## 42 Facts about 42!

Who said that numbers can’t be fun? Numbers aren’t only fun to deal with, but they often lead to many fun facts that you didn’t know before.

Such a number is 42, and there are many mysteries revolving around this number. In this article, we’ll look at 42 facts about 42 that’ll leave you surprised. So, let’s get started, shall we?

1. 42 is a pronic number, and this has been attracting mathematicians towards it for a long time. It means that 42 is the product of two consecutive integers. There aren’t many pronic numbers in the universe, and this makes 42 one of the rarest ones.
2. Then again, 42 is a sphenic number as well. It means that 42 is the product of three prime numbers. The three prime numbers are distinct. Sphenic numbers aren’t as rare as Pronic numbers, but these are quite rare.
3. 42 is also an abundant number. It means that the number itself is smaller than the sum of its proper divisors.
4. In the book called “The Hitchhikers Guide to the Galaxy” by Douglas Adams, the number 42 is stated to be the answer to the ultimate question of life. Give this book a read to know and understand more about this context.
5. Most wolves and adult dogs end up with 42 teeth.
6. A marathon is 42,195 meters long. However, it was 42 kilometers originally. The extra 195 meters were added later on so that the race could finish right in front of the royal box. This change was made in the 1908 Olympics.
7. If you’re a fan of paintings, probably you’ve heard of the “Cheese Shop” painting by Monty Python. In this picture, many cheese wheels come with the number 42.
8. Jackie Robinson, the first African-American baseball player, used to wear a jersey labeled 42.
9. The movie that’s been made on the life of Jackie Robinson is named ‘42’.
10. The element ‘Molybdenum’ has an atomic number of 42.
11. The standard oil barrels of the US contains 42 gallons of oil. Each gallon is usually defined as 3.8 liters.
12. The band known as ‘Level 42’ was initially known as ‘42’ only. However, after the release of the book “The Hitchhikers Guide to The Galaxy”, the management team of this band decided to add ‘Level’ to the name.
13. In an episode of The Simpsons, Wiggum the police chief replies to a question with ‘42’.
14. The number of dots on a pair of dice always sums up to ‘42’.
15. Roman emperor Claudius took the throne at an age of 50 years, following the assassination of his nephew Caligula. Caligula was assassinated in the year 42 AD.
16. The TIFF-file format is important as it helps store image files. Every TIFF file starts with the number ‘42’. What’s more interesting is that this number was chosen due to its philosophical significance.
17. A rainbow can only be seen if the observer is at an angle of 42 degrees opposite to the light source.
18. There are a total of 42 illustrations in the book “Alice in Wonderland” by Lewis Carroll.
19. The real 42nd president of the USA is George W. Bush.
20. The favorite number of Dr. House from the House MD series is 42.
21. Apartment 42 is the apartment of Fox Mulders from The X-Files.
22. In Toy Story, you’ll find that the shipping number of Buzz Lightyear is also 42.
23. Coldplay has a song called ‘42’.
24. If you ask for the answer to life, the universe, and everything else on Wolfram Alpha, it’ll reply with ‘42’.
25. The Gutenberg bible comes with 42 lines on each page.
26. The episode of Dr. Who titled ‘42’ runs exactly for 42 minutes.
27. The souls of the dead in ancient Egypt had to face 42 judges.
28. There are exactly 42 laws of cricket!
29. The country calling code of Czechoslovakia was +42. As this country got split back in 1993, the calling codes used are +420 and +421.
30. In Romeo and Juliet were written by the famous Shakespeare, Juliet had fallen asleep for 42 hours.
31. The new building built to house the growing number of scientists at CERN was named Building 42.
32. In the book of revelation, it’s said that a beast will rule all the human beings on earth for 42 months.
33. The three best selling albums of all time are Back in Black by AC/DC, The Dark Side of the Moon by Pink Floyd, and Thriller by Michael Jackson, all have a playtime of 42 minutes.
34. There’s a 183-meter long building in London made back in the 1980s which was the tallest building in London back then, and it’s called Tower 42.
35. Harry finds out that he’s a Wizard on the 42nd page of the philosopher’s stone book.
36. The board game ‘Risk’ comes with 42 territories in total.
37. Prince Albert, Queen Victoria’s husband, passed away when he was 42 years old, leaving a total of 42 grandchildren.
38. The Birdman of Alcatraz was imprisoned in cell number 42.
39. There’s a red dwarf with a 42 in its name, and it’s called Kepler-42.
40. Elvis Presley had passed away only at an age of 42.
41. You’ll find tons of references to the number ‘42’ on the TV show Lost. You’ll find planes with 42 rows of seats and much more.
42. 42nd Street is where you’ll find one of the most important buildings in New York.

As you can see, the number 42 is much more interesting than you ever thought it could be. You can find more mathematical properties of 42 here. Now that you know 42 amazing facts about the number ‘42’, you’ll be able to surprise your friends with these!

## The Difference between A Theorem, A Lemma, And A Corollary

Mathematicians label mathematical equations with exactly four labels if they’re true. If a mathematical equation is true, they label it with either lemma, corollary, theorem, or proposition. We all have used these in our lives, as we’re instructed to write these once we’ve proven a specific equation. However, most of us don’t know what these mean.

In essence, all four of these labels mean the same thing more or less. All of these indicate that a specific equation is true, provided some axioms or previous true statements. However, there are some subtle differences between them, which is why mathematicians use different labels for different equations.

## Terms You Must Know:

To understand these differences between a theorem, a lemma, and a corollary, we must know a few terms. We’ll provide a short description of these here.

## Equation:

Equations are mathematical statements that comprise of two algebraic expressions connected by an ‘equal’ (=) symbol. This indicates that the two expressions on either side are of the same value. If there’s a variable in either of the expressions, they must be true irrespective of the value of the variable.

## Axiom:

Axioms are propositions or statements that are proven to be established. In a word, these are considered universal truths. Unlike theorems, lemmas, or corollaries, the axioms are taken as true without a second question.

For example, stating 2+2=4 requires no further evidence to back it up, but it is self-evidence. This is a perfect example of the axiom.

## The Difference between A Theorem, A Lemma, And A Corollary:

In this section, we’ll discuss the differences between a theorem, a lemma, and a corollary in a way that’s easier for you to understand. So, let’s get started.

## Theorem:

A theorem is probably one of the most common terms we use in studying mathematics. We need to memorize and prove tons of mathematical and geometric theorems in our math courses.
But what is a theorem? Well, a theorem is a mathematical or geometric calculation that you can prove to be true, with the help of some mathematical statements that are proven to be true.

A common example of the theorem is this:

As you can see, it’s a very common and important statement, as it must be used to prove more or less every geometric theorem that you’ll ever come across.

Unlike lemma or corollary, theorems are treated to be the primary proofs and of the utmost importance. However, it’s seen that the difference between a lemma and a theorem is very subjective, and it’s a bit hard to distinguish between these two.

We’ll talk about this in detail later on.

## Corollary:

It’s far easier to understand what a corollary is than it is to understand what a theorem and a lemma are. However, to understand what a corollary is, we must dive a bit deeper into what a theorem is. A theorem is usually derived with the help of one or multiple other lemma or theorems. However, the final product will be very different from the other theorems that have been used to prove this one right, and this result will add value in a completely different manner.

On the other hand, corollaries are direct derivatives of a theorem. Once you see a corollary, you’ll instantly recognize the theorem it has stemmed from, if you know that particular theorem already. In fact, in some cases, the corollary is a reverse proof of a theorem.

For example, if a theorem states that the opposite angles between two parallel lines intersected by another line are always true, the corollary is that the lines are always parallel if the opposite angles created by the intersection of a third line are equal.

## Lemma:

Now, things get a bit more challenging when you take lemma into account. Here’s the definition of a lemma:

A lemma is a mathematical statement that has proven to be true with the aid of some other axioms, and it helps in proving other theorems right.

Now, it can be very confusing as you can see that the definition of lemma and theorem are almost the same. Theorems can be used to prove other theorems as well, and they are also proved with the aid of axioms provided previously.

The only difference between lemma and theorem, and this might sound subjective, is that the theorems have a higher priority than lemmas. Now, as we’ve said, this is considered to be highly subjective, as to whether the equation is of major importance or not may depend on the individual.

This is why it can be tough to differentiate between a lemma and a theorem. We’ll try to make things clearer with the help of an example.

We all know that the angle inscribed on the circumference of a circle is always half of the angle created at the center. Now, this is a theorem as this statement is of great importance, and it can be used to prove other theorems.

Now, the theorem stated above talks about all the angles. This theorem is true no matter what you consider as the angle.

However, the lemma of this theorem goes like this:

This is quite evident. If the central angle forms the diameter of the circle, then the angle is essentially equal to 180-degree. According to the theorem, the angle at the circumference will be exactly half of that of the central one. We get exactly 90-degree, which is a right angle.

## Conclusion:

As you can see, it might be a challenge for you to find the difference between a theorem, a lemma, and a corollary at first. Once you get to know more mathematical equations, you’ll gradually be able to distinguish these. However, you’ll need a lot of practice to reach there.