# Pythagorean Theorem -- Geometry and Applications in Real Life

- Geometric Sequences -- Real Life Applications

Practical and real life applications for geometric sequences.

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.

**HANDS ON...**

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

**a**^{2} +b^{2} =c^{2}

^{2}+b

^{2}=c

^{2}

**HERE WE GO**

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.

**SPEEDING UP THE STORY**

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.

**DO WE NEED MATH?**

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 }= L^{2}

^{2}+ (7)

^{2 }= (ladder span needed)

^{2 }= L

^{2}

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

### 1806.25 + 49 = L^{2}

### L^{2 }= 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.

**SAVED BY THE SMOKING BELL THAT WILL DESTROY ITSELF IN 5 SECONDS!**

## RAMP LENGHT

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 ??)**

**x**^{2} =23^{2} + 2^{2}

^{2}=23

^{2}+ 2

^{2}

**x**^{2} = 529 + 4

^{2}= 529 + 4

**x**^{2 }=533

^{2 }=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 }+ 4^{2} = 5^{ 2}

^{ 2 }+ 4

^{2}= 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? **

**5**

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## Comments 16 comments

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. :)

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.

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!

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.

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.

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

Lord..you 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

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!

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.

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

THE THEROEM IS PRETTY AWESOME! Especially for me.

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