![]() ![]() ![]() In both math and engineering, values are often represented as between 0 and 1: "100%" is just a fancy way of saying 1. It's the only positive integer that's neither prime nor composite. It's the only number divisible by exactly one positive integer (itself, 1). One is the only number by which all other numbers divide into integers. "I suppose this is a boring answer, but I'd have to choose 1 as my favorite, both as a number and in its different roles in so many different more abstract contexts," he told Live Science. (Image credit: Shutterstock)Įd Letzter, a mathematician at Temple University in Philadelphia (and father of former Live Science staff writer Rafi Letzter), had a practical answer: The number 1 has many interesting properties, such as being the only number that is neither prime nor able to be factored into two numbers. (Because of this, it's unlikely we'll ever celebrate an "i to the power of i day.") "As Euler pointed out, i to the i power does not have a single value," Richeson said, but rather takes on "infinitely many" values depending on the angle you're solving for. At least, in the case of a 90-degree angle. It sounds confusing ( here's the full calculation, if you dare to read it), but the result equals roughly 0.207 - a very real number. When you solve the formula for a 90-degree angle (which can be expressed as pi over 2), you can simplify the equation to show that i to the power of i equals e raised to the power of negative pi over 2. "But, in fact, as Leonhard Euler wrote in a 1746 letter, it is a real number!"įinding the value of i to the i power involves rearranging Euler's identity, a formula relating the irrational number e, the imaginary number i, and the sine and cosine of a given angle. "At a glance, this looks like the most imaginary number possible - an imaginary number raised to an imaginary power," David Richeson, a professor of mathematics at Dickinson College in Pennsylvania and author of the book " Tales of Impossibility: The 2,000-Year Quest to Solve the Mathematical Problems of Antiquity" (Princeton University Press, 2019), told Live Science. ![]() For example, you can raise i to the power of i - in other words, take the square root of -1 raised to the square root of -1 power. (Image credit: Shutterstock)īelieve it or not, there are ways to make i even weirder. The number i raised to the power of i is actually a real number roughly equal to 0.207. And, "like pi, it comes up all the time in mathematics, physics and engineering," Devlin said. In other words, if the value of a function is, say, 7.5 at a certain point, then its slope, or derivative, at that point is also 7.5. " has the wonderful definition as being the one number for which the exponential function y = e^x has a slope equal to its value at every point," Keith Devlin, emeritus professor and former director of the Stanford University Mathematics Outreach Project in the Graduate School of Education, told Live Science. The base of natural logarithms is most often used in equations involving logarithms, exponential growth and complex numbers. So, while 3.14 is celebrated on March 14, natural log base - the irrational number beginning with 2.718 - is lionized on Feb. The base of natural logarithms - written as "e" for its namesake, the 18th-century Swiss mathematician Leonhard Euler - may not be as famous as pi, but it also has its own holiday. We'll summarize the results in a table.The natural log is expressed as the symbol "e." (Image credit: Shutterstock) ![]()
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