The Useless Number (Get ready for some Donuts)

Wasn’t math itself useless to learn, especially at school?

Image result for boring math classes

Shout-outs to those desks! Neat and polished.

We are back with some interesting concept that lead perhaps not precisely the scientists of today, but the scientists of the 16th-17th century into wondering how and why did it turn out to be so. Meh, as usual, misconception after misconception.

Let the controversy session begin!


Italians go first!

Image result for italian hand meme

Nope, the meme isn’t the controversy epicenter this time! It’s this one number that we will defining in the follow sections.

So, it all started from how mathematicians from the XVI century were interested in cubic polynomials such as this one:

\[ x^3+5x+7 \]


Calculations incoming!

In general, Cubic Polynomials are graphically represented as:

And here is the terrifyingly mysterious part the gurus of its time thought was impossible to be implemented. The first (from the left) and the last picture represented common ideas–1 function solution–idyllically considered by “General Mathematics”. Yet, if lowered to make 3 whole y-axis intersections, it turned out to be something absolutely absurd and incomprehensible!

Many of you, dear readers, may be questioning whether who could claim such an evident concept wrong without most likely passing their basic algebra 2 class.

Well, first of all we are living in the so called “era of prosperity and technological elevation“; subsequently, we perceive a lot more information than hundreds of years ago. Secondly, the person was…

(1501-1576)

Basically, in order to pass the “Cubic Equation Mystery”, the perplexed scientists of their time had to pass this magical theater of Imaginary numbers.

So did Cardano! He had to use an imaginary number of -15 to find resolution towards revealing the mystery’s key side under the title of:

By multiplying these 2 groups of numbers, using simple algebraic calculations, he eventually interpreted that the imaginary numbers were eliminated!

Thus, he claims in one of his works:

By multiplying 5 plus the square root of -15 by 5 minus the square root of -15, we obtain 25 minus minus 15 and therefore the product is 40. Thus far does arithmetic ‘el subtlety go of which this the extreme is 

as I have said so subtle, that it is

useless.
Woah! Some complicated logic just hit the cerebral portion of ideas, yes indeed!
What he meant was that he hadn’t yet got his mathematical repertoire of understanding this awkward creature’s functions, it is was a good reason to start discovering the world of complex numbers more precisely.

 


Thanks for reading!

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Written by Shohruh Artaman
A typical writer illustrating typical principles
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