After a few general questions that I asked them, they (the children) said that they had some questions to ask me. And then one after the other, the children began to ask questions. In some sense, to me, it reflected the freedom of expression that the school seemed to be inculcating.

# Visual proof

After looking at visual justifications for properties of additon for whole numbers and fractions, this poster considers the properties of multiplication for the same number sets.

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- Read more about Geometric Proof of a Trigonometric Identity
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Visual Proof of the two variable AM-GM inequality

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Here is an elegant visual proof of the Pythagorean Theorem (check the links 1, 2, 3 ) developed by the 12th century Indian mathematician

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Here are the remaining 3 proofs of algebraic identities

**(a + b)(a - b) = (a ^{2} - b^{2})**

**(a + b) ^{2} + (a - b)^{2} = 2(a^{2} + b^{2})**

**(a + b) ^{2} - (a - b)^{2} = 4ab **by using algebra tiles.

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See the visual proof of (a - b)^{2} +2ab using coloured tiles,

You may download the attached ppt & pdf.

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See the visual proof of (a+b)^{2} - 2ab using coloured tiles,

You may download the attached ppt & pdf.

Click here for (a - b)^{2} + 2ab proof

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Swati Sircar invites you to explore the cubic identities (a - b)^{3} through 3D models.

A downloadable ppt is attached below.

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- Read more about On Proofs Without Words
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