We enquired as to which non-pi integers were the favorites of various scientists. These are a few of their responses.
We at Live Science adore figures. And on March 14, also known as 3/14, we adore to honor pi, the most well-known irrational number in the world whose first 10 numbers are 3.141592653.
Pi is not only irrational, which means it cannot be expressed as a straightforward number, but it is also the relation of a circle’s circumference to its width. It is also transcendental, which means that no algebraic equation, including x+2X2+3 = 0, has it as the root or answer. Pi may be one of the most well-known numbers, but the circular constant can get tedious for those who are hired to think about numbers all day. We enquired as to which non-pi integers were the favorites of various scientists. These are a few of their responses.
According to mathematician John Baez(opens in new browser), who works at the University of California, Riverside, using tau makes every calculation more understandable and rational than using pi. Our preference for pi over 2pi is a historical coincidence,
The most significant formulae contain tau, he claimed. Tau, on the other hand, connects a circle’s circumference to its radius; many scientists contend that this connection is much more significant than that which links a circle’s circumference to its width (pi). A circle’s area equation and an equation describing kinetic and elastic energy are two examples of apparently unconnected equations that Tau renders neatly symmetrical.
On Pi Day, tau will not be overlooked though! The Massachusetts Institute of Technology will release judgments tonight at 6:28 p.m. It will be Tau Day on June 28 in a few months.
Although less well-known than pi, the base of natural logarithms also has a holiday. It is abbreviated “e” in honor of its namesake, the Swiss scientist Leonhard Euler, who lived in the 18th century. Natural log base, the illogical number that starts with 2.718, is therefore honored on February 7 while 3.14 is recognized on March 14.
Equations containing logarithms, exponential growth, and complex numbers are the ones that most frequently use the basis of natural logarithms(opens in new tab). “[It] 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(opens in new tab), emeritus professor and former director of the Stanford University Mathematics Outreach Project in the Graduate School of Education, told Live Science. In other words, if a function’s value, let’s say, is 7.5 at a certain position, then its slope, or derivative, is also 7.5 at that same place. Like pi, it also frequently appears in mathematics, physics, and engineering, according to Devlin.
What do you get if you take the “p” out of pi? The letter i, that’s correct. I is a fairly interesting number, but that’s not really how it works. Since you shouldn’t take the square root of a negative integer, the fact that it is the square root of -1 makes it an exception to the norm.
Eugenia Cheng, a mathematician at the School of the Art Institute of Chicago, wrote to Live Science in an email, “Yet, if we violate that law, we get to create the imaginary numbers, and so the complex numbers, which are both lovely and practical. (Complex numbers can be expressed as the sum of both real and imaginary parts.)
According to Cheng, the fictitious number i is particularly strange because -1 has two square roots: i and -i. But we are unable to distinguish between them. Mathematicians only need to choose one square root to represent as i and the other as -i. It’s strange and amazing, said Cheng.
Unbelievable as it may seem, there are methods to make it stranger still. For instance, you can take the square root of -1 increased to the power of the square root of -1, or raise i to the power of i.
“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(opens in new tab)” (Princeton University Press, 2019), told Live Science. However, it is a real integer, as Leonhard Euler stated in a correspondence from 1746.
Euler’s identity, a formula connecting the irrational number e, the imaginary number i, and the sine and cosine of a particular angle, must be rearranged in order to determine the value of i to the i degree. You can simplify the equation to demonstrate that i to the power of i = e raised to the power of negative pi over 2 when you answer the formula for a 90-degree angle (which can be expressed as pi over 2).
If you venture to peruse the entire computation, it may sound confusing, but the outcome equals approximately 0.207, which is a very real figure. At least when the slope is 90 degrees. Richeson stated that based on the angle you’re attempting to solve for, “i to the i power does not have a single value, as Euler pointed out,” instead taking on “infinitely many” values. It’s doubtful that we will ever observe a “i to the power of i day” because of this.
The palindromic prime number of Belphegor contains a 666 concealed between 13 zeros and a 1 on each side. The terrifying number is represented by the abbreviation 1 0(13) 666 0(13) 1, where (13) represents the amount of zeros between 1 and 666.
Despite not having “discovered” the number, author and physicist Cliff Pickover(opens in new browser) gave it a sinister moniker by choosing Belphegor (or Beelphegor), one of the seven biblical demon rulers of torment.
It seems that the number even has a diabolical sign that resembles an upside-down pi. The symbol was taken from a glyph in the enigmatic Voynich manuscript, an early-15th-century collection of drawings and writing that no one seems to comprehend, according to Pickover’s website.
W. Hugh Woodin, a scientist at Harvard, has spent many years studying limitless numbers. The fact that his favored number is an endless one, 2aleph_0, or 2 raised to the level of aleph-naught, also known as aleph-null, should come as no surprise. In mathematics, a set is any group of unique items, and aleph numbers are used to define the sizes of endless sets. (So, for example, the numbers 2, 4 and 6 can form a set of size 3.)
With regard to the rationale behind his choice, Woodin explained, “Realizing that 2aleph_0 is not aleph_0 (i.e., Cantor’s theorem(opens in new tab)) is the recognition that there are various scales of infinite. In light of this, 2aleph_0’s idea is rather unique.
There is never just one biggest cardinal number because infinite cardinal numbers are also infinite, which means that there is always something larger.
Oliver Knill, a Harvard mathematician, told Live Science that zeta(3), the Apéry’s constant, is his best number because “there is still some mystery associated with it.” Roger Apéry, a French scientist, established in 1979 that a quantity that would later be called Apéry’s constant is an irrational integer. (It begins with 1.2020569 and continues infinitely.) The constant is also represented by the notation zeta(3), where zeta(3) represents the Riemann zeta function when the integer 3 is substituted.
The Riemann hypothesis, which is one of mathematics’s largest open questions, asserts that the Riemann zeta function equals zero at a certain point and, if true, would enable mathematicians to forecast the distribution of prime numbers more accurately.
Famous 20th-century scientist David Hilbert once said(opens in new tab) of the Riemann hypothesis: “If I were to awaken after a thousand years of sleep, my first question would be, Has the Riemann hypothesis been proven?”
So what makes this constant so awesome? Apéry’s constant turns out to appear in a variety of interesting physics formulae, such as those controlling the magnetism and orientation of the electron to its angular momentum.
Mathematician Ed Letzter (opens in new browser), who is also the father of former Live Science team member Rafi Letzter, had a useful response: He told Live Science, “I guess this is a dull response, but I’d have to say that 1 is my best, both as a number and in its various functions in so many different more abstract situations.
All other numbers split into integers by one, but not by any other number. It is the only number that can be divided by a single positive integer. (itself, 1). The only positive number that is neither compound nor prime is this one.
Values are frequently expressed as being between 0 and 1 in both math and engineering: “100%” is just a fancy way of stating 1. It is full and whole. Of course, 1 is used to denote fundamental quantities in all of the disciplines. The charge of one proton is referred to as its mass. A 1 in binary reasoning denotes an affirmative. It is also the length of a straight line and the atomic number of the heaviest substance.
According to the late scientist Richard Feynman, Euler’s identity, which is an equation, is a true mathematical gem. It’s been likened to a Shakespearean poem as well.
Pi, natural log e, and the imaginary unit i are three mathematical variables that are connected by Euler’s equation. It links these three variables to the basic math identities of the additive identity 0 and the multiplicative identity: ei*Pi + 1 = 0.
THE SQUARE ROOT OF 2
The square root of 2, arguably the most lethal number ever created, is said to have been the cause of the first recorded mathematical homicide. According to the University of Cambridge, it was discovered in the fifth century B.C. by the Greek scholar Hippasus of Metapontum.(opens in new tab). Hippasus is said to have discovered the truth that an isosceles right triangle with two base sides that are each one unit long will have a hypotenuse that is 2, which is an odd number, while working on a different issue.
Hippasus’ peers, who belonged to the Pythagorean quasi-religious order, allegedly threw him into the water after learning of his important finding. This is because according to the Pythagoreans, everything in the world is made up of whole numbers and their ratios. Insane numbers like 2 (and pi), which can never end after the decimal place and cannot be stated as a fraction of whole numbers, were viewed as abominations.
Nowadays, we refer to 2 as Pythagoras’ constant and are a little less tense about it. It begins with 1.4142135623… (and, of course, never ends.) There are many applications for Pythagoras’ constant. The International Organization for Standardization (ISO) uses it to determine the A paper size in addition to demonstrating the presence of irrational integers. According to the specification of the A paper in 216(opens in new tab), the ratio of the sheet’s length to its breadth should be 1.4142. This implies that cutting an A1 sheet of paper in half across will result in two A2 pieces of paper. Two A3 sheets of paper will result from dividing an A2 in half once more, and so forth.
SLICE OF PI
Sometimes, a shortened form of pi is a better number than pi. At least according to NASA and the researchers at the California-based Jet Propulsion Laboratory (JPL). According to Marc Rayman, Chief Engineer for Mission Operations and Science at JPL, the organization employs the figure 3.141592653589793 for interplanetary guidance. (opens in new tab). According to Rayman, NASA can get everything it constructs to the desired location with that degree of accuracy.
It’s useful to do some figure crunching to understand why. The Voyager 1 ship, which is more than 14.6 billion miles (23.5 billion kilometers) away from Earth, is the most remote object in space. Adding additional decimal places to pi only reduces the calculation’s inaccuracy by about a half-inch (1.2 centimeters), according to Rayman. At this distance, it is possible to compute the diameter of a circle that is approximately 94 billion miles (more than 150 billion km) around.
It would only take 37 digits after the decimal point for experts to compute the radius of a circle the size of the known universe with a precision of the width of a hydrogen molecule, according to Rayman.
What then is more interesting than pi? A slice of pi.