Pythagorean Theorem and Bhaskara's Proof

The Pythagorean Theorem is one of the most celebrated mathematical theorem in the world. According Guinness Book World of Records, it boasts more than 500 proofs. Most famous of the proof is the proof provided by Euclid in Elements

Many mathematicians from antiquity to modern times had marveled at this rule and proved it in different ways. Here we will see how Bhaskara, one of the most important mathematicians of old India proved it geometrically.
The theorem says a² + b² = c² : where a and b are sides of a right triangle and c is its hypotenuse
Bhaskara gives the following diagram to prove the theorem:

Bhaskara’s description of Pythagoras Theorem

From the picture, you can see that
Area Large squire is = Area of all 4 triangles + area of smaller squire
c * c = 4 * ( 1/2 ) a * b + (b-a) * (b-a) = 2ab – ( a² + b² + 2ab)
c² = a² + b²
which is the Pythagorean theorem

Is Book a Failed product?

A good product creates and maintains two way communications between the user and the product. A successful product, software or otherwise, creates a more natural form of interaction, an interaction that can take place subconsciously, without effort, whereby the communication in both directions is done so naturally, so effortlessly, that the result is a smooth merger of person and the product, jointly performing a task.

Given that definition, see what Socrates had to say about Books, one of the most enduring and successful product ever in human history:

SOCRATES: You know, Phaedrus, that’s the strange thing about writing, which makes it truly analogous to painting. The painter’s product stands before as if they are alive, but if you question them, they maintain a most majestic silence. They seem to talk to you as if they were intelligent, but if you ask them anything about what they say, from a desire to be instructed, they go on telling you just the same thing forever. And once a thing is put into writing, whatever it may be, drifts all over the place, getting into the hands not only of those who understand it, but equally of those who have no business with it: it does not know how to address the right people, and not address the wrong.

—Plato: Collected Dialogues, 1961.

Is the product Book, a failure? We know its not. Then how does it follow the definition of a good product, described in the beginning of this note?

Credits:

The Design of Future Things by Donald A. Norman

Books.Google.com for complete quote by Socrates