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The Book of Threes Video

Something, nothing, and everything comes in threes. Enjoy this 9 minute expose on why we conceptualize, organize, and tri-compartmentalize in threes.

”Three is the magic number”

The Book of Threes
The Book of Threes Video
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How was Morse Code Invented? History and Systems

Morse Code

Humans have been attempting to communicate across distances for a very, very long time—far before we even considered the potential of the cellphone. That is a morse code if you were alive in the 1850s or are a modern amateur radio operator. This form of communication was once essential to keeping things moving around the world.

Morse first created an encryption code that was comparable to the semaphore telegraphs that were already in use. It involved allocating three- or four-digit numbers to the words and entering them into a codebook. Words were transformed into these number groups by the sending operator. Using this codebook, the receiving operator changed them back to words. The creation of this code dictionary took Morse several months.

It was employed during the world wars to transmit widespread public messages. It might be used to send mail across continents. In a sense, texting was developed before Morse code.

We examine the Morse Code’s mechanisms and history in great detail in this extensive article.

What is the Morse Code? The Inventor Behind Morse Code:

There are two systems that are referred to as Morse codes. Morse Code uses a combination of dots, dashes, and spaces to represent alphabetic characters, numbers, and punctuation. The codes are sent as varying-length electrical pulses or similar mechanical or visual signals. The first, the “American” Morse Code, and the second, later, widely used International Morse Code are the two codes.

American artist and inventor Samuel F.B. Morse created one of the Morse code systems in the 1830s for electrical telegraphy in the United States. In order to accommodate letters with diacritical markings, a meeting of European nations developed a variation known as the International Morse Code in 1851.

How does Morse code work?

All letters in the International Morse Code are represented by combinations of dots and short dashes. The International Morse Code also substitutes constant-length dashes for the variable-length dashes used in the first Morse Code. For instance, three dots, three dashes, and three dots are used to express the universal distress signal “SOS”—three dots standing in for the letter “S” and three dashes for the letter “O.”

The History of Morse Code

Continue reading How was Morse Code Invented? History and Systems
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Fibonacci & Pythagoras Help save a beautiful discovery from oblivion

Pythagorean Triples

This is another brillian video from Mathologer. In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. If you want more details go to the video on Mathologer.

Pascal’s Triangle

  • One of the most interesting Number Patterns is Pascal’s Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). …
  • Diagonals. …
  • Symmetrical. …
  • Horizontal Sums. …
  • Exponents of 11. …
  • The same thing happens with 116 etc.
  • Squares. …
  • Fibonacci Sequence.

The Coefficients of the Binomia Theorem from Pascal’s Triangle

Pascal’s triangle formula is (n+1)C(r) = (n)C(r – 1) + (n)C(r). It means that the number of ways to choose r items out of a total of n + 1 items is the same as adding the number of ways to choose r – 1 items out of a total of n items and the number of ways to choose r items out of a total of n items.

The Fibonacci sequence with Pythagorean triples

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have the following right triangle. The hypotenuse will always be irrational because the only Fibonacci numbers that are squares are 1 and 144, and 144 is the 12th Fibonacci number.

Pascal’s triangle is commonly used in probability theory, combinatorics, and algebra. In general, we can use Pascal’s triangle to find the coefficients of binomial expansion, the probability of heads and tails in a coin toss, the probability of certain combinations of things, and so on


About Mathologer

Enter the world of the Mathologer for really accessible explanations of hard and beautiful math(s). In real life the Mathologer is a math(s) professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster. These days Marty Ross another math(s) professor, great friend and collaborator for over 20 years also plays a huge role behind the scenes, honing the math(s) and the video scripts with Burkard. And there are Tristan Tillij and Eddie Price who complete the Mathologer team, tirelessly proofreading and critiquing the scripts and providing lots of original ideas. If you like Mathologer, also check out years worth of free original maths resources on Burkard and Marty’s site