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Pythagorean Theorem -- Geometry and Applications in Real Life

Updated on March 2, 2016
Somehow, Egyptians knew the theorem. Can you tell?
Somehow, Egyptians knew the theorem. Can you tell? | Source

Putting aside the fact that Pythagoras had a struck of luck when he fell from his bed that morning of July of 555 B.C. in breeze Samos Greece. He actually saw polynomials instead of birds. If we could make our kids understand better his horrifying formula, we could save this country to be relegated to a third world mind.


Let's assume that you already have seen the following formula and you want to use it in real pulsing timing:

a2 +b2 =c2


You live on a 5th floor on a building near Downtown Los Angeles. Suddenly, your freaking neighbor, who lives on the 4th floor, starts (ignites) a fire. All because he caught his girl chatting with another guy-- familiar?

Not that she was talking to a colleague on FB. Not that we know or were told. But before we know it, he bashes the whole apartment to sheer delight. He leaves her girlfriend unconscious and you happen to see him running downstairs. You become a hero and take things into matter. You decide to drag her out across the hallway -- flames catch up with you both. The only way to stay alive is keep going up into the top floor and roof. You call 911 and they get hold of your emergency.


A fire engine gets there in 6 minutes. You are by the top floor window and hope and pray that the telescopic aerial ladder will be able to reach you both.


A fireman does a quick calculation:

We have 5 floors, each floor is 8.5 feet high (Hurry up Lord!!)

Total height of the target is 8.5x5= 42.5 feet

The closest an Engine can get (sideways) is roughly 7 feet (Lord please!!)

We don't worry about nothing else and apply the theorem:

(42.5)2 + (7)2 = (ladder span needed)2 = L2

The fire-guys will solve this equation in 5 seconds...

1806.25 + 49 = L2

L2 = 1855.25 Then L= 43.072613108563544 or: L=43.1 FEET

The ladder span is 43.1 feet!

YES! The aerial span needed is about 43 feet, and luckily the fire engine mount aerial ladder can be extended up to 50 feet. Our 'finest' can go up, with no problem at all.


A ramp too short for side of the House?
A ramp too short for side of the House? | Source


On the picture above, the unionized brother contractor made an approximate ramp length. What would've happened if he knew our method?

We have the height from the ground to sliding door porch which is 2 feet.

The actual distance from the bottom side of the sliding door to the sidewalk is 23 feet as you see.

Lets call the actual length of the ramp X (in the picture is represented by ??)

x2 =232 + 22

x2 = 529 + 4

x2 =533

Solving the square root of 533, we obtain the answer

x= 23.086 feet

So, the Contractor will be in better shape by knowing the length of the ramp in advance.

The Ramp will be 23.086 feet long.


MNEMONICS, surreal but effective.

You can remember the formula by using mnemonics.

3 2 + 42 = 5 2

3 persons have ducks on their head in one corner

4 persons have more ducks on their head on the other corner

How many persons will be able to match that kind of setting, being caught in the middle of the room with ducks over their head?



Submit a Comment
  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    7 years ago from New York

    MTR, math can be understood better when it's used in everyday life. You have a nice day! Thanks for stopping by!

  • profile image


    7 years ago

    THE THEROEM IS PRETTY AWESOME! Especially for me.

  • Janine Huldie profile image

    Janine Huldie 

    7 years ago from New York, New York

    Not a problem and you are quite welcome. Totally agree about loving mafutons our future generations as well. Hope to also talk again soon!

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    7 years ago from New York

    Hi Janine!

    Back at ya! Thnaks for being one of the sweetest hubber, besides my 201 true followers, of course. The thing is, we love our math..and we love our future generations. They are really the ones behind all this science ranting. We cannot be so stupid to keep all these knowledge inside. Take care my friend!

  • Janine Huldie profile image

    Janine Huldie 

    7 years ago from New York, New York

    Thank you again too, seriously I so enjoy writing hubs about a topic I have always loved and be able to put a more colorful spin on topics otherwise thought of as possibly dull and difficult. I am also happy to see someone else on here doing similar and love being able to learn from you as well.

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    7 years ago from New York

    Hi Janine,

    Just hold of you. Was away for a little. Seems that we can push some math ideas into colorful hubs huh? Glad to have a mom writing wonderful hubs for our kids. Thanks!

  • Janine Huldie profile image

    Janine Huldie 

    7 years ago from New York, New York

    I finally got to check out your real-life examples on the Pythagorean Theorem and loved them too. Great job here and of course have also voted up and shared too!

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    7 years ago from New York

    Christy writes,

    We try to diversify our skills and our inspiration, along with our poetry. Thanks!

    Oh Debborah Brooks,

    We suspect the egyptians knew even trigonometry and advance math, before Pythagoras. You are welcome to check on us and maybe share this math tutorials with your grandkids. You are an adorable follower indeed.

  • Deborah Brooks profile image

    Deborah Brooks Langford 

    7 years ago from Brownsville,TX know i am not good at math but every time i read your hubs i learn something..thankyou friend....i am fascin ated with the egyptians how they knew all this math......excellent hub....debbbie

  • ChristyWrites profile image

    Christy Birmingham 

    7 years ago from British Columbia, Canada

    Wow a math hub AND relationship hubs - you have variety Lord!

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    7 years ago from New York

    Tammy, Morning!

    Yeah, fell from my bed this morning. You always checking on us and praising our work. HP is the place to be! Thanks for your kind words, even though you skipped the numbers. LOL... Just joking!

    @Tenkay, that was funny. Common sense will tell us that if your shadow is 5.5 feet lond at 45 degrees, then you are 5.5 feet tall as well. Great to have fun with you and teaching our kids as well.

    @ Audray, Thanks for stopping by. I though you were checking your lenses and deciding if f: 1/8 was much better that f:1/4 for an outing picture. You know what we mean. Lol! Math can be fun if we see it with a different kind of eye...and mind.

    @ Mike Pugh, You always surprise us with your visit. Don't know why when I see your site, I get lost in cloud 9. Lol! Glad this examples can be useful for our kids. Do you remember when we were 13-14 and the darn teacher would flow our minds with crazy Set theory and those freaking polynomials? Forget about Newton...! Life can be easier with today's technology, and I'm proud of you supporting our work. Thanks!

    @ Mary,

    We used to laugh at the teacher like a clown. Your daughter knows that type of kid. Our Father, rest in peace dad, changed our lives by getting us a particular tutor when we were 14. The difference is... that this tutor ws an engineer. Still remember that summer of 76, and I wish I could go back and thank him for all he did for us. Thanks Mary... don't want to reach the sentimental mode.

  • tillsontitan profile image

    Mary Craig 

    7 years ago from New York

    If you had been my high school math teacher I might be better at math today! Your explanations are not only correct (of course) but so interesting. I would imagine students relating to this rather than the nonsense they use in math books!

    Voted up, useful, awesome and interesting AND sharing with my daughter who is a high school math teacher. I know she'll appreciate this.

  • CloudExplorer profile image

    Mike Pugh 

    7 years ago from New York City

    This is so cool Lord, your mathematics skills is truly awesome here LOL, you've managed to make some funnies here, wow how do you do it with technical subjects.

    I find it very tough to bring such humor to the digital stage of mathematics of all subjects, and you do it with ease.

    Awesome stuff! voted up and getting shared no doubt.

  • profile image


    7 years ago

    I used to be really good in math. I wish you were my teacher. You spell it out so we can understand t. Well done!

  • TENKAY profile image


    7 years ago from Philippines

    I love this. It looks awesome but it really is simple. The practical and useful side of mathematics.

    I used to impress my students with this problem: If my shadow is 5.5 ft long and the angle of the ray of the sun is at 45 degree, how tall am I? hehehe.

  • tammyswallow profile image


    7 years ago from North Carolina

    Ummmm... Great hub. I clicked useful because it is probably useful to someone. I saw math problems and started sweating. But I did get through it unscathed. I know enough math to be dangerous. I am glad there are geniuses like you who understand these things. :)


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