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.

The following diagram is a “proof without words” (also known as a ‘visual proof’) for the trigonometric identity.

Visual Proof of the two variable AM-GM inequality

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

Here are the remaining 3 proofs of algebraic identities

(a + b)(a - b) = (a2 - b2)

(a + b)2 + (a - b)2 = 2(a2 + b2)

(a + b)2 - (a - b)2 = 4ab by using algebra tiles. 

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

You may download the attached ppt & pdf.

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

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

A downloadable ppt is attached below.

A “proof without words” sounds like a contradiction in terms! How can you prove something if you are not permitted the use of any words? In spite of the seeming absurdity of the idea, the notion of a proof without words — generally shortened to PWW — has acquired great popularity in mathematics in recent decades, and every now and then we come across new, elegant PWWs for old, familiar propositions. In this short article the seemingly contradictory nature of a PWW is discussed, and some examples of PWWs are presented.
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