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Can a single picture prove that a formula holds true for every positive number in the universe?

What Makes a Diagram a Proof?

In a rigorous mathematical argument, a diagram is not merely decorative artwork. A diagrammatic proof uses geometric structures and spatial arrangements to establish an undeniable logical relationship between algebraic terms.
In 12th-century India, the mathematician Bhāskara II famously wrote a complete proof for the Pythagorean theorem by drawing four identical right triangles inside a square with the single instruction: Behold!
The area of the entire large square is (a+b)2(a+b)^2, which can also be calculated by adding the four right triangles to the central square: 4(12ab)+c24\left(\frac{1}{2}ab\right) + c^2.
Expanding both sides gives a2+2ab+b2=2ab+c2a^2 + 2ab + b^2 = 2ab + c^2. Subtracting 2ab2ab from both sides deductively yields a2+b2=c2a^2 + b^2 = c^2.
Can we use this same visual dissection strategy to prove purely algebraic identities?

Dissection Proofs for Algebraic Identities

A dissection proof is a visual argument where a geometric region is partitioned into smaller pieces and rearranged to form a new figure with identical area.
Let's prove the difference of two squares identity: a2βˆ’b2=(aβˆ’b)(a+b)a^2 - b^2 = (a-b)(a+b) for any real numbers where a>b>0a > b > 0.
Removing a small square of area b2b^2 from a large square of area a2a^2 leaves an L-shaped region of area a2βˆ’b2a^2 - b^2.