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42 Facts about 42!

Forty Two

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!

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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:

No matter how many times you divide the angle on a straight line, the segments will always add up to 180 degrees.

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:

If the central angle forms the diameter of the circle, then the angle inscribed at the circumference will be a right angle.

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.

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How Math Flashcards Can Help Teach Students

Math Flash Cards

Math flashcards have been used for decades to help students retain math facts and formulas. Experts and educators believe that the use of flashcards for grades kindergarten through high school years are extremely helpful and beneficial to a child’s learning experiences.

Students of all ages typically struggle with remembering certain math facts, problems, sequences, and formulas. It’s a lot to take in and so hard to retain at times. This is why using flashcards help students become better and sharper at math.

First, to understand this concept, one must understand the actual power and efficiency of using flashcards to learn. A flashcard may seem simple, easy to understand, and inexpensive. However, using visual tools like flashcards helps students remember things. The brain works in a special way when people are visually taught. Seeing a lesson versus just hearing a lesson can make a huge impact on any learner.

For example, imagine a fifth-grade teacher trying to teach her students their multiplication facts. Teachers often time use charts and flashcards for students to learn this fact. It is more difficult to teach a class full of ten and eleven-year-old students how to remember their multiplication facts by lecturing them on numbers and multiples. However, teaching with a visual component, like flashcards, makes the experience less complicated to understand. It’s almost like making a game out of the lesson, and studies show that if a student is enjoying themselves, the teacher has a greater chance of successfully teaching the lesson.

True, math is complicated and the number of things to retain can be difficult, at any level, grade, and age. It is true, however, that understanding math, integers, fractions, geometry, trigonometry, and calculus can all be understood once the content is broken down and visually taught.


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John Forbes Nash Jr.: Mathematician and Modern Genius

John Forbes Nash, Jr. will go down in history as a Math God of his time. His contributions to game theory, differential geometry, and the study of the partial differential equations paved a clear way for future mathematicians. He provided keen insight into the factors that govern chance and decision-making inside complex systems that we use in everyday life. It is because of Nash that today, we have a clear understanding of how to apply certain theories in math.

He’s the answer to that pupil who raises his hand and annoyingly asks “Why do we even need math?!”

He earned a Ph.D. in 1950 with his dissertation on non-cooperative games. The Nash embedding theorem is also one of his infamous contributions to math and his contributions to the theory of nonlinear parabolic partial differential equations and singularity theory. 

Nash served as the Senior Research Mathematician at Princeton during the later parts of his life. In 1994 he was the recipient of the Nobel Memorial Prize in Economic Sciences and recipient of the Abel Prize for his work on nonlinear partial differential equations. He is the only person to have ever received both words. 

Nash grew up in West Virginia living with a father who worked as an engineer and a mother who served as a school teacher. His parents got him involved in advanced math courses at local community colleges during his final year of highs school. He later attended Carnegie Institute of Technology majoring in chemical engineering. Later on he graduated in 1948 at the young age of 19 with a B.S. and M.S. in mathematics. 

Ten years go by and in 1959, Nash began to display signs of mental illness and was treated for paranoid schizophrenia. His continued improved but the illness continued. This was actually vividly illustrated in the biography by Sylvia Nasar titled, A Beautiful Mind; later on becoming a film starring Russell Crowe as Nash. Nash later passed away in 2015 leaving behind two sons and a longstanding understanding of mathematics. 

Credits: The image pictured in this article is from Wikipedia.

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Real life uses of LCM and GCF

In math, the GCF is better known as the Greater Common Factor. The greatest common factor is commonly used to simplify a fraction by dividing both the numerator and denominator by the greatest common factor of both. This is very common in math computation when considering fractions. 

The LCM is better known as the least common multiple of the denominators. This is often called the lowest common multiple. It is helpful to find the lowest common denominator, since each of the fractions can be shown as a fraction with the denominator. When using addition and subtraction to compare fractions, it is useful to use the LCM. 

Now, considering your real life, did you even realize that LCM and GCF plays into your real life? Think about it…when dividing something equally, you subconsciously are using GCF and LCM. For example, when the children ask for slices of pie, a parent will divide the pie to equally among the children. Without even thinking of it in mathematical terms, you’ve used fraction formulas to solve a problem. And make the children smile!

Now, consider counting and dividing your money. When standing at the counter, you decide how to use certain amounts as fractions to get the job done. You consider dividing your money for the best utilization. For example, when spending, you are recommended to put aside a fraction of money to save, and a fraction to spend. 

You also use GCF and LCM in comparing prices. When thinking of buying a pound of bananas for a cheaper price, you’ll use fractions to determine which price is cheaper. You do this to save money and most times get the best bargain. Coupons also help save and this is also a real-life example of using GCF and LCM in your day to day life. 

Time…an element of life that we of course use in our daily lives. Understanding time, however, is just fractions! Think about how you determine time. When determining time, to learn the minutes of the clock, you determine the fraction of the clock. Without even realizing you’re using GCF and LCM, you are using fractions to determine time! Again, another real-life use of GCF and LCM.

So, when you hear someone tell you that math isn’t necessary, think twice! You use fractions in your everyday life, subconsciously. When considering time, money, comparing prices, and dividing items equally, you are using GCF and LCM. To learn more about GCF and LCM and, visit https://math.tools/calculator/lcm/ & https://math.tools/calculator/gcf/). The Math Tools website allows for you to learn more about fractions, numbers and computing both. 

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Significant Numbers and Their Meanings

Math is particularly special because of the array of significant numbers. There are certain numbers and formulas that has likely stuck with you since high school math class – and they always will. Some of these significant numbers are necessary in certain computations. Some of these numbers are used in physics to help explain natural things, such as speed, and depth. 

Computations like the ration of a circle’s circumference to its diameter is universally recognized as pi. The significance of pi is that it is always approximately equal to 3.14159. For example, for any circle, when dividing that circle’s circumference by its diameter, it will give you the answer of 3.14159. Pi is an irrational number, meaning that its value cannot be precise, like a simple fraction. Pi is widely known in mathematical studies including geometry and algebraic equations. 

Sounds cool, right? To checkout more about the significance of Pi, visit https://math.tools/api/numbers/ and get lost in the meanings and significance of numbers! 

The power in numbers and how some have meaning should be recognized. For example, the speed of light, better known as C, computes at exactly 299792458 meters per second. The C stands for celeritas, which comes from the Latin word speed. The number is a universal constant in physics. The precise value is what makes it significant and has been studied for centuries. Understand that some of these numbers break down exact and were discovered by early day mathematicians who paved the way for an understanding of how to use numbers to measure.

Ever heard of the number to everything, also known as the number of the Universe? 42 is said to be the number of the universe, later known to the number of everything. It gets its significance from a famous radio show that eventually was turned into a novel then a movie “The Hitchhiker’s Guide to the Galaxy” by Douglas Adams delved into in the book, he wrote that the number 42 is “The Answer to the Ultimate Question of Life, the Universe, and Everything”. It is said that the answer was determined by the supercomputer Deep Thought after 7.5 million years of calculations. The number is considered a perfect number, which means a number that is a positive integer that is equal to the sum of the number’s suitable divisors.  The number 42 became a staple in math culture after the movie appeared in 2005. However, buzzfeed reported that Adams went on record to say it was all centered around a joke and he just randomly chose the number 42. The answer remains unknown. However, people still hold a great belief that there is some truth to the number 42 being the number and the answer to the universe. 

Some numbers are like household names, you’ll know its significance the moment you hear it. It becomes a natural knowing. In fact, pi is such a special thing in the math culture that it has its own day – March 14th (3.14) of every year is considered “Pi Day”. To learn more about significant numbers, checkout out https://math.tools/ . The website has built in calculators, math tables, information on formulas, flashcards and more! Math Tools is your virtual math tutor, right at the palm of your hands!

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The meaning of Pi

As a child, you may recall learning about Pi in math class. Remembering the term may have triggered a smell of your grandmother’s baked pies. However, that isn’t quite what your math teacher meant during that lesson.

It was first called “pi” in the year 1706 by William Jones, the Welsh mathematician.  Pi is the first letter in the Greek word perimitros, which means “perimeter.”

Pi is approximately 3.142 and it is the circumference of any circle that is divided by its diameter. The word Pi comes from the Greek letter π. It is pronounced “pie” and is one of the most common constants in math.

To arrive at pi, you must correctly use the formula. The circumference of a circle is found using the formula C= π*d = 2* π*r. When using a calculator to compute pi, the results should always be approximately 3.14. 

Several math lovers have dubbed March 14 or 3/14 as the day to honor the infamous mathematical constant. However, unlike the date, Pi cannot be written like a fraction since it is an infinite number. 

Pi is usually used in the subjects of both science and math, but mostly associated with math. When determining the area or circumference of a circle or a round object, students use the Pi formula. 

No other math formula is as popular as Pi. It was discovered long ago that Pi turns out as an irrational number and its exact value is not known. However, its formula stands strong in mathematics for centuries. 

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Teaching math in today’s century

If you’re a parent raising a child in the 21st century in the public-school system, you’re most definitely no stranger to the idea that the way math is taught has changed. The methods in which we were taught how to do math has significantly taken a turn and it’s no secret that some parents can barely keep up with their child’s math homework.

Like Shakespeare said:

Though this be madness, yet there is method in’t. – William Shakespeare

Here’s why: In several states, a new idea of Common Core State Standards was adopted to create a new and improved (so, the government promised) way of how we taught young people in this country. Common Core State Standards is an initiative that began in 2010 that details how students in grades K-12 should understand and learn English language arts and math at a certain level.

Common Core math standards has received much criticism over the years. The common core standards offer a new approach. What it does is a bit more complicated for students, parents, and even educators. Common Core State Standards, especially in math, created a national uproar. What is happening in math is an emphasis more on concepts of understanding the numbers and problems. The breakdown of numbers has become more explicit and takes more time to solve problems. This became a challenge and created an evolution in mathematics.