Batch 2 - Class 10 - Magic Squares
Attendance Muskaan, Hriday, Aastha, Kushaan, Anisha, Smiti, Aryan, Avy
Class puzzles
Magic square is a n x n grid filled with numbers from 1 to n^2, non-repeating, such that every row, every column, and each of the two diagnols have the same sum.
- Draw a 3x3 Magic square
Instructor Notes: Check that each kid has understood the meaning of magic square. Let kids try and draw a 3x3 magic square by hit and trial. After that, go methodically to see all combinations of sums of 1-9 which total to 15, and how to lay those out on a magic square.
Story of Divine Tortoise: There was recurrent flooding in river Lo. Emporer Yu-Huang was standing by a river, and saw a divine turtle at his feet. He believesd that it was a symbol of good luck. Slowly, the details of the shell appeared before the emperor. Emperor Yu looked at the turtle's back and noticed a pattern of dots engraved on it. Emperor Yu thought about whether the turtle was giving a signal? He added up the numbers many different ways, and they all added up to 15. He then offered 15 sacrifices, and that took the floods away.
- Join the numbers on magic square in order, and see the pattern.
- If you see the line connceting 8-5-2, what is the symmetry.
- Calculate the difference of 5 with every other number and see what happens.
- Draw a 2x2 Magic square
Instructor Notes: Let kids arrive at the conclusion that a 4x4 magic square doesn't exist
- Illustrate a 4x4 Magic squares (note that 880 of these exist) - In 1514, Albrecht Dürer created an engraving named Melancholia that included a magic square. In the bottom row of his 4 X 4 magic square you can see that he placed the numbers "15" and "14" side by side to reveal the date of his engraving.
- Join the numbers on magic square in order, and see the pattern.
- What kind of symmetry do you see?
- Can you find a formula for sum of a n x n magic square side?
- Benjamin Franklin's 8x8 magic square with lines
- Let kids total up the rows and columns to verify this magic square.
- Sum up the numbers half-way down the column and see what happens?
- Add the numbers on four corners - see what happens?
- Consider each of the 4x4 units - what is true of them?
- Homework: Can you find more numerical relationships?
- See the symmetry in the magic square.
- Where are numbers 1-10, where are 54-64?
- Where are 1,2,63,64 - what is the sum?
- Where are 31,32,33,34 - what is the sum?
- What is the overall symmetry in the pattern?
- Vedic Square: Variation of 9x9 multiplication table, with each entry as remainder of the product of row and column label (0 is represented as 9).Highlight different numbers on a vedic square and see what happens
- Atomic structure of Titanium Dioxide - by joining all 1s or all 8s. Putting both together gives Platinum Crystal.
- Islamic Art - finds patterns out of Vedic math -
- Homework: Try your own pattern on http://people.revoledu.com/kardi/download/download.php?file=DigitalRootHomework: Find out a way of creating a magic square.
- There are nine cards on a table labeled by numbers 1 trough 9. Alice and Bob take turns choosing one card. The player that has collected a set of cards with the property that the sum of numbers on three cards out of total set is 15 wins. There’s a tie if none of the players has a set of cards with this property at the end of the game. Does any of the players have a winning strategy? A non-losing strategy?(Answer: Same as magic square and tic tac toe combined - so first player wins)
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