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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.
Let's assume that you already have seen the following formula and you want to use it in real pulsing timing:
a2 +b2 =c2
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 = 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.
SAVED BY THE SMOKING BELL THAT WILL DESTROY ITSELF IN 5 SECONDS!
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
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?
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