How to calculate mentally the square of a number close to 50?

Have you ever wondered what it was like to be at the heart of the atomic bomb project? Imagine walking through the corridors of Los Alamos, where some of the greatest minds in physics worked tirelessly to change the course of history. In this blog post, we’ll take you on a journey through the dynamic partnership of Hans Bethe and Richard Feynman, two brilliant scientists whose collaboration was as explosive as the project they were working on. By the end, you’ll gain a deeper understanding of their unique relationship and the incredible scientific breakthroughs they achieved together.

The Heart of the Atomic Bomb Project

In the bustling environment of Los Alamos, the epicenter of the Manhattan Project, one could witness a hive of activity. Scientists were engrossed in complex calculations within the two-story green building known as "Building T" (where "T" stood for "theoretical"). This building served as the headquarters for Robert Oppenheimer, the project's scientific director, who appointed Hans Bethe, a renowned nuclear physicist from Cornell, as its head.

The narrow corridors and thin walls of Building T often echoed with the sounds of intense scientific discussions. Among these, Hans Bethe's thunderous laughter was a frequent occurrence, signaling the presence of Richard Feynman, a young and exuberant physicist known for his sharp intellect and vibrant personality.

The Unlikely Partnership: Bethe and Feynman

Hans Bethe and Richard Feynman formed an extraordinary duo. Bethe, a reserved and meticulous German professor, contrasted sharply with Feynman, an energetic and sociable genius from New York. Their interactions were a blend of rigorous analytical debates and lively exchanges, often punctuated by Feynman's animated gestures and loud exclamations like, “No, no, you're crazy!” or “Nonsense!”

Bethe, known for his calm demeanor, would methodically work through problems, explaining his reasoning with precision. Feynman, after a brief period of contemplation, would often challenge Bethe's conclusions with renewed vigor. This dynamic earned them the nicknames "The Battleship" for Bethe and "The Torpedo" for Feynman, reflecting their intense yet productive exchanges.

Mental Math Mastery: Calculating Squares Near 50

One memorable incident early in the project involved a mathematical challenge. Bethe and Feynman were working on a formula that required calculating the square of 48. Bethe quickly stated, “It's 2300,” while Feynman reached for the Marchant calculator to verify.

Bethe then shared a mental math trick with Feynman: the square of 50 is 2500, a straightforward calculation. For numbers close to 50, the square can be approximated by adjusting 2500 by a few hundred. Since 48 is 2 less than 50, the approximate square of 48 is 2500 minus 200, or 2300.

To refine this approximation, Bethe explained, one must add the square of the difference between 50 and 48, which is 4. Thus, the precise square of 48 is 2304. This simple yet effective method showcased Bethe's mathematical prowess and his ability to simplify complex calculations.

Conclusion

The collaboration between Hans Bethe and Richard Feynman at Los Alamos was a testament to the power of diverse intellectual approaches. Their unique partnership not only advanced the Manhattan Project but also left a lasting impact on the field of physics. By understanding their dynamic interactions and innovative problem-solving techniques, we gain insight into the minds that shaped one of the most significant scientific endeavors of the 20th century. At FreeAstroScience.com, we celebrate such remarkable stories, bringing you closer to the fascinating world of science.