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.
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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.
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| 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.
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| 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.
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.
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| pic courtesy mathworld.wolfram.com |
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| pic courtesy google images |
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.
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| fractals from basic shapes pic courtesy mathworld.wolfram.com |
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| pic courtesy google images |
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.
