The phrase "the answer to the ultimate question about life, the Universe, and everything" has been popularized by Douglas Adams in his book The Hitchhiker’s Guide to the Galaxy. In this tale, a supercomputer spends an astonishing 7.5 million years calculating an answer, only to reveal that it is 42. However, the actual ultimate question remains unknown.

Despite this mystery, there are numerous significant inquiries in both mathematics and physics that yield 42 as their answer. While it’s uncertain if any of these could be deemed the ultimate question, here are five captivating queries where 42 emerges as the solution.

1.) What is the angle at which a rainbow is formed relative to the Sun? Rainbows can be created through various means: from raindrops to mist. They all share common traits: they stem from light reflecting off water droplets and appear opposite the light source. The peak intensity of a primary rainbow is always seen in a 42° arc from the light source's direction. This phenomenon is a result of the bending of light as it transitions between air and water, leading to consistent angles across different situations.

As light enters a water droplet, it refracts and reflects, ultimately emerging at angles that vary slightly but peak at 42°. This 42° phenomenon holds true for any planet with clear atmospheres and pure water droplets, although variations may occur depending on the atmosphere's properties or the droplet composition.

2.) How many distinct ways can the number 10 be partitioned? In mathematics, partitioning refers to the act of expressing a number as the sum of positive integers. For the number 10, there are precisely 42 unique partitions. This intriguing relationship between 10 and 42 extends further into binary notation, where the representations of these numbers reveal fascinating connections in both mathematics and physics.

3.) What is the largest integer for which there exists a solution to the equation involving reciprocals? In a mathematical challenge, can you find four distinct positive integers such that their reciprocals sum to 1? While there are many solutions if repetition is allowed, the largest unique integer that satisfies this condition is 42. This intriguing connection is enhanced by the fact that the prime factors of 42—2, 3, and 7—are integral to the solution.

4.) How many times will the Sun orbit the Milky Way before transforming into a red giant? As the Sun ages, it will undergo significant changes, eventually becoming a red giant. During its lifecycle, it orbits the center of the Milky Way roughly every 250 million years, or a galactic year. Estimates suggest that the Sun will complete about 42 galactic orbits before entering its red giant phase, leading to the potential destruction of Earth.

5.) How rapidly is the Universe currently expanding? In our Universe, 13.8 billion years have passed since the Big Bang, during which the cosmos has been expanding. The current expansion rate, expressed in kilometers per second per megaparsec, varies based on the methods of measurement. Interestingly, converting one of the derived values to miles per second per megaparsec yields 42, aligning with the cosmic significance of this number.

In summary, '42' is not just a whimsical answer from science fiction; it resonates throughout mathematics and physics, presenting itself as the solution to several fundamental questions. Whether in the context of rainbows, number theory, or cosmic expansion, its significance invites deeper exploration into the mysteries of life, the Universe, and everything.

Starts With A Bang is authored by Ethan Siegel, Ph.D., known for works such as Beyond The Galaxy and Treknology: The Science of Star Trek from Tricorders to Warp Drive.