Whoa, I have thick hair?

[Ermine]

I've been wondering how thick my hair is lately. It's pretty hard to tell by just looking at it since I can't get it all into a ponytail, and my hair is fine with lots of layers. So curiosity got the better of me and I got almost all my hair into tiny ponytails and added up the circumference of each. I got a grand total of 5 inches! :D This is excluding the hair at the nape of my neck that's too short to get into a ponytail, so hopefully this gives me a good margin of error. I think this might be a new development, since my new growth is a lot healthier than the rest. Thanks for the tips, LHC!

[BlazingHeart]

Em, just so you know, adding up the circumference of different things doesn't give you the circumference of the total.

To give you an easy example, I'll use squares rather than circles becasue the math is easier. If I have a square that is 1" on each side, that means it has 4" of circumference and 1" squared area. If I have a square that is 3" on each side, it has 12" circumference and 9" squared area. So if you have 3 of these 1" squares, you'll have the same circumference as the 3" square, but only 1/3 of the area.

While what we measure is circumference, we're really looking at the area to figure out how much hair there is. Does that make sense?

~Blaze

[Audhumla]

If you wanted to find the equivalent circumference of hair that was long enough to be in a single pony tail you'd have to calculate and add the area of the cross section of each small pony tail and then translate that total cross sectional area into a radius and then a circumference. For example if you added two circles with radii 2 and 3 using your method you get an answer of around 31. If you add the areas and translate the new area to a circumference you get 23.
Sorry to burst your bubble :( I would totally be willing to spend my time calculating a better approximation from a list of small pony tail circumferences if you'd like :)

[Elenna]

That's a lot of hair! Enjoy your thickness!

And what lovely color hair you have.

[Unnamed]

Don't want to be the bearer of bad news, but to get a guess at overall thickness you'd need to not add the circumferences together, but calculate area, add that together, then back calculate to get an estimated circumference...which will be lower than just adding up the circumferences of the smaller ponytails, possibly by quite bit.

For example, five 1" circ ponies have a combined area of ~0.398 square inches (or equivalent of about a single 2.25" ponytail), four 1.25" ones about 0.497 square inches (low ii--2.5" circ), or say, two 2" ones and one 1" one would be a combined 0.716 (or about 3", or mid-ii). If you'd like a closer estimate, I'd be glad to calculate/add them up for you!

[Audhumla]

Oh man now I have a hankering to get sets of small ponytail circumference data and translate them into full ponytail estimates. If anyone with short hair would like to give me a list of small pony circumferences to get an estimate they would be more than welcome to do so :D . . .I have a problem :p

[racrane]

Yeah, I think you got your math wrong. Don't worry, I get my math wrong all the time, too. :D But I"m so glad your hair is healthier. :)

[Lollipop]

Oh, my fellow math nerds. Reading this makes me itch for a little Euclidean geometry :eyebrows:

[Spring]

Since you already have the individual circumferences of each small section, you could divide each individual section by 3.14, then add those numbers up for a total. Take the total (which is the total diameter) and multiply that by 3.14. HTH :)

[Audhumla]

Since you already have the individual circumferences of each small section, you could divide each individual section by 3.14, then add those numbers up for a total. Take the total (which is the total diameter) and multiply that by 3.14. HTH :)
. . Isn't that the same thing as assuming that if you add two 2unit diameter circles you get a 4unit diameter circle which is what she was already doing ? If you add two 2 unit diameter circles (with 2π circumferences) in terms of area you get a 2√2 (=2.83) unit diameter circle with 2π√2 circumference not a 4 unit diameter with a 4π circumference.

[BlazingHeart]

No, you can't just add up diameters like that. It's the same mistake as just adding up circumferences. The ratio of radius (half of diameter) to circumference is NOT just multiplying by pi - you square the radius and multiply it by pi. The thing you multiply by pi increases exponentially as the radius of the circle gets bigger.

~Blaze

[Darkhorse1]

I am so lost by math, but it's interesting. Whatever the case,the OP has great hair!

[Sewas]

Huh? I am so math challenged...so if all my hair is in one ponytail and I use my cloth measuring tape...it is not accurate?

[Audhumla]

Huh? I am so math challenged...so if all my hair is in one ponytail and I use my cloth measuring tape...it is not accurate?
No that is the normal way and it definitely works.
The problem here is that people are assuming that if you can't fit all your hair in one pony you can make a bunch of small ones and simply add the diameters or the circumferences to get an equivalent of a pony with all your hair in it. This is wrong.
As a visual representation of an attempt to add diameters of little pony tails all over your head to get a theoretical big one:
http://forums.longhaircommunity.com/picture.php?albumid=8512&pictureid=110721
You can see here that if you just add the diameters and take the new circle to be a representation of your hair you're overestimating by quite a bit. Since the circumference is just the diameter times pi adding circumferences will get you the same error multiplied by 3.14159 etc

The right way:
Of course there is a way to estimate your hair thickness if your hair is too short for one pony but it involves adding the _cross sectional area _ and not the diameter or the circumference. To do this you would need to measure the circumference of each little pony you've made, divide by pi to get the diameter, halve to get the radius and square the radius then multiply it by pi to get a cross sectional area. After you've got this area for each pony add the area together then that area will be equal to pi times the radius squared for your new theoretical ponytail so divide your total area by pi and take the square root to get the radius then double to get the diameter and then times by pi again to get a circumference which you can then compare to the thickness classification system.

[MissManda]

There was a thread (http://forums.longhaircommunity.com/showthread.php?t=73796) about this a while back. :flower:

ETA: Okay, being the curious person that I am, I HAD to try it to see if it really works. After doing all the math, my final result was about what I get when I measure, albeit a wee bit bigger by 1/8th of an inch. :D

[Ermine]

Wow, I never cease to amaze myself... I would make a mistake like that... :o Sorry about that.

Thanks for the math tip though. It's been a while since I ever encountered a similar math problem. Makes more sense though. You'd think that if my hair was thick, I would have known it already just by the looks of it.

[Mesmerise]

Thanks MissManda! I was going to go look for that thread myself (since I started it and all :o).

So yeah, there are ways to estimate your ultimate circumference, but they're a little more mathematically involved than just adding your ponytails together :).

[Lollipop]

I am sure that other members, including myself, would be willing to help in the calculating aspect of this conundrum :). I can't explain the process very well but i can do the math for you. I've never been a fan of doing calculations with words. I think I'll try to explain. I will try to be detailed and not make leaps for those that aren't comfortable with geometry.

Let's assume that there are three ponytails with a 2" circumference each. To find the circumference of a combined pony you would have to go:circumference--> diameter--> radius--> area--> total area--> total radius--> total circumference.


Blue indicates math for the small ponies
Purple is for the combined pony
Black are explanations

Key:
A=area
C=circumference
R=radius
D=diameter
and I'll use ^ for exponents and (pi) to represent pi=3.14

Formulas:
D=2R
C=2R(pi)=D(pi)
A=(pi)R^2


Process:
So starting with the three ponytails with a 2" inch circumference, you need to find the diameter. Since C=D(pi), if you divide both sides by (pi) you get C/(pi)=D

C=2 in
C/(pi)=2/(pi)
D=2/(pi)
D=0.637 in

Now you need to find the three areas (well, they're the same, but don't forget there are three of them). You need the R for this formula, and since D=2R, R=D/2.

D=0.637 in
R=0.637/2
R=0.318 in

Then plug this into the formula for A

A=(pi)(0.318)^2
A=0.318 in^2

Since there are three, identical ponytails, multiply by three to get the total area.

3A=3(0.318)
3A=0.954 in^2

To go from area to radius, you need to divide by (pi) and take the square root.

(0.954)/(pi)=.304 in^2
The squre root would be
R=0.551 in

And, finally, you need to go from radius to circumference.

C=2(0.551)(pi)
C=3.462 in

This is a detailed, step by step process. It may seem comlicated or long, but that's because I tried to include all the steps so that someone that doesn't understand can read over it a few times if they wish.While it looks a bit like a mess, I am actually anawesome tutor in real life. Sorry, math doesn't translate into words, or over the internet for me.

[Lollipop]

Thanks MissManda! I was going to go look for that thread myself (since I started it and all :o).

So yeah, there are ways to estimate your ultimate circumference, but they're a little more mathematically involved than just adding your ponytails together :).

What I posted is a more detailed, step by step version of Mesmerise's explanation. The same in terms of the process, I just tried to be detailed for the math-challenged folks. I like to help tutor my friends and classmates when I can (although most people don't want to listen:(), and I think I am actually pretty good at it. However, it is much easier in person-on both ends. I usually get a feel for how people learn and try to include as much information to see what would help. Although trying to decipher my last post can be a bit intimidating :o.

[Audhumla]

What I posted is a more detailed, step by step version of Mesmerise's explanation. The same in terms of the process, I just tried to be detailed for the math-challenged folks. I like to help tutor my friends and classmates when I can (although most people don't want to listen:(), and I think I am actually pretty good at it. However, it is much easier in person-on both ends. I usually get a feel for how people learn and try to include as much information to see what would help. Although trying to decipher my last post can be a bit intimidating :o.
I like words and pictures myself. I'm always talking myself through my working in the middle of labs :p So I guess my method would be better for people who like words over properly noted calculations.

[Spring]

There was a thread (http://forums.longhaircommunity.com/showthread.php?t=73796) about this a while back. :flower:

ETA: Okay, being the curious person that I am, I HAD to try it to see if it really works. After doing all the math, my final result was about what I get when I measure, albeit a wee bit bigger by 1/8th of an inch. :D


Thanks MissManda! I was going to go look for that thread myself (since I started it and all :o).

So yeah, there are ways to estimate your ultimate circumference, but they're a little more mathematically involved than just adding your ponytails together :).

This sounds about right ;).

[Spring]

. . Isn't that the same thing as assuming that if you add two 2unit diameter circles you get a 4unit diameter circle which is what she was already doing ? If you add two 2 unit diameter circles (with 2π circumferences) in terms of area you get a 2√2 (=2.83) unit diameter circle with 2π√2 circumference not a 4 unit diameter with a 4π circumference.

.... :laugh: thanks for catching this... so much for taking a short cut :p