The Flawed Pursuit: Edward J. Goodwin's Claim on Pi’s Value

Edward J. Goodwin, an American mathematician and inventor, is known for his controversial argument that the mathematical constant (pi) equals 3.2, rather than the widely accepted value of approximately 3.14159. This article delves into the details of Goodwin's claim and the reasons why it was not accepted by the mathematical community.

The Unconventional Argument

Goodwin's claim that (pi) equals 3.2 was based on a series of flawed assumptions and incorrect geometric interpretations. His argument was primarily presented in a document he published in 1897, unaware of the rigorous methods that had been developed over centuries to determine the value of (pi).

Misinterpretation of Circle Geometry

Goodwin's method involved inscribing and circumscribing polygons around a circle to approximate its circumference. He believed that the perimeter of a circle could be determined using simple geometric shapes, leading him to conclude that the ratio of the circumference to the diameter was 3.2. However, this approach is fundamentally flawed and does not accurately reflect the true value of (pi).

Mathematical Errors and Misconceptions

Goodwin's calculations were deeply flawed, underpinned by incorrect assumptions. For instance, he did not account for the more accurate methods of determining (pi) that had been established through extensive mathematical development. His use of visual approximation and assumptions rather than rigorous geometric principles doomed his argument from the outset.

Legislative Action and Public Outrage

Goodwin's claim gained some notoriety when he attempted to introduce a bill in the Indiana legislature in 1897 that would officially adopt his value of (pi) as 3.2 for all mathematical calculations in the state. Although the bill was presented seriously, it was ultimately rejected. This incident, however, brought attention to the importance of rigorous mathematical proof and critical evaluation of such claims.

The Circle's Deception

Goodwin's method of squaring the circle was based on visual approximations rather than accurate geometric principles. His method was not only incorrect but also misleading. For instance, in his proposed solution, he claimed that a circle with a diameter of 10 and a circumference of 48 could be used to prove that (pi) equals 3.2. However, these values do not correspond to a true circle; rather, the shape is significantly distorted, making it clear that it is not a circle at all.

Visual Flaws and Mathematical Errors

Deeply erroneous in his approach, Goodwin's method was based on flawed assumptions, incorrect geometric interpretations, and mathematical errors. He claimed that (pi) could be derived from a visual approximation of a squashed circle, with a circumference of 48 and a diameter of 10, yielding a ratio of 3.2. However, this is not a true circle and thus, the claim is invalid.

Wider Implications

The incident with Goodwin highlights the need for rigorous mathematical proofs and critical evaluation of unconventional claims. The value of (pi) is a cornerstone of mathematics, and it is essential to adhere to accurate and rigorously proven methods to ensure the integrity and reliability of mathematical knowledge.

Key Takeaways:

Goodwin's claim that (pi) equals 3.2 was based on a series of flawed mathematical and geometric assumptions.

Beyond the visual deception, his methods did not accurately reflect the true nature of a circle.

The incident serves as a reminder of the importance of rigorous proof and critical evaluation in the field of mathematics.

While Goodwin's efforts were misguided, his work does serve as a cautionary tale about the dangers of accepting unproven claims without rigorous examination.