Analytic Geometry -- "I Think, therefore I am.."

Research, Research...

René Descartes announced this philosophical phrase back in 1637 when he worked on his 'discourse of Method.' Living his time and thinking ahead, his thoughts got him in big time trouble that could've sent him to jail or to 'hell.'

Today we wanted to work on an article about Analytic Geometry and tried to dive into the mind of this genius -- and we did find things that at first, for the average guy, couldn't mean nothing but a simple biographical essay.


If you notice the notation: (x, y). Given an unknown variable there is an aftermath for everything, like life itself; for each specific action you shall expect a reaction within certain parameters. René left a legacy that changed and paved the way for Calculus. Which mean, he was behind the man on the moon, your IPad and that crazy roller coaster.

We came with this discovery thinking and asking him... in our mind, "why philosophy was intrinsically related to science...?" --- He frowns

Descartes and Queen Christina of Sweden, 1650
Descartes and Queen Christina of Sweden, 1650 | Source

So, Analytic Geometry makes sense after all

Just imagine René Descartes facing the European inquisition and Royalty. Actually, four months before his death, he was invited by Queen Christina from Sweden to exchange thoughts and ground breaking science.

Rumors has it that René slept on a bed that was cold. To our opinion, his body temperature added to low and freezing conditions, soaked the bed after contact. Unfortunately René died on February 11, 1650.

In a mathematical analysis:

x= cold bed

y= 2nd law of Thermodynamics -- Cold and hot meet in the middle

Mechanics, limits, integration and differentiation...
Mechanics, limits, integration and differentiation... | Source

The World of today...

Just a quick ranting about this crazy world. Imagine that roller coaster that we love so much! Engineers came out with the safest designs for curves and centrifugal strength. Analytically speaking, if we knew that we were going to fit 24 people on a hellish ride, structural designers had to come up with formulas and equations to build the right 'monster of fun.'

Our engineers had to face Physics, Statics, Dynamics and strength of materials. Which eventually would boil down to calculus. But guess what? As we said: without Analytic Geometry there would never be a function Y=f(x) and there wouldn't be differentiation dx, or furthermore, F=m.a wouldn't have made sense without Descartes enunciation.

"we all have a purpose in life"

Life applications...

Imagine a dead beat dad, who barely paid child support for the last 18 years, and son Ted is already grown and ready to face the world on his own. We can create a formula of our own, measuring this kid's feelings toward his dad's lack of commitment:

L(T)= Σ 18(P) + R

felt on both sides

meaning that the Love L from Ted 'T' was related to the time and money spent by his dad (P). This formula condenses a 'real life axiom.'

R is a variable that changes with every regret felt on both sides. We notice again the action reaction relationship and its mathematical representation, Y=f(x)

The Basics of Analytic Geometry

By now you should be interested in this subject that we took on our first year in College. So great to know that Descartes, Liebniz, Spinoza, LaPlace, Fermat, Newton and Pascal, besides mathematicians, were famous philosophers as well.

Why is so important?

Before you lay the foundations for a skyscraper, you needed to level the ground and use all the architectural designs taught at Engineering school.

At first it was considered a branch of algebra used to model complex curves and shapes. Let's borrow a small curve equation: if Y=X², a graphical representation of those parameters was needed. Descartes and Fermat came out with the well known 'Cartesian Plane.'

A bi-dimensional solution to tridimensional thinking -- there was no computers back then... just a quill and a will.


Just picture your kids leaving MySpace for 'FaceBook.' Wrong moves and dreadful decisions left one giant, speechless and in agony. Did you hear us 'Bebo' and ''? Going back to the point: In Analytic Geometry, Curves, lines and shapes can be defined as a set of points that satisfy linear, second degree and third degree equations. At some point, Descartes must've said 'eureka!' when he came with a graphical representation of numbers. Two perpendicular lines made sense in his mind. Celestial bodies and tridimensional shapes had to be represented on a manuscript...

A 180 degrees graphic was not 'aesthetic' and practical enough, and was discarded :


We don't want to go in detailed terms of abscissas and ordinates (x, y). There is a limit for the average mind.

We just hope we gave our younger generations a reason to look at this subject with respect.

Joseph De Cross

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Comments 16 comments

rahul0324 profile image

rahul0324 4 years ago from Gurgaon, India

Nice Write Lord!

You have given some serious implications of Analytical Geometry!

John Sarkis profile image

John Sarkis 4 years ago from Los Angeles, CA

Great hub Lord. I knew Descartes dabbled in science and math, but not to this extent. Thanks for brining this topic into light for me.

Voted up and interesting


ChristyWrites profile image

ChristyWrites 4 years ago from British Columbia, Canada

Now I am wondering what Descartes would think of Facebook... thumbs up and a "Like" perhaps..?! Oh Lord you have me thinking again.. LOL

bmcoll3278 profile image

bmcoll3278 4 years ago from Longmont, Colorado

Can we say woooooosh. The sound I heard. Very interesting , But so far above my head I need a latter. Great hub. I learned something.

tammyswallow profile image

tammyswallow 4 years ago from North Carolina

You know, I haven anxiety when I see grids, numbers and equations. I am familiar with the philosophical tenants of Descartes. This is one of my favorites:

Descartes walks into a bar. The bartender asks him if he would like a shot. He says, "No, I don't think so." POOF.. he vanishes and is gone.

Great hub!

Lord De Cross profile image

Lord De Cross 4 years ago Author

Hi there Rahul, fellow hubber,

This was one of our math ranting, and we think we discovered a meaning behind his philosophy. Thanks for your kind words my friend!

@ John Sarkis, there were several Chaldeo Asirian mathematicians before Descartes, who did some discoveries, and we don't know for sure if he (Rene) really read their work. Much appreciated for taking your time!

@ChristyWrites, We thank you for bringing that smile to us. Did we make you think? That is a proof that you liked our hub. Great to see you around!

@BMcoll3278, Thanks for leaving a comment. We could've done a more technically chalenging hub, but we said, " This is good enough to keep our young readers interested/

@Tammy Lol! That was great! Even Rene was laughing all the way! Thanks for showing up! You always checking on us and we feel honored to have you at HP as well.


mwwa profile image

mwwa 4 years ago

beautifully done! Must say through this perspective i have a new founding respect for math:)

Lord De Cross profile image

Lord De Cross 4 years ago Author

Hi there MWWA, There you go man! Well, is better to know that due to math and right computation, we will get paid by adsense periodically. Charts and statistics have a sound influence from Descartes... as you realize by now. Have a happy #ff.


Faith Reaper profile image

Faith Reaper 4 years ago from southern USA

Wow, love your analytic mind(s)! Excellent hub. In His Love, Faith Reaper

Lord De Cross profile image

Lord De Cross 4 years ago Author

Thanks Faith for leaving a comment in one of our analytical hubs. These articles are written in order to help our young kids to understand math from a fresher point of view. Thanks for your words! Much appreciated!


PurvisBobbi44 profile image

PurvisBobbi44 4 years ago from Florida

Professor Lord,

You have excelled above many with your great reintroduction of Rene---and I wish he had live the same time Isaac Newton had lived. I can see them immersed in a calculus discussion.

I voted up, awesome and interesting.

Your Hub Friend


Lord De Cross profile image

Lord De Cross 4 years ago Author

Thanks Bobbi! Great analysis, Rene would've been talking to Issac like a long gone father. Newton was born in 1647, 3 years before Descartes left this World. What we know for sure is that Newton based his studies for the introduction of Calculus, in Rene's dissertations and Fermat's. Thanks for commenting and have a great Sunday Barbara!


Eiddwen profile image

Eiddwen 4 years ago from Wales

A great hub as always Lord and here's to so many more to come.


Lord De Cross profile image

Lord De Cross 4 years ago Author

Hi Eddy, wonderful to see you! I can imagine those green areas in Ireland. Most of us have lived in asphalt and modernism. Thanks for your sound comments and hope your family is fine. Thanks for your follow my friend.

unknown spy profile image

unknown spy 4 years ago from Neverland - where children never grow up.

i always hate math but then why did i took computer engg? now my world only revolves around it :)

Lord De Cross profile image

Lord De Cross 4 years ago Author

unknown spy, We never know what thye future is holding out there for us. Math can be fun if we get the right teachers. At least your hubs show your analythical thoughts and we hope to have you for a long time in HP. Thanks for sharing with us a little about you!

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