Understanding Squares on a Dotty Grid

The video explores drawing squares on dotty paper, focusing on square numbers and slanty squares. It discusses calculating areas, introduces a shortcut for area calculation, and proves Pythagoras' theorem using slanty squares. The video delves into number theory, examining which numbers can be expressed as the sum of two squares, and concludes with resources for further learning.

What is the area of a 4 by 4 square on a dotty grid?

• 20 units

• 16 units

• 12 units

• 8 units

What is the area of a slanty square with sides 4 down and 2 across?

• 12 units

• 20 units

• 24 units

• 16 units

Which of the following areas cannot be drawn as a square on the grid?

• 20

• 5

• 3

• 10

What is the notation used for a slanty square with sides 2 down and 1 across?

• (2,1)

• (1,2)

• (2,4)

• (4,0)

What is the formula for the area of a slanty square using (a,b) notation?

• a + b

• 2ab

• a^2 + b^2

• a^2 - b^2

What famous theorem is proved using the slanty square method?

• Fermat's Last Theorem

• Euler's Theorem

• Gauss' Theorem

• Pythagoras' Theorem

Which number cannot be expressed as the sum of two squares?

• 6

• 10

• 5

• 9

What is the condition for a number to not be expressible as the sum of two squares?

• It has a prime factor of the form 4k+3 to an odd power

• It is a perfect square

• It is a prime of the form 4k+1

• It is even

Which of the following numbers can be expressed as the sum of two squares?

• 11

• 12

• 15

• 14

What is the significance of the number 27 in the context of this video?

• It is a perfect square

• It can be expressed as the sum of two squares

• It cannot be expressed as the sum of two squares

• It is a prime number