Math Adventures at CROCUS

Here is my second post at CROCUS 2012.

Math can be fun. Puzzles, games and stories are some ways in which it can be made. Stories, especially work very well with children. And more so if they are stories of a mathematical cat!

A mathematical cat? What's that? Penrose is a mathematically gifted cat, who belongs to Theoni Pappas, the author of the stories.

The Adventures of Penrose
the mathematical cat        

The Further Adventures of Penrose
the mathematical cat

Fractals, Googols and other
mathematical tales
                         
Written by Theoni Pappas
Published by World Wide Publishing/Tetra
Ages: 8+

At the beginning of 'The Adventures...', she tells us the story of how she realised that the cat was interested in math. So she wrote down all of Penrose's stories for children- these stories tackle one concept at a time, and can be read as stand-alone stories, too.

The stories point out the association of math with the things we encounter in the real world: in nature and in man-made things.  Pappas is that rare mathematician, who breaks down the overwhelmingly complex into easily digestible bites, makes them palatable to all- children and adults alike. The books take into consideration the youngest possible reader, and the harried parent, who would much appreciate these handy stories to delve into the breathtakingly beautiful, yet sometimes alarming world of math.

pic courtesy domusweb.it

One day, Penrose finds his mistress playing with soap bubbles. He runs to play with them, and is amazed with the perfect sphere shapes, that magically change shapes as they coalesce. He discovers, (as did my daughter A, while playing with soap one day instead of washing her hands quickly and coming for dinner) that soap bubbles are always perfect spheres when discrete, as the sphere is the most stable form occurring in nature with the maximum volume for the smallest surface area - No matter what the shape of the bubble blower? Or that when they coalesce to form a cluster, they tessallate to form regular shapes once they stabilise? That if you draw a plane through this cluster, they will look like a cut-section of a honeycomb?

What is tessallation? Figures that fit together perfectly without any space in between. They could be the same figure or different figures. Nature creates many beautiful designs using this concept. Designs that are often copied by man in the arts.Quilts, tile designs, even the hexagons on a football are examples of tessallation.

pic courtesy scienceray.com

One day, Penrose comes across a snail in its shell. He is mesmerised by the shell- it is such a beautiful pattern. In conversation with the snail, Penrose discovers the secret of the golden rectangle- a very common concept that occurs in nature, creating breathtakingly beautiful designs. The ratio of length to breadth always tends to 1.618.

Start with a 1 by 1 square. Then, add another square of the same size. Subsequently, add squares whose sides are equal to the longest side of the existing rectangle. This can go on infinitely in both directions- increasing as well as decreasing. The rectangle that is formed every time is the golden rectangle. The numbers also form an interesting pattern-

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

These can be written as each consecutive number being the sum of the two numbers preceding it.

1, 0+1, 1+1, 1+2, 2+3, 3+5, 5+8, 8+13, 13+21, 21+34,...

This sequence is also called the Fibonacci sequence. How does this tie up with a snails shell? If you draw a curve inside each square in the figure, and join all the curves, they form what is called the golden spiral, that can extend infinitely inwards as well as outwards.

pic courtesy mathworld.wolfram.com
  

pic courtesy google images

More examples occurring in nature? Whorls of a flower, arrangement of seeds in spirals in flowers like the sunflower, branching of a tree, ...you may check this out at howstuffworks.

Art copying nature? Check this out. A very modern use of the golden rectangle- the credit card..

More of what occurs in nature? Fractals. What are those, and where do they come in daily life? Penrose was amazed when he found out how ubiquitous they were, as we are, too when we dig a little deeper. The definition says- duplication of a form inwards or outwards. So his, by definition, will incorporate and go beyond the golden spiral or Fibonacci numbers.

fractals from basic shapes
pic courtesy mathworld.wolfram.com

Ever seen a snowflake grow? The original nidus decides what design it will form- so that no two snowflakes are the same. Or just any crystals grow? Think clouds, galaxies, fern fronds, diffusion and movements of fluids, music, population explosion...the list could go on.

pic courtesy google images

Does Penrose encounter only these slightly unusual math concepts? Not at all. He comes across the very basics that our children might encounter on a daily basis too- numbers, the magic of prime numbers, number line, conventions in math, number processes, pi, irrational and rational numbers, graphs, estimates, probability, two-and-three-dimentional figures, x - the unknown in algebra, the concept of zero...and much more.

Each short story, illustrated with pictures of Penrose and simple figures for the math concept, ends with a puzzle which we are left to solve along with the cat. Pappas, of course, gives a very helpful solutions and explanations section at the end of each book that completely de-mystifies the concept at hand.    

On occasion of the International Day for the Girl Child - The Evolution of Calpurnia Tate

The world has very few women scientists, although the first and only person ever to have received the Nobel  in two different branches of science, was Marie Curie, a woman. It is an unfortunate, though proven fact that there is a decided gender bias against women in the STEM fields of education and careers.

The damage starts early. Gender studies have proved that girls are considered not good enough in math and the sciences. This bias is often carried by female math and science teachers too, unfortunately sending the subliminal message to girls in their formative years, that they cannot do well at these subjects. It becomes a chicken-and-egg situation, leading to fewer girls taking up the STEM faculties at higher levels.

Today, on the International Day of the Girl Child, here is a book that looks at a historically significant period in science- a time when the world was poised on the brink of the new, technologically rich world- with a scientifically inclined 12-year old girl as the protagonist.

pic courtesy flipkart

The Evolution of Calpurnia Tate
Written by Jacqueline Kelly
Published by Square Fish, an imprint of MacMillan
Ages 8+

It is the summer of 1899. The only girl in a family of seven siblings, Calpurnia Virginia Tate (Callie Vee, as she is called) is expected to apply herself to the task of crafting a lady out of herself. Her mother's sole dream for her only daughter is that she be tutored in the arts befitting a lady- music, drawing, dance, embroidery, cooking- so that she would make a stunning debut on their social circuit and land the most eligible bachelor before she becomes 'an old maid of twenty.'

There is a slight hitch in the plan, though. Callie Vee has not the slightest inclination towards these achievements, and is encouraged by her naturalist grandfather in her scientific forages. The only grandchild that matches his interests.

"The laws governing inheritance are quite unknown; no one can say why...the child often reverts in certain characters to its grandfather..." 

The Origin of Species plays a large part in the book. Each chapter begins with a fitting epigraph quoted from Darwin's book. Callie Vee knows of the book, but it is a banned book, and she has no chance absolutely of laying her hands on it. Until her formidable, cantankerous grandfather discovers her interest in, and keen observations of the strange case of large yellow and small green grasshoppers- that she dutifully notes down in her 'observations notebook.'

"He stared at me for a moment with an odd expression on his face- perhaps surprise, perhaps consternation- as if I were a species he'd never seen before...He extracted a book covered in rich green morocco leather handsomely tipped with gold. Ceremoniously, he bowed and offered it to me. I looked at it. The Origin of Species. Here, in my own house. I received it in both my hands. He smiled. Thus began my relationship with Granddaddy."

It was a beginning of a wondrous journey of scientific discovery. The beginning of a dream that showed her the path out of a possible life of drudgery like countless other girls like her. A life that she could not visualise herself enjoying, no matter what her parents and society at large expected of her. The beginning of an old man's dream of at least one among his heirs carrying the light of his discoveries into the future.

This refreshing debut book by the author, Jacqueline Kelly, was devoured and thoroughly enjoyed by the resident 11 year old, who has to often be-labour under expectations from her peers, and sometimes from elders, to conform to stereotyping by her gender. Be that in clothes, interests, behaviour, dreams or priviledge. She applauded with Granddaddy, when Callie Vee ensured that she is paid for her work during the harvest season, not just the boys, and when she stressed on her right to make a choice about her life.

A has loved the book, and has been recommending it to all her friends. It makes a lot of sense to her since she has been doing evolution and taxonomy at school this year. She also identifies with Callie Vee on a more basic level - she has often been the butt of jokes among her peers for being different - more science and literature minded than the average 11 year old girl, not so interested in what is considered 'cool behaviour.'

Here is some talk with the author, Jacqueline Kelly. I did a google-search for contact information, and Ms Kelly responded promptly and graciously to my questions, despite a busy schedule on account of the forthcoming release of a new book.

pic courtesy bookpeople.com

Me: You have a medical background. How and why did this book happen?
Jacqueline Kelly: I prefer not to talk about my medical past, but I can say that I have wanted to be a writer my whole life.

Me: Did the idea of using quotes from 'The Origin of Species' occur to you after the book was drafted, or was it one of the things that inspired the book?
Jacqueline Kelly: The quotes came after I had finished the book. I then read Darwin's entire work looking for appropriate quotes that would best fit each chapter. Some of them fit amazingly well, and some of them didn't. By the way, Darwin wrote the book for a general audience, and not for scientists, so it is an amazingly accessible read. I recommend it.

Me: Why was the story placed in Texas?
Jacqueline Kelly: The story was placed in Texas because it was inspired by a 150-year-old farmhouse I bought years ago in Fentress. The house in the book was my house. Sadly, it was struck by lightning and burned to the ground three years ago. I still miss it badly. I wrote large parts of the book sitting on the front porch as Callie did, waiting for something to hop or scurry or fly by and give me something to write about.

Me: I was deeply moved as I finished the book and put it down. Somehow I was not convinced that Callie's parents had taken her scientific temperament very seriously, and might renege on any support when Granddaddy is no longer around. Have you left Callie Vee's fate hanging like that on purpose? Is there a sequel in the offing that might put girls' minds at rest regarding that concern? (This is something that has been bothering my 11 year old daughter!)
Jacqueline Kelly: I didn't mean to be quite as vague as I apparently was about Callie's future. But fear not, there is a sequel in the works that will make everything clear! I have only recently started it, so I don't yet know when it will be published.

Me: That is certainly we would be looking out for. Speaking of sequels, could you tell us a little bit about your next book, Return to the Willows, that we are waiting eagerly for? I believe it is being released on October 23rd 2012.
Jacqueline Kelly: Return to the Willows was inspired by my life-long love of Kenneth Grahame's The Wind in the Willows, a book I have loved since reading it in bed with the flu' at age eight.
I have loved his book for so long, and his characters have lived in my head for so long, that I thought I would write a sequel as a tribute to him, my way of saying thank-you for creating Rat and Mole and Toad and Badger. (Well, maybe not Toad.)

That makes it three new books that we have on our reading wish-list. The Origin of Species, the full text of which is available here online, Return to the Willows and the forthcoming sequel that will tell us more about what happened to Callie Vee.

Cross-posted at Saffrontree.

Book Review: The Diddakoi

Pic courtesy flipkart

The Diddakoi
Written by Rumer Godden
Cover illustration by Christian Birmingham
Published by Macmillan Children's Books
Ages 8-12 yrs

I've learned a lot about adoption and attachment from Sangi's posts, and there are many nuances to the whole issue that I would not have otherwise being sensitised to. Thanks, Sangi!

So it was hardly a surprising thing that I unwittingly picked up quite a few books that deal with that on different levels. A few are books for children, and here is one of them. A complex, well written book that draws one into it.

A spirited, half-gypsy, half-Irish girl. An orphan. A misfit at school, targeted with some serious bullying for being different. The fact that 'normal, nice' children can, in fact, be very cruel, especially if they reflect the prejudices of their elders. The fact that prejudices can lead to fear of a situation/ person, and that it can become difficult to overcome.

An ordinary 'Miss Marple-ish' British village in the 1960s where everyone knows everybody. A legal care system where the best interests of a child is decided by the letter of the law, and not by what the child would want, or what might be truly best for the child. Some well meaning going wrong. Others unaware of their own ability to give and heal.

'It's good of you, Edna,' Miss Brooke repeated, but it might spoil your holiday. Besides, I don't think Kizzy would go.'
'Heavens, you don't have to ask her.'
'I think I do. People should always be asked before being disposed of.'
'A child?'
'Children are people, Edna,' said Miss Brooke as she had said it to Mrs Blount.
'Well, please yourself,' said Mrs Cuthbert. 'But I tell you, Olivia, that child's too much on your mind.'
'Isn't that what she came for?'
'For what?'
'To be on my mind.'

An ordinary children's story of extraordinary meanings, the book takes one on a roller coaster ride of emotions, which nevertheless unfold very gently at times and with the dramatic quality of a tempest at others. That brings home to us the fact that the human spirit is more resilient than one can imagine, and that we all that the light with the dark in all of us. That patience, love and care can wrought wonders.

Rumer Godden herself was very difficult, and different in many ways as a child, and in this book she writes from  her own memories of it. Kizzy Lovell, our central girl character, the 'diddakoi'=half-gypsy, who is picked on by the other children for being different, and who is in the centre of a controversy over who should foster her, and how, is a throwback to that childhood. In some ways Kizzy reminded me of some of Enid Blyton's similar characters- Carlotta from the St. Clare series, and Lotta from her Circus books.

This is her best known book for children, which got the Whitbread Award in 1972. It has been called "the sort of book children had to fight for to get it from adults". The book should be read in the context of the period in which it is set, as there is much that can be considered 'politically incorrect'. And inspite of the many negatives, the many questions it raises, especially in young minds, it is an incredibly uplifting book, with a happy ending. A loved it!

Crossposted at Saffrontree.   

Review: Oranges in no man's land

Pic courtesy books.google.com

Oranges in no man's land
Written by Elizabeth Laird
Illustrated by Gary Blythe
Published by  Macmillan Children's Books
Ages 8-12 years.

10 yr old Ayesha lives with her mother, grandmother and two brothers in Civil war torn Beirut. Her mother gets killed by a bomb that also destroys their home, and they become refugees living in a shelter. Here Ayesha makes a friend, the deaf-mute girl her age, Samar. Life goes on, her grandmother their only parent.

Until one day, her grandmother becomes seriously ill. She has been ill for a long time now, and had medicines that she took for it, given to her by Dr Leila, for whom she had worked for many years. But now her medicines are over, and Dr Leila lives beyond the Green line, on the other side of the divide, beyond the 'no man's land' that lies between their portion of the city and hers.

So what is a mere 10 yr old to do? Does she manage to go to the good doctor and get medicines for her grandmother? How does she get past the armed solders gaurding the entrances to both sides and come back unscathed?

This is a touching story written by Elizabeth Baird, who lived in Beirut during the Lebanese Civil War which stretched from 1975-1990. It is based on some real life events and experiences, as she writes in her preface to the book.

The story brings home to us the fact that there are both good and bad people on both sides of any divide, and the common man usually wishes for peace, not war, so that normal life can go on. And that a war usually serves the few in power, with vested interests.

The sketch of Ayesha, running swiftly for all it's worth, looking furtively at something in the distance that she probably needs to be wary of, is a repeated motif throughout the book, at the title of each chapter. Done by Gary Blythe, (illustrator of other well known books like The Whale's Song, Rumer Godden's Miss Happiness and Miss Flower and Michael Morpurgo's I believe in Unicorns) they lend a sense of urgency to the books.

Crossposted at Saffrontree.

I am entering this book at the Reading The World Challenge 2011 over at Papertigers, for A. Under Fiction, Lebanon.

And for some hypnotic magic: Molly Moon

This is a fun book that was recently recommended to us by Choxbox's FB, and we were thrilled to realise that we had picked it up at the recent Strand book sale. There's a picture at the bottom of this post.

Pic courtesy flipkart

MOLLY MOON'S Incredible Book of Hypnotism
Written by Georgia Byng
Published by Macmillan Children's Books
Ages 8-12 yrs

Hardwick House, the decrepit orphanage where Molly, our 10 yr old heroine lives, is a Dickensonian place, owned and run by the mean and spiteful Miss Adderstone and Edna, the equally mean and spiteful cook whose cooking is horrible. There are other bullies, too, the older children who make life extremely difficult for the younger ones.

Molly, too, is no angel, and often gets into trouble because of her lazy and stubborn ways, although she is good to those younger than her. Her only friend is Rocky, a boy at the orphanage, who has a calming personality, the one person who can motivate Molly and keep her from getting into trouble.

Then everything goes further wrong one day when Rocky is taken away by an American couple who want to adopt him, and he goes away without saying goodbye. Molly's one support in her short life is gone.

Just when things begin to look very bad indeed, Molly finds a book on hypnotism in the library. She 'borrows' it, and learns the art by following the very clear instructions in the book. What follows is an out-and-out fantasy that any 10 yr-old might have and thoroughly enjoy.

We have Molly winning a talent show, and using her winnings to travel all the way to New York, with Petula, the pug belonging to Miss Adderstone who is now hypnotised into loving Molly. In New York, along the way to finding Rocky, she becomes a huge star, which draws her into the clutches of Simon Nockman, a crook out to use her talents for big-time robbery.

How does it all end? Since the fantastical seems to escalate? Well, you have to read the book to find out. The narrative is just as hypnotic, and both A and I read it at one go, unable to put the book down. Things do resolve, and a lot of good lessons are learnt. All around. Molly and the reader included. While having a good laugh as we read.

The book reminded me of Mathilda by Roald Dahl, another book about an extraordinary little girl belittled by her own parents and bullied by the monstrous school headmistress, Miss Agatha Trunchbull, and who uses her magical powers to teach her a lesson.

A loved this one, and we will be looking out for the sequels, Molly Moon stops the world, Molly Moon's hypnotic time-travel adventure, Molly Moon Micky Minus and the time machine and Molly Moon and the morphing mystery. They all sound delicious.

Crossposted at Saffrontree.