always tells me that tho I have had such a lot of trouble I am to
be very rich and happy. I believe her because she has told so
many things that have come true. So I will keep on working in
the factory for a time. Of course it is hard, but I would have to
work hard even if I was married.
I get up at half past five o'clock every morning and make myself
a cup of coffee on the oil stove. I eat a bit of bread and perhaps
some fruit and then go to work Often I get there soon after six
o'clock so as to be in good time, tho the factory does not open
till seven I have heard that there is a sort of clock that calls you
at the very time you want to get up, but I can't believe that
because I don't see how the clock would know.
At seven o' clock we all sit down to our machines and the boss
brings to each one the pile of work that he or she is to finish
during the day, what they call in English their" stint" This pile
is put down beside the machine and as soon as a skirt is done it
is laid on the other side of the machine. Sometimes the work is
not all finished by six o'clock and then the one who is behind
must work overtime. Sometimes one is finished ahead of time
and gets away at four or five o'clock, but generally we are not
done till six o'clock.
The machines go like mad all day, because the faster you work
the more money you get Sometimes in my haste I get my finger
caught and the needle goes right through it It goes so quick tho,
that it does not hurt much. I bind the finger up with a piece of
cotton and go on working. We all have accidents like that
Where the needle goes through the nail it makes a sore finger,
or where it splinters a bone it does much harm. Sometimes a
finger has to come off. Generally, tho, one can be cured by a

salve.
All the time we are working the boss walks about examining the
finished garments and making us do them over again if they are
not just right So we have to be careful as well as swift But I am
getting so good at the work that within a year I will be making
$7 a week, and then I can save at least $3.50 a week. I have
over $200 saved now.
The machines are all run by foot power, and at the end of the
day one feels so weak that there is a great temptation to lie right
down and sleep. But you must go out and get air, and have some
pleasure. So instead of lying down I go out, generally with
Henry. Sometimes we go to Coney Island, where there are good
dancing places, and sometimes we go to Ulmer Park to picnics.
I am very fond of dancing, and, in fact, all sorts of pleasure. I
go to the theater quite often, and like those plays that make you
cry a great deal "The Two Orphans" is good. Last time I saw it I
cried all night because of the hard times that the children had in
the play. I am going to see it again when it comes here.
For the last two winters I have been going to night school at
Public School 84 on Glenmore avenue. I have learned reading,
writing and arithmetic. I can read quite well in English now and
I look at the newspapers every day. I read English books, too,
sometimes. The last one that I read was"A Mad Marriage," by
Charlotte Braeme. She's a grand writer and makes things just
like real to you. You feel as if you were the poor girl yourself
going to get married to a rich duke.
I am going back to night school again this winter. Plenty of my
friends go there. Some of the women in my class are more than
forty years of age. Like me, they did not have a chance to learn
anything in the old country. It is good to have an education; it
makes you feel higher. Ignorant peole are all low. People say
now that I am clever and fine in conversation.
We have just finished a strike in our business. It spread all over
and the United Brotherhood of Garment Workers was in it That
takes in the cloakmakers, coatmakers, and all the others. We
struck for shorter hours, and after being out four weeks won the

fight We only have to work nine and a half hours a day and we
get the same pay as before. So the union does good after all in
spite of what some people say against it that it just takes our
money and does nothing.
I pay 25 cents a month to the union, but I do not begrudge that
because it is for our benefit The next strike is going to be for a
raise of wages, which we all ought to have. But tho I belong to
the union I am not a Socialist or an Anarchist I don't know
exactly what those things mean There is a little expense for
charity, too. If any worker is injured or sick we all give money
to help.
Some of the women blame me very much because I spend so
much money on clothes. They say that instead of a dollar a
week I ought not to spend more than twenty five cents a week
on clothes, and that I should save the rest But a girl must have
clothes if she is to go into high society at Ulmer Park or Coney
Island or the theatre. Those who blame me are the old country
people who have old fashioned notions, but the people who have
been here a long time know better. A girl who does not dress
well is stuck in a corner, even if she is pretty, and Aunt Fanny
says that I do just right to put on plenty of style.
I have many friends and we often have jolly parties. Many of
the young men like to talk to me, but I don't go out with any
except Henry.
Lately he has been urging me more and more to get married -but
I think I'll wait
Brooklyn, N. Y.
A Miner's StoryThe Independent, LIV (June 12, 1902), 1407-10.
I am thirty five years old, married, the father of four children,
and have lived in the coal region all my life. Twenty three of
these years have been spent working in and around the mines.
My father was a miner. He died ten years ago from "miners'
asthma"
Three of my brothers are miners; none of us had any
opportunities to acquire an education. We were sent to school (
such a school as there was in those days) until we were about

twelve years of age, and then we were put into the screen room
of a breaker to pick slate. From there we went inside the mines
as driver boys. As we grew stronger we were taken on as
laborers, where we served until able to call ourselves miners.
We were given work in the breasts and gangways. There were
five of us boys. One lies in the cemetery fifty tons of top rock
dropped on him. He was killed three weeks after he got his job
as a miner a month before he was to be married.
In the fifteen years I have worked as a miner I have earned the
average rate of wages any of us coal heavers get To day I am
little better off than when I started to do for myself. I have $100
on hand; I am not in debt; I hope to be able to weather the strike
without going hungry.
I am only one of the hundreds you see on the street every day.
The muscles on my arms are no harder, the callous on my palms
no deeper than my neighbors' whose entire life has been spent in
the coal region. By years I am only thirty five. But look at the
marks on my body; look at the lines of worriment on my
forehead; see the gray hairs on my head and in my mustache;
take my general appearance, and you'll think I'm ten years
older.
You need not wonder why. Day in and day out, from Monday
morning to Saturday evening, between the rising and the setting
of the sun, I am in the underground workings of the coal mines.
From the seams water trickles into the ditches along the
gangways; if not water, it is the gas which hurls us to eternity
and the props and timbers to a chaos.
Our daily life is not a pleasant one. When we put on our oil
soaked suit in the morning we can't guess all the dangers which
threaten our lives. We walk sometimes miles to the place to the
man way or traveling way, or to the mouth of the shaft on top of
the slope. And then we enter the darkened chambers of the
mines. On our right and on our left we see the logs that keep up
the top and support the sides which may crush us into shapeless
masses, as they have done to many of our comrades.
We get old quickly. Powder, smoke, after damp, bad air all

combine to bring furrows to our faces and asthma to our lungs.
I did not strike because I wanted to; I struck because I had to. A
miner the same as any other workman must earn fair living
wages, or he can't live. And it is not how much you get that
counts. It is how much what you get will buy. I have gone
through it all, and I think my case is a good sample.
I was married in 1890, when I was 23 years old quite a bit
above the age when we miner boys get into double harness. The
woman I married is like myself. She was born beneath the
shadow of a dirt bank; her chances for school weren't any better
than mine; but she did have to learn how to keep house on a
certain amount of money. After we paid the preacher for tying
the knot we had just $185 in cash, good health and the good
wishes of many friends to start us off.
Our cash was exhausted in buying furniture for housekeeping.
In 1890 work was not so plentiful, and by the time our first
baby came there was room for much doubt as to how we would
pull out Low wages, and not much over half time in those years,
made us hustle. In 1890 91, from June to May, I earned
$368.72. That represented eleven months' work, or an average
of $33.52 per month Our rent was $10 per month; store not less
than $20. And then I had my oil suits and gum boots to pay for.
The result was that after the first year and a half of our married
life we were in debt Not much, of course, and not as much as
many of my neighbors, men of larger families, and some who
made less money, or in whose case there had been sickness or
accident or death. These are all things which a miner must
provide for I have had fairly good work since I was married I
made the average of what we contract miners are paid; but, as I
said before, I am not much better off than when I started.
In 1896 my wife was sick eleven weeks. The doctor came to my
house almost every day. He charged me $20 for his services.
There was medicine to buy. I paid the drug store $18 in that
time. Her mother nursed her, and we kept a girl in the kitchen at
$1.50 a week, which cost me $15 for ten weeks, besides the
additional living expenses.

In 1897, just a year afterward, I had a severer trial. And mind,
in those years, we were only working about half time. But in the
fall of that year one of my brothers struck a gas feeder. There
was a terrible explosion. He was hurled downward in the breast
and covered with the rush of coal and rock. I was working only
three breasts away from him and for a moment was unable to
realize what had occurred Myself and a hundred others were
soon at work, however, and in a short while we found him,
horribly burned over his whole body, his laborer dead alongside
of him.
He was my brother. He was single and had been boarding. He
had no home of his own. I didn't want him taken to the hospital,
so I directed the driver of the ambulance to take him to my
house. Besides being burned, his right arm and left leg were
broken, and he was hurt internally. The doctors there were two
at the house when we got there said he would die. But he didn't.
He is living and a miner to¬day. But he lay in bed just fourteen
weeks, and was unable to work for seven weeks after he got out
of bed He had no money when he was hurt except the amount
represented by his pay. All of the expenses for doctors,
medicine, extra help and his living were borne by me, except
$25, which another brother gave me. The last one had none to
give. Poor work, low wages and a sickly woman for a wife had
kept him scratching for his own family.
It is nonsense to say I was not compelled to keep him, that I
could have sent him to a hospital or the almshouse. We are
American citizens and we don't go to hospitals and poorhouses.
Let us look at things as they are to day, or as they were before
this strike commenced.
My last pay envelope shows my wages, after my laborer,
powder, oil and other expenses were taken off, were $29.47;
that was my earnings for two weeks, and that was extra good
The laborer for the same time got some $21. His wages are a
trifle over $10 a week for six full days. Before the strike of
1900 he was paid in this region $1.70 per day, or $10.20 a week
If the ten per cent. raise had been given, as we expected, his

wages would be $1.87 per day, or $11.22 per week, or an
increase of $1.02 per week. But we all know that under the
present system he doesn't get any eleven dollars.
Well, as I said, my wages were $29.47 for the two weeks, or at
the rate of$58.94 per month My rent is $10.50 per month. My
coal costs me almost $4 per month. We burn a little over a ton a
month on an average and it costs us over $3 per ton. Light does
not cost so much; we use coal oil altogether.
When it comes down to groceries is where you get hit the
hardest. Everybody knows the cost of living has been extremely
high all winter. Butter has been 32, 36 and 38 cents a pound;
eggs as high as 32 cents a dozen; ham, 12 and 16 cents a pound;
potatoes away up to a dollar, and cabbage not less than a cent a
pound Fresh meat need not be counted Flour and sugar did not
advance, but they were about the only staples that didn't.
Anyhow, my store bill for those two weeks was $11. That makes
$22 per month The butcher gets $6 per month Add them all, and
it costs me, just to live, $42.50. That leaves me $17 per month
to keep my family in clothes, to pay my church dues and to keep
the industrial insurance going. My insurance alone costs me 55
cents a week, or $2.20 a month.
The coal president never allows his stable boss to cut the
amount of fodder allotted to his mules. He insists on so many
quarts of oats and corn to the meal and so much hay in the
evening. The mule must be fed; the miner may be, if he works
hard enough and earns money to buy the grub.
Company stores are of the time that has been Their existence
ended two years ago. But we've got a system growing up that
threatens to be just as bad Let me explain. Over a year ago I
was given a breast to drive at one of our mines and was glad to
get it. My wife took her cash and went around the different
places to buy. When I went to the office for my first pay the
"supee" met me and asked me if I didn't know his wife's brother
George kept a store. I answered "Yes," and wanted to know
what that had to do with it." Nothing, only I thought I'd call
your attention it it," he answered.

No more was said then. But the next day I got a quiet tip that
my breast was to be abandoned This set me thinking. I went to
the boss and, after a few words, told him my wife had found
brother in law George's store and that she liked it much better
than where she had bought before. I told him the other store
didn't sell the right kind of silk waists, and their patent leather
shoes were away back. Brother in law George had the right kind
of stuff and, of course, we were willing to pay a few cents more
to get just what we wanted. That was sarcastic, but it's the cash
that has the influence. I have had work at that colliery ever
since. I know my living costs me from 10 to 15 per cent extra.
But I kept my job, which meant a good deal.
Now you must take into consideration that I am a contract miner
and that my earnings are more than the wages of three fourths
of the other fellows at the same colliery. It is not that I am a
favorite with the boss. I just struck a good breast Maybe next
month my wages would be from two to six or seven dollars less.
In the days of Pardee, Coxe, Fagley, Fulton, Dewees, Paterson,
Riley, Replier, Graeber and a hundred others, men were better
paid than they have ever been since the centralization ideas of
the late Franklin B. Gowen became fixed institutions in the
anthracite counties. It may be true that in the days of the
individual operation the cost per ton of mining coal was less
than it is to day. But it is not right that the entire increase in the
cost of mining should be charged to the miner. That is what is
being done, if you count the reductions made in wages.
We miners do not participate in the high prices of coal. The
operators try to prove otherwise by juggling with figures, but
their proving has struck a fault, and the drill shows no coal in
that section One half of the price paid for a ton of coal in New
York or Philadelphia goes into the profit pocket of the mine
owner, either as a carrier or miner.
We all know that the price of coal has advanced in the past
twenty years. We also know that wages are less, that the cost of
living is higher. I remember the time, when I was a wee lad, my
father used to get his coal for $1 per ton. Now I pay $3. In those

days we lads used to go to the dirt banks and pick a load of
coal, and it cost our parents only a half a dollar to get it hauled
home. We dare not do that now. Then we did not need gum
boots, safety lamps or any such things as that; and for all of
them we must now pay out of wages that have been reduced.
Our condition can be no worse; it might and must be better. The
luxuries of the rich we do not ask; we do want butter for our
bread and meat for our soup. We do not want silk and laces for
our wives and daughters. But we want to earn enough to buy
them a clean calico once in a while. Our boys are not expecting
automobiles and membership cards in clubs of every city, but
they want their fathers to earn enough to keep them at school
until they have a reasonably fair education.
Pennsylvania
A Cap Maker's Story: Rose Schneiderman
The Independent, LVIII, no. 2943 (Apr. 27, 1905), 935-38.
Rose SchneidermanMy name is Rose Schneiderman, and I was
born in some small city of Russian Poland. I don't know the
name of the city, and have no memory of that part of my
childhood. When I was about five years of age my parents
brought me to this country and we settled in New York.
So my earliest recollections are of living in a crowded street
among the East Side Jews, for we also are Jews.
My father got work as a tailor, and we lived in two rooms on
Eldridge Street, and did very well, though not so well as in
Russia, because mother and father both earned money, and here
father alone earned the money, while mother attended to the
house. There were then two other children besides me, a boy of
three and one of five.
I went to school until I was nine years old, enjoying it
thoroughly and making great progress, but then my father died
of brain fever and mother was left with three children and
another one coming. So I had to stay at home to help her and
she went out to look for work.
A month later the baby was born, and mother got work in a fur
house, earning about $6 a week and afterward $8 a week, for

she was clever and steady.
I was the house worker, preparing the meals and looking after
the other children - the baby, a little girl of six years, and a boy
of nine. I managed very well, tho the meals were not very
elaborate. I could cook simple things like porridge, coffee and
eggs, and mother used to prepare the meat before she went away
in the morning, so that all I had to do was to put it in the pan at
night.
The children were not more troublesome than others, but this
was a hard part of my life with few bright spots in it. I was a
serious child, and cared little for children's play, and I knew
nothing about the country, so it was not so bad for me as it
might have been for another. Yet it was bad, tho I did get some
pleasure from reading, of which I was very fond: and now and
then, as a change from the home, I took a walk in the crowded
street.
Mother was absent from half past seven o'clock in the morning
till half past six o'clock in the evening.
I was finally released by my little sister being taken by an aunt,
and the two boys going to the Hebrew Orphan Asylum, which is
a splendid institution, and turns out good men. One of these
brothers is now a student in the City College, and the other is a
page in the Stock Exchange.
When the other children were sent away mother was able to
send me back to school and I stayed in this school (Houston
Street Grammar) till I had reached the Sixth Grammar Grade.
Then I had to leave in order to help support the family. I got a
place in Hearn's as cash girl, and after working there three
weeks changed to Ridley's, where I remained for two and a half
years. I finally left because the pay was so very poor and there
did not seem to be any chance of advancement, and a friend told
me that I could do better making caps.
So I got a place in the factory of Hein & Fox. The hours were
from 8 a m. to 6 p. m., and we made all sorts of linings or,
rather, we stitched in the linings golf caps, yachting caps, etc. It
was piece work, and we received from 3 h cents to 10 cents a

dozen, according to the different grades. By working hard we
could make an average of about $5 a week. We would have
made more but had to provide our own machines, which cost us
$45, we paying for them on the installment plan. We paid $5
down and $1 a month after that.
I learned the business in about two months, and then made as
much as the others, and was consequently doing quite well when
the factory burned down, destroying all our machines 150 of
them. This was very hard on the girls who had paid for their
machines. It was not so bad for me, as I had only paid a little of
what I owed.
The bosses got $500,000 insurance, so I heard, but they never
gave the girls a cent to help them bear their losses. I think they
might have given them $10, anyway,
Soon work went on again in four lofts, and a little later I
became assistant sample maker. This is a position which, tho
coveted by many, pays better in glory than in cash It was still
piece work, and tho the pay per dozen was better the work
demanded was of a higher quality, and one could not rush
through samples as through the other caps. So I still could
average only about $5 per week.
After I had been working as a cap maker for three years it began
to dawn on me that we girls needed an organization. The men
had organized already, and had gained some advantages, but the
bosses had lost nothing, as they took it out of us.
We were helpless; no one girl dare stand up for anything alone.
Matters kept getting worse. The bosses kept making reductions
in our pay, half a cent a dozen at a time. It did not sound
important, but at the end of the week we found a difference.
We didn't complain to the bosses; we didn't say anything except
to each other. There was no use. The bosses would not pay any
attention unless we were like the men and could make them
attend.
One girl would say that she didn't think she could make caps for
the new price, but another would say that she thought she could
make up for the reduction by working a little harder, and then

the first would tell herself, "If she can do it, why can't I?" They
didn't think how they were wasting their strength.
A new girl from another shop got in among us. She was Miss
Bessie Brout, and she talked organization as a remedy for our
ills. She was radical and progressive, and she stimulated
thoughts which were already in our minds before she came.
Finally Miss Brout and I and another girl went to the National
Board of United Cloth Hat and Cap Makers when it was in
session, and asked them to organize the girls.
They asked us:
"How many of you are there willing to be organized?"
"In the first place about twelve," we said We argued that the
union label would force the bosses to organize their girls, and if
there was a girls' union in existence the bosses could not use the
union label unless their girls belonged to the union.
We were told to come to the next meeting of the National
Board, which we did, and then received a favorable answer, and
were asked to bring all the girls who were willing to be
organized to the next meeting, and at the next meeting,
accordingly, we were there twelve strong and were organized.
When Fox found out what had happened he discharged Miss
Brout, and probably would have discharged me but that I was a
sample maker and not so easy to replace. In a few weeks we had
all the girls in the organization, because the men told the girls
that they must enter the union or they would not be allowed to
work in the shop.
Then came a big strike. Price lists for the coming season were
given in to the bosses, to which they did not agree. After some
wrangling a strike was declared in five of the biggest factories.
There are 30 factories in the city. About 100 girls went out. The
result was a victory, which netted us- I mean the girls- $2
increase in our wages on the average.
All the time our union was progressing very nicely. There were
lectures to make us understand what trades unionism is and our
real position in the labor movement I read upon the subject and
grew more and more interested, and after a time I became a

member of the National Board, and had duties and
responsibilities that kept me busy after my day's work was done.
But all was not lovely by any means, for the bosses were not at
all pleased with their beating and had determined to fight us
again. They agreed among themselves that after the 26th of
December, 1904, they would run their shops on the "open"
system. This agreement was reached last fall, and soon notices,
reading as follows, were hung in the various shops:
NOTICE
After the 26th of December, 1904, this shop will be run on the
open shop system, the bosses having the right to engage and
discharge employees as they see fit, whether the latter are union
or nonunion.
Of course. we knew that this meant an attack on the union. The
bosses intended gradually to get rid of us, employing in our
place child labor and raw immigrant girls who would work for
next to nothing.
On December 22nd the above notice appeared, and the National
Board, which had known about it all along, went into session
prepared for action.
Our people were very restive, saying that they could not sit
under that notice, and that if the National Board did not call
them out soon they would go out of themselves.
At last word was sent out, and at 2.30 o'clock all the workers
stopped, and, laying down their scissors and other tools,
marched out, some of them singing the "Marseillaise."
We were out for thirteen weeks, and the girls established their
reputation. They were on picket duty from seven o'clock in the
morning till six o'clock in the evening, and gained over many of
the nonunion workers by appeals to them to quit working
against us.
Our theory was that if properly approached and talked to few
would be found who would resist our offer to take them into our
organization.
No right thinking person desires to injure another. We did not
believe in violence and never employed it.

During this strike period we girls each received $3 a week;
single men $3 a week, and married men $5 a week This was
paid us by the National Board.
We were greatly helped by the other unions, because the open
shop issue was a tremendous one, and this was the second fight
which the bosses had conducted for it.
Their first was with the tailors, whom they beat. If they now
could beat us the outlook for unionism would be bad.
Some were aided and we stuck out, and won a glorious victory
all along the line. That was only last week The shops are open
now for all union hands and for them only.
While the strike lasted I tried to get work in a factory that was
not affected, but found that the boss was against me.
Last spring I had gone as a member of a committee to appeal to
this boss on behalf of a girl who had been four years in his
employ and was only getting $7 a week. She wanted $1 raise
and all legal holidays. Previously she had had to work on
holidays. After argument we secured for her the $1 raise and
half a day on every legal holiday.
When the strike broke out, looking for work, I went to this boss,
and he stared at me, and said: "What do you want?"
"You asked for a girl."
"You you I don't want you," said he. "Can't I have my choice?"
"Certainly," said I, "I could never work where I am not wanted"
I suppose he expected me to revenge myself by keeping other
girls away, but I sent him others till he filled the place. He
resented my having served on the committee, and so he did not
want me, but I felt honored by the manner in which I was
treated. It showed that I had done my duty.
The bosses try to represent this open shop issue as tho they
were fighting a battle for the public, but really it is nothing of
the sort. The open shop is a weapon to break the unions and set
men once more cutting each other's throats by individual
competition.
Why, there was a time in the cap trade when men worked
fourteen hours a day, and then took the heads of their machines

home in bags and setting them up on stands, put mattresses
underneath to deaden the sound and worked away till far into
the morning. We don't want such slavery as that to come back.
The shops are open now for all union people, and all nonunion
people can join the union. In order to take in newcome
foreigners we have for them cut the initiation fees down to one
half what we Americans have to pay, and we trust them till they
get work and their wages.
In order to give the newcomers a chance we have stopped night
work, which doesn't suit the bosses, because it causes them to
pay more rent when they can't use their buildings night and day.
It costs them the price of another loft instead of costing the
workers their health and lives as in the old days.
Our trade is well organized, we have won two victories and are
not going backward.
But there is much to be done in other directions. The shop girls
certainly need organization, and I think that they ought to be
easy to organize, as their duties are simple and regular and they
have a regular scale of wages.
Many saleswomen on Grand and Division streets, and, in fact,
all over the East Side, work from 8 a m till 9 p. m. week days,
and one-half a day on Sundays for $5 and $6 a week; so they
certainly need organization.
The waitresses also could easily be organized, and perhaps the
domestic servants. I don't know about stenographers. I have not
come in contact with them.
Women have proved in the late strike that they can be faithful
to an organization and to each other. The men give us the credit
of winning the strike.
Certainly our organization constantly grows stronger, and the
Woman's Trade Union League makes progress.
The girls and women by their meetings and discussions come to
understand and sympathize with each other, and more and more
easily they act together.
It is the only way in which they can hope to hold what they now
have or better present conditions.

Certainly there is no hope from the mercy of the bosses.
Each boss does the best he can for himself with no thought of
the other bosses, and that compels each to gouge and squeeze
his hands to the last penny in order to make a profit.
So we must stand together to resist, for we will get what we can
take just that and no more.
New York, March 20, 1905

2) We looked at Triangle numbers in our last class (the sequ.docx

More Related Content

Similar to 2) We looked at Triangle numbers in our last class (the sequ.docx (20)

More from felicidaddinwoodie (20)

Recently uploaded (20)

2) We looked at Triangle numbers in our last class (the sequ.docx