Thursday, December 30, 2010

Happy New Year!

This is that time of the year when you suddenly realize that only one last day is left for all the things you wanted to accomplish this year.
 May be that is even better - to have still things to do on a list. It means that instead of making a new list there will be already "to do" list to keep going!
Thank you for visiting my blog and hope you will come back here next year!

Wednesday, December 22, 2010

No need to know the area of the rectangle?

Last time I was in New York I saw an exhibition at New York University's Institute for the Study of the Ancient World about  Babylonian mathematics. It is not particularly large but it was very special for me. The first book on the history of mathematics I ever read was a book on mathematics in Ancient Egypt and Babylon by Vygotsky M. Ya. Арифметика и алгебра в древнем мире, 1967
This book was given to me as a present from my beloved math teacher. Since then I was dreaming one day to see these mathematical cuneiform tablets and now finally my dream came true.
These tablets are showing that in Ancient Babylon people knew equivalent of Pythagorean Theorem which nowadays children in US schools first learn in grade 8 according to new Common Core Standards.
Pictorially this theorem is known as:
or we can say that the area of the green square equals the sum of the areas of the blue and red squares.
Too often when I talk about hyperbolic planes people say "oh, I am not good at math". Usually that is said with some regret that they did not have good math teachers at school or were discouraged to be more serious about learning math.  I have often wondered - what is wrong with school math? Why it leaves in so many people so bad memories?
There is a saying in Latvian - ' Fish begins to rot at its head." meaning that the source of the problem is at the top not bottom - e.g. we should not blame teachers without first looking how they have been prepared.
Today I heard a shocking quote:
"I got to be a full professor without knowing how to find the area of a rectangle.  Why should you expect third graders to learn that?" I think that ANY person should know that but this was not an ordinary person who said that - it was  the Dean of Education School of one of NJ colleges.
This story really struck me, so I decided to post it on my blog:

 Pat Kenschaft wrote to my husband : "... my spouse was fired last Thursday, allegedly because of an email that I wrote to my list of people who want New Jersey to require preservice elementary school teachers to
take at least one course in mathematics relevant to their teaching. (I'm told on good authority that a dozen NJ deans of education oppose this.Montclair State's said to me, "I got to be a full professor without knowing how to find the area of a rectangle. Why should you expect third graders to learn that?" I have taught areas of rectangles to hundreds of third graders without failure in the sense that they knew it when I left the room.) ".

Here follows the e-mail that had such dramatic consequences:

---------- Forwarded message ----------
Date: Tue, 14 Dec 2010 20:43:48 -0500 (EST)
From: Pat Kenschaft <>
To: undisclosed-recipients:  ;
Subject: letter to editor re math for elementary school teachers

I had the letter below about the need for elementary school teachers to be taught more mathematics in the "Montclair Times" this past Thursday It is not copyrighted and you are free to use or forward it however you like.
The importance of this issue was emphasized to me recently when a friend reported a conversation with a Monclair second grade teacher. She said she knew plenty of math for her job because the teacher's manual of "Everyday Mathematics" tells her just what she should say each day. She said the children should learn only one way, so there is no need for her to answer probing question or explore their ideas of other methods for solving problems. This, I know, is not in the spirit of those who wrote "Everyday Math," nor is Montclair an impoverished school district. It is exactly the kind of approach that keeps children from growing mathematically. Alas, I fear it is all too typical of American elementary school teachers.
What can be done? I fear that our current governor might use this issue as another reason to undermine teachers, which would mean we would continue to lose our good and experienced teachers. Teaching has always been a challenging career, and now it is losing its advantages with alarming rapidity.
On the other hand, if the state and municipalities really want to improve mathematics education, I believe this is the most crucial step.

To the Editor:

Improving Math Education

After New Jersey's first high school proficiency test was instituted, I noticed a remarkable DROP in the math preparation of my non-majors in college. Test-prep is not education, despite the pressure for AYP.
What to do? Teach the mathematics to elementary school teachers that they are supposed to teach the children! They are capable and eager to learn. They are angry when they realize how much they have been deprived the needed knowledge. Once the children are damaged, it is VERY difficult
to undo when they reach middle or high school. Many again take remedial courses in college.
A national coalition of fifteen mathematics organizations recommends four APPROPRIATE mathematics courses for future elementary school teachers. I know of only two states requiring four, but quite a few require three. New Jersey requires NONE. A reliable source I dare not reveal assures me there are a dozen deans of education in New Jersey adamantly opposing a certification requirement that future elementary school teachers be taught appropriate mathematics.
Concerned citizens can let state officials know of their concern and email me at kenschaft @pegsasus. They can read about my seven years of helping elementary school teacher mathematically in my paper "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" .
At the beginning of this program I worked with two fine Montclair teachers. Montclair stiffed its teachers, so we didn't contract with Montclair again. Both teachers worked hard anyway. Their students improved greatly, but then one was switched to full-time social studies. We have a new administration now, so Montclair might want to help its elementary school teachers mathematically.
I repeat: the teachers are plenty smart and eager enough! Like the children, they have been let down by our system."

Pat Kenschaft  added in today's e-mail:
"This stuff is politically dangerous, but we who do not have a lifetime career to lose any more need to work at it. "(bold/underlining mine -DT)

Tuesday, December 14, 2010

Art Break in NYC

yes, indeed, this is that time of the year when people go to New York to see Christmas lights and all what goes with it. I had two days full of art there. First, to the DUMBO in Brooklyn - I went to see Maddy Rosenberg in Central Booking where we chose 9 of my works which will be in the upcoming show. Then my dear friend Gail took me to the Park Avenue Armory to see Peter Greenaway's vision "Leonardo's Last Supper".   Peter Greenaway was trained as a painter, so it was really interesting to see what he saw in this painting. The first experience walking in and having a first glimpse of the painting reminded me of the time last year when David and I saw the original in Milan, except there you come in through the door on the right side of the painting. In this performance there is a time in the beginning to take it in as it is. I had another opportunity to check the lines of perspective in this painting, this time avoiding security guards jumping at me and checking what I have in my hand as it happen in Milan - there they thought I am taking forbidden pictures.  the look on their faces after I explained that I am mathematician and looking for geometric constructions in the painting was worth the entrance fee...
There is a special border, the border between art and life that often shifts deceptively. Yet, without this border, there is no art. In the process of being produced, art borrows material from life, and the traces of life still shine through the completed work of art. But, at the same time, the distance from life is the essence, the substance of art. And, yet, life has still left its traces. The more scarred the work of art is by the battles waged on the borders between art and life, the more interesting it becomes.
--Anselm Kiefer
Then Gail took me to the two openings - both near Chinatown - it was already dark and I was happy that Gail was leading the way. 

When we walked in the first one I saw a guy offering some wine to the guests, he had only one glass left on his try and I thought I should take it. When I took it, I could read in his eyes that he thought I did not deserve it because I am certainly not the one from this crowd. He was right. I found a huge gap in my art appreciation palette. I noticed a tiny sketch of nude, like the ones my classmates in 6th grade where drawing when they first discovered that girls are different from the boys. I thought it was a joke to frame it and put it on a show. I was wrong - these were all donated works and this one had a price....$17,500.....
At that point it was clear that I do not understand this show and it is time to move to the next, several blocks away.
Sorry for forgetting the author's name but he was a handsome man, originally trained as a painter. This place was small but tightly packed with a younger and more democratic crowd than the first place.
Then we returned to Brooklyn to see Gail's own painting.
More of Gail's work is on her webpage. I got to know Gail through her interest in my work, and I am so happy we found each other. I am really thrilled about the unexpected side effect of "hyperbolic crochet" - hundreds of people who did not know each other, get together and connect. One day I will write more about my own experiences, but my friendship with Gail is certainly one of them. Some times I never meet people but we have only e-mail contact. Like it was with Cat Bordhi - she has wonderful knitting books with a mathematical twist. Marie-Christine Bevington came to my talk in Kitchen (February 5, 2005). She told me that she was surprised to find out then that she was making hats with some hyperbolic crochet in them. That talk inspired her to further explore the possibilities and she came up with many more interesting hats. On Friday I had a chance to see all these hats.
This hat is Christine's original design - made of hexagons, pentagons, squares, and triangles. This hat snugs any head really nicely due to positive curvature formed.
All these different hats were fiber art objects on their own right. Thanks, Christine, for inviting me!
I visited also Cooper-Hewitt museum to see the National Design Triennale, and of course, The Bleached Reef in it.
How about the Christmas lights? Well, did catch some just before the bus back to Ithaca.

Saturday, December 4, 2010


First - this is a reason for not posting:
It is not all new - this is the same large pink hyperbolic plane made of 88 skeins of yarn seen in my book with a cat. Now it is 20 skeins larger (I found some leftover stock of discontinued yarn on eBay). It actually is just two more rows added but with more defined outer edge and some support and now it measures 30 x 30 x 22 in and weighs about 6 kg.

Hyperbolic Crochet Coral Reef is featured in today's National Geographic News blog - look for a video and nice pictures from the exhibit in Museum of Natural History in Washington, DC.

Monday, November 29, 2010

Geometry continues its presence in high fashion

In the autumn of 2010, ISSEY MIYAKE’s Reality Lab. is presenting “132 5. ISSEY MIYAKE”.  Reality Lab. is a research and development team lead by Issey Miyake and two staff members, Manabu Kikuchi (textile engineer) and Sachiko Yamamoto (pattern engineer) and comprised of a group of designers, some of whom are young and relatively new to the Miyake Design Studio. The Reality Lab’.s team first met computer scientist Jun Mitani (Associate Professor at the Graduate School of System and Information Engineering, University of Tsukuba) who is specialized in form modeling in computer graphics and were introduced to his unique geometric shapes in 2008. Inspired by CG application* developed by Dr. Mitani that creates three-dimensional paper model with smoothly curved surface out of a single flat sheet of  paper, the team embarked upon a new adventure in research.

The name, 132 5. was born from the above-mentioned process. Each of the numerals has a special significance. The numeral “1” refers to a single piece of cloth, while “3” refers to its three-dimensional shape. The following “2” comes from the fact that a 3D piece of material is folded into a two-dimensional shape, and the “5” separated by a single space refers to the time between when the folded forms are made and people actually put them on, giving birth to clothing. The numeral “5” also signifies our hope that this idea will have many other permutations.

More about it here
and  a nice interview

Friday, October 29, 2010

Where I grew up

I arrived in Riga from Washington to find the snow which melted in couple hours letting still to enjoy colors of autumn leaves. So far it has mostly been raining (or wet snow) with some wonderful exceptions of bright sunshine, allowing me to take some pictures of my native city.

 Riga does not have a central plaza. In 1990 part of the street near The Freedom Monument was closed to traffic and that made a central plaza for public gatherings.
The Freedom Monument is dedicated to "Fatherland and Freedom", erected 1935 (author K. Zale) it is 42 m high and has a nickname Milda for a woman holding three stars that represent three parts of Latvia. During Soviet times this monument was considered for demolition but the prominent Soviet sculptor Vera Mukhina, who was born in Riga and was a student of K. Zale, is credited for saving it. 

These houses in Old Riga were built against the medieval city wall.
This is one of the favourite spots for postcard pictures and paintings of Old Riga
Part of old city wall which at some point was nicely restored but now is "getting old" again

I love to walk in Old Riga to find houses nicely restored.
It is clear that tourist season is over, also some of my favourite places on this street has disappeared due to current economic crisis.

This is the house where my family lived until 1961.There has always been a store on the first floor. This was the first store in my life where I did shopping - my parents sent me down to buy a bottle milk which I proudly bought and was carrying back but dropped on a door step and the glass bottle broke. I guess this unfortunate first experience with shopping left lasting impact on me - I still do not like shopping. There is an earlier story about me and this grocery store. The most expensive sweets there were truffles wrapped in golden paper like a little parcels.I never was a big candy lover, but that one time I decided that I must have a truffle. I had seen adults at neighbour's party eating them with after dinner coffee. I was about 2 or 3 years old at that time. Nobody would allow me to taste coffee (anyway, I knew from some left over drops in cups and glasses that it was bitter and the liqueur with it was just awful). But truffles were something I had not tried and one time I decided not to leave the store until I got one. When my mother had paid for her groceries and continued to ignore my requests for a truffle and instead pulling me by the hand out of the store, I decided to stay there and screamed as loud as I could, "Iwant those truffles!". At least it was what I thought I insisted. I did not know how to pronounce that fancy French name correctly, and there is a Latvian word in folklore not suitable for use in literary language or by a child. My mother blushed and tried to get me out of the store - that of course made me more determined then ever. The ladies in the store were laughing until they cried, and they gave me a truffle. Was it so special as I expected? No, it had a lot of pure cocoa powder around it, and it was a little bitter too. There came a lesson that if you can not get something, maybe it is even not worth longing for it.  By the way, I like only bitter chocolate now.

This is the courtyard of the house we lived. Windows of our room were 2nd and 3rd from left on third floor - the first one which is not in line with others is a window on stairwell. Next two narrow ones are from so called "maid's room", that was used as a pantry for everybody in the appartment. Next one is kitchen window with a little opening on right side that was for "a cold cabinet" - there were no refrigerators in the appartment. We lived in this appartment together with other people. There was an elderly couple who once owned the whole building but now had only two rooms left for them.  It is a mystery to me how they managed to escape "a free trip to Siberia" in 1940 when mass deportations from Baltic States took place. In one of the rooms there was a single woman, director of bread factory. She used to bring occasional pastries for me. Two other rooms were for Professor's family. Prof. Skuja (1886-1983) was a very special person to me. He was my first teacher - taught me to read at the age of 4, taught me that the most valuable thing one can possess is knowledge. He said: "Everything else can be taken away from you, but what is in your head will always be with you and will help you to survive." He knew what he was talking about - he was a doctor and professor but for political reasons had a knowledge of cells in KGB, after 1950 was banned from teaching and forced to retire. He was working on Latin-Latvian-Russian dictionary of medical terms but it was published as "the lifetime work" of somebody else (K. Rudzītis. Terminologia medica in duobus voluminibus („Latīņu-krievu-latviešu medicīnas terminu vārdnīca divos sējumos”). - R. Liesma, 1973. - vol 1 -1039 pages, 1977. -  vol.2 - 866 pages. Those little index cards for the dictionary are very vivid in my memory - I was not allowed even to blow on them. I saw how much time he spent on this work. I do not know the details of the agreement to do the work that will be published by somebody else, but this was my first experience when intellectual property laws were violated, and the feeling of unjustice has stayed with me ever since making me very sensitive to these issues. I could not know at that time that my own work will be published as somebody else's research.
Professor was often my babysitter. We had an agreement that if I let him finish what he had planned for the day, I could sit in his lap and we would go through books together. He taught me anatomy by the age of six and lots of interesting things. He taught me to play chess but I never became too fond of it, I liked checkers much better. Because of him I always wanted to be the best student..We already had moved out of this place when I started to go to school but at the end of each school semester I would come to visit him to show my report card.        

All other rooms inn the appartment had windows on a street side with sun coming in, our room was originally a hallway for the appartment, so this was scene I remember looking out of the window being left home alone when I was sick and my parents had to go to work. There were no cars at that time and walls were grey and dirty because of smoke - there was no central heat, we had wood stoves, and my father was carrying wood up to our appartment from a storage place which was in the other courtyard through the gate in corner.

Sometimes I would be let to go out on my own in the courtyard and then I would violate the rule not to go to the street because there was another door leading to the grey building next to  ours, and I would come out on street through it, walk around the corner and come back to the courtyard. I was scared to be alone on a street but I pushed myself to do it in order to build my selfconfidence that I can do it.
This fenced parking lot used to be a little neighbourhood park with a sandbox and benches around it. This was very close to our place so I would be there often with some of the adults who would chat or read newspapers while I was playing with other children.
To prolong my time outside I was walking back asking questions about the buildings on our way like on this one next to the little park. I was curious about the people living there - who are they, how their appartments look like. I visited tis house couple times when I was in middle school - one of my classmates lived there.
This was the way back home - downhill one block.
I always was fascinated with this corner house
and its continuation on a little side street.
Across from it in the basement/ground floor of this red building was my first "restaurant" - it was a pancake place which was the first place I remember where waitress would come at the table and ask what kind of pancakes would I like. And then we had to wait some time until pancakes would arrive piping hot and crisp with jam and sour cream.
Those two modern buildings are bult on place of two story wood buildings across the street from ours.

This is the next street corner.
Across from the  building above is this three story building which was the newly built furniture store where my mother worked. I liked to go there because they had whole rooms on display and they were so different from the one we lived in. But mostly I liked to sit on the windowseels while waiting for my mother and watch the street. That was so much more fun than looking out the window of our room.
That two story building - I am amazed it still exists - was my day care center. It was just a block away from our appartment, therefore convinient, but it was for Russian speaking children. So I learned Russian very early. Unfortunately my language learning was not very consistent because I was sick a lot.
This is me in 1957 and the day care place is behind me. The next picture was taken in March 1957 and is still my most favorite of me:-) 
Turning on the same corner to the other direction I was taken for a longer walk - usually towards the church you can see at the end of the street.
This was a modern building I guess in 30-ies and still counted as modern and fancy in 50-ies. Pancake place I mentioned before is at the other end of this little street.

I was very happy to see that bending houses around the church are nicely restored.
On the way back from a walk around the church if I was lucky we would stop in shop that was in the building you see in the middle. There were candies plain and fancy, cookies, halva several different kind, pastries, cakes... I would get something very simple but I liked to see that all as a symbol of the life in different world - of the world for people who could eat whatever they desire, who were wearing fancy outfits and would not notice me.
Riga is famous for its Jugendstyle (Art Nouveau) buildings. This one is particularly important as an example of national romanticism at the beginning of 20th century (architect Eizens Laube).
Couple more pictures from the same area for my friends who wanted to see the architecture in Riga.