Calculus/math question! I'm trying to figure out the speed of a blade storm. [Archive] - Wizards Community

Calculus/math question! I'm trying to figure out the speed of a blade storm. [Archive] - Wizards Community

Post/Author/DateTime Post
EvilVegan
06-01-07, 03:43 PM I've got the distance worked out to 80' times the sum of squares from 1 to 120 (1^2 + 2^2 + 3^2 + . . . + 119^2 + 120^2), but how would I write that and what does it equal?

I'm trying to figure out the speed a javelin travels of a character executing a bladestorm with a javelin if surrounded on all sides out to the maximum range of a javelin with far shot and distance (600' radius).

I found an equation that said that the sum of squares = n(n+1)(2n+1)/6 Is that right?

That would be 46,657,600 feet in 6 seconds.

7,776,266 & 2/3 feet per second!
LivingShadow
06-01-07, 05:46 PM I believe you have the math right but I'll double check

Another way of finding the sum of the squares up to 120 is integration which forms the equasion:

1203
____
3

Which simplifies to 576,000.

Multiply that by 80 and you get 46,080,000.

Then I guess you divided that by the time in a round making it 7,680,000 ft/sec

It seems your calculations were very similar to mine answer wise.
ShubNiggurath
06-01-07, 07:13 PM The sum is 583,220. I did it brute force in excel (30 seconds). Integration is wrong since the numbers are not contiguous.

Your formula is right
Kresalak
06-01-07, 07:41 PM I don't know how to write sigma notation on a computer, but what you want is the series X^2 from 1 to 120, which is, as the above poster said, 583,220. Times 80 feet would be 46,657,600 feet.
ShubNiggurath
06-02-07, 07:18 AM On a side note, I demonstrated the above formula for fun... it ain't easy I tell ya.

It involves some serie manipulation and some lateral thinking. Try it if you want to have fun, it took me almost an hour to figure it out, and another half hour to work on the details
EvilVegan
06-02-07, 08:02 AM Ok, anyone want to contine this problem by extending it to a sphere of targets instead of a circle?
LivingShadow
06-02-07, 10:42 AM Defending my use of integration. It can be used to find area under a curve. In this case the curve was X2 and the values were needed between 0 and 120. Besides we are getting similar answers either way.
General_Ridley
06-02-07, 11:52 AM The sum is 583,220. I did it brute force in excel (30 seconds). Integration is wrong since the numbers are not contiguous.

Your formula is right

the numbers make an x squared graph. Summing an equation by integration is perfectly allowable.

from 0 to 120, integrate x^2
StoneStokes
06-02-07, 02:52 PM Defending my use of integration. It can be used to find area under a curve. In this case the curve was X2 and the values were needed between 0 and 120. Besides we are getting similar answers either way.

They are NOT the same. The sum, S, we are looking for is the same as finding the area under the step function curve f(x), where

f(x)=1, if 0<x<1;
f(x)=4, if 1<x<2;
f(x)=9, if 2<x<3;
.
.
.
f(x)=120^2, if 119<x<120;

on the interval [0, 120].

This works out to
120(121)(241)/6 = 583,220,
by the formula given.

Conversely, the integral from 0 to 120 of x^2 gives
120^3/3 = 576,000.

Notice that the two numbers are different. That means that the two methods produce different answers. That means that the two methods are measuring different things.

However, you are correct in that the two answers are similar. The reason WHY is that the sum S is actually a Riemann sum approximating the integral of x^2. It is an upper bound on the integral because the rectangles forming the sum circumscribe (lie above) the curve y = x^2.

For a more detailed discussion, please consult your friendly neighborhood calculus teacher.
EvilVegan
06-02-07, 03:36 PM Anyone want to do the math on a sphere? :P
Ubasrawr
06-02-07, 03:48 PM Intergral of 4Pi*r^2 [1,120]

or something along those lines. V = 4/3 Pi r^3 is the result of the integral.

the number crunching you guys can do on your own.
Electric_Zombie
06-04-07, 12:12 PM I mentioned this story at the Minis forum. This reminds me of when my friends got into a big argument about how much cubic inches of water would be turned into ice from a cone of cold at some strange angle. At one point they were nearly at each others' throats regarding which equation to use and what the final answer was.

At that point, my other friend, Tony, jumped in and shouted: "GUYS! GUYS! IT'S D&D! The world doesn't spin because of gravity, it spins because a god takes the planet..." (makes a motion of spinning a ball) "...and goes, 'WHEEEEEEEE!!!'"
stargate525
06-04-07, 12:43 PM I mentioned this story at the Minis forum. This reminds me of when my friends got into a big argument about how much cubic inches of water would be turned into ice from a cone of cold at some strange angle. At one point they were nearly at each others' throats regarding which equation to use and what the final answer was.

At that point, my other friend, Tony, jumped in and shouted: "GUYS! GUYS! IT'S D&D! The world doesn't spin because of gravity, it spins because a god takes the planet..." (makes a motion of spinning a ball) "...and goes, 'WHEEEEEEEE!!!'"
You need to head over to the 'best lines ever' thread and plunk that in.

And you need to know the heat of the water, the total amount of water, and the temperature of the cone in order to figure that out...
Kresalak
06-04-07, 03:17 PM You need the specific heat, the volume of water, the pressure, the temperature, the temperature of the cone, the specific heat of the cone...

Post/Author/DateTime	Post
EvilVegan 06-01-07, 03:43 PM	I've got the distance worked out to 80' times the sum of squares from 1 to 120 (1^2 + 2^2 + 3^2 + . . . + 119^2 + 120^2), but how would I write that and what does it equal? I'm trying to figure out the speed a javelin travels of a character executing a bladestorm with a javelin if surrounded on all sides out to the maximum range of a javelin with far shot and distance (600' radius). I found an equation that said that the sum of squares = n(n+1)(2n+1)/6 Is that right? That would be 46,657,600 feet in 6 seconds. 7,776,266 & 2/3 feet per second!
LivingShadow 06-01-07, 05:46 PM	I believe you have the math right but I'll double check Another way of finding the sum of the squares up to 120 is integration which forms the equasion: 1203 ____ 3 Which simplifies to 576,000. Multiply that by 80 and you get 46,080,000. Then I guess you divided that by the time in a round making it 7,680,000 ft/sec It seems your calculations were very similar to mine answer wise.
ShubNiggurath 06-01-07, 07:13 PM	The sum is 583,220. I did it brute force in excel (30 seconds). Integration is wrong since the numbers are not contiguous. Your formula is right
Kresalak 06-01-07, 07:41 PM	I don't know how to write sigma notation on a computer, but what you want is the series X^2 from 1 to 120, which is, as the above poster said, 583,220. Times 80 feet would be 46,657,600 feet.
ShubNiggurath 06-02-07, 07:18 AM	On a side note, I demonstrated the above formula for fun... it ain't easy I tell ya. It involves some serie manipulation and some lateral thinking. Try it if you want to have fun, it took me almost an hour to figure it out, and another half hour to work on the details
EvilVegan 06-02-07, 08:02 AM	Ok, anyone want to contine this problem by extending it to a sphere of targets instead of a circle?
LivingShadow 06-02-07, 10:42 AM	Defending my use of integration. It can be used to find area under a curve. In this case the curve was X2 and the values were needed between 0 and 120. Besides we are getting similar answers either way.
General_Ridley 06-02-07, 11:52 AM	The sum is 583,220. I did it brute force in excel (30 seconds). Integration is wrong since the numbers are not contiguous. Your formula is right the numbers make an x squared graph. Summing an equation by integration is perfectly allowable. from 0 to 120, integrate x^2
StoneStokes 06-02-07, 02:52 PM	Defending my use of integration. It can be used to find area under a curve. In this case the curve was X2 and the values were needed between 0 and 120. Besides we are getting similar answers either way. They are NOT the same. The sum, S, we are looking for is the same as finding the area under the step function curve f(x), where f(x)=1, if 0<x<1; f(x)=4, if 1<x<2; f(x)=9, if 2<x<3; . . . f(x)=120^2, if 119<x<120; on the interval [0, 120]. This works out to 120(121)(241)/6 = 583,220, by the formula given. Conversely, the integral from 0 to 120 of x^2 gives 120^3/3 = 576,000. Notice that the two numbers are different. That means that the two methods produce different answers. That means that the two methods are measuring different things. However, you are correct in that the two answers are similar. The reason WHY is that the sum S is actually a Riemann sum approximating the integral of x^2. It is an upper bound on the integral because the rectangles forming the sum circumscribe (lie above) the curve y = x^2. For a more detailed discussion, please consult your friendly neighborhood calculus teacher.
EvilVegan 06-02-07, 03:36 PM	Anyone want to do the math on a sphere? :P
Ubasrawr 06-02-07, 03:48 PM	Intergral of 4Pi*r^2 [1,120] or something along those lines. V = 4/3 Pi r^3 is the result of the integral. the number crunching you guys can do on your own.
Electric_Zombie 06-04-07, 12:12 PM	I mentioned this story at the Minis forum. This reminds me of when my friends got into a big argument about how much cubic inches of water would be turned into ice from a cone of cold at some strange angle. At one point they were nearly at each others' throats regarding which equation to use and what the final answer was. At that point, my other friend, Tony, jumped in and shouted: "GUYS! GUYS! IT'S D&D! The world doesn't spin because of gravity, it spins because a god takes the planet..." (makes a motion of spinning a ball) "...and goes, 'WHEEEEEEEE!!!'"
stargate525 06-04-07, 12:43 PM	I mentioned this story at the Minis forum. This reminds me of when my friends got into a big argument about how much cubic inches of water would be turned into ice from a cone of cold at some strange angle. At one point they were nearly at each others' throats regarding which equation to use and what the final answer was. At that point, my other friend, Tony, jumped in and shouted: "GUYS! GUYS! IT'S D&D! The world doesn't spin because of gravity, it spins because a god takes the planet..." (makes a motion of spinning a ball) "...and goes, 'WHEEEEEEEE!!!'" You need to head over to the 'best lines ever' thread and plunk that in. And you need to know the heat of the water, the total amount of water, and the temperature of the cone in order to figure that out...
Kresalak 06-04-07, 03:17 PM	You need the specific heat, the volume of water, the pressure, the temperature, the temperature of the cone, the specific heat of the cone...