### Getting All Mathematical

Jun. 16th, 2011 02:39 am**kiyakotari**

So I've been thinking about the doll crew. Big surprise, huh? Anyway, I've been specifically thinking about the heights of the characters, and the relative heights of the dolls that represent them. Because these are the kinds of things that are important to me.

Wren is always supposed to have been 5' 7" tall. Jian Yuan's height has shifted a bit over the years (he and Wren were originally the same height), and he is supposed to be 5' 4" tall. Darryl has always been right around 6'. Talon has fluctuated a bit, but is generally right around the same height as Darryl, as is Tekla. And so on and so forth.

Wren 2.0 is a 60cm doll. Darryl 2.0 is 65cm, the intended Talon 2.0 is also 65cm, and Tekla is 65cm-66.5cm depending on what feet and shoes she's wearing. Since Wren is pretty much in the middle of the group, and since the height of the doll is a conveniently even number of centimeters, I worked off of her. 5' 7" is 67". There are 2.56 centimeters in an inch, so Wren is 171.52cm tall. Dividing the height of Wren 2.0 (60cm) by 171.52cm gives us .349813432, or thereabouts.

Now it's time to check this. If Darryl is supposed to be around 6' tall, is 65cm the correct height for the Darryl 2.0 doll? 65cm divided by .349813432 is 181.82cm. If we divide that again by 2.56, we end up with 72.59", or 6' ½". So yes, Darryl 2.0 is (delightfully) just the right height. From this, I can infer that Talon 2.0 and Tekla are also the right size without having to work their exact heights out.

This means that my formula for determining the necessary height of a WUNPO doll based on the height of a character (when "C" is the height of the character in inches and "D" is the height of the doll) is:

By this formula, the total height of Jian Yuan 2.0 needs to be 57.3cm. We can also reverse the formula, as we saw with Darryl, to determine the height of a character based on the doll that represents them:

Using the reversed formula, Rupali (doll is 58cm) is just a hair under 5' 5" tall, which is perfect for her character (she's supposed to be between Wren and Jian Yuan in height, but I never set a specific height for her). And Rafe is 5' 9½", while Laith is just a smidgen over 6' 6". Again, perfect for the characters (I had been concerned that the Laith doll was too tall, but he's supposed to be 6½', so that's spot on).

The awesome thing about this isn't consistency in the doll collection, though. It's the fact that I can apply this formula to

This entire thing was brought on by the fact that I'm at work, and am supposed to be studying for my first attempt at an IAHSS certification, which my job now requires. I test in four hours. So far, only two of the six officers in my department who have taken this test have passed it. If we fail it, we have thirty days to prepare for a second attempt. If we can't pass on the second try, we're fired. I haven't read the book yet, and it's 38 chapters long.

Yeah. To say I'm unenthusiastic about this textbook would be an understatement.

EDIT: Passed the test. It was actually really easy (and I

Wren is always supposed to have been 5' 7" tall. Jian Yuan's height has shifted a bit over the years (he and Wren were originally the same height), and he is supposed to be 5' 4" tall. Darryl has always been right around 6'. Talon has fluctuated a bit, but is generally right around the same height as Darryl, as is Tekla. And so on and so forth.

Wren 2.0 is a 60cm doll. Darryl 2.0 is 65cm, the intended Talon 2.0 is also 65cm, and Tekla is 65cm-66.5cm depending on what feet and shoes she's wearing. Since Wren is pretty much in the middle of the group, and since the height of the doll is a conveniently even number of centimeters, I worked off of her. 5' 7" is 67". There are 2.56 centimeters in an inch, so Wren is 171.52cm tall. Dividing the height of Wren 2.0 (60cm) by 171.52cm gives us .349813432, or thereabouts.

Now it's time to check this. If Darryl is supposed to be around 6' tall, is 65cm the correct height for the Darryl 2.0 doll? 65cm divided by .349813432 is 181.82cm. If we divide that again by 2.56, we end up with 72.59", or 6' ½". So yes, Darryl 2.0 is (delightfully) just the right height. From this, I can infer that Talon 2.0 and Tekla are also the right size without having to work their exact heights out.

This means that my formula for determining the necessary height of a WUNPO doll based on the height of a character (when "C" is the height of the character in inches and "D" is the height of the doll) is:

**(C x 2.56) .349813432 = D**By this formula, the total height of Jian Yuan 2.0 needs to be 57.3cm. We can also reverse the formula, as we saw with Darryl, to determine the height of a character based on the doll that represents them:

**(D ÷ .349813432) ÷ 2.56 = C**Using the reversed formula, Rupali (doll is 58cm) is just a hair under 5' 5" tall, which is perfect for her character (she's supposed to be between Wren and Jian Yuan in height, but I never set a specific height for her). And Rafe is 5' 9½", while Laith is just a smidgen over 6' 6". Again, perfect for the characters (I had been concerned that the Laith doll was too tall, but he's supposed to be 6½', so that's spot on).

The awesome thing about this isn't consistency in the doll collection, though. It's the fact that I can apply this formula to

*anything*that I want to make for the dolls, to make sure it's in scale, as long as I know the full-size measurements of the item. For example, a WUNPO doll-scale AA12 shotgun would be 34.67cm (13.54") long, and the seat of a dining chair should be 16.12cm-17.91cm (6.3"-7") high.This entire thing was brought on by the fact that I'm at work, and am supposed to be studying for my first attempt at an IAHSS certification, which my job now requires. I test in four hours. So far, only two of the six officers in my department who have taken this test have passed it. If we fail it, we have thirty days to prepare for a second attempt. If we can't pass on the second try, we're fired. I haven't read the book yet, and it's 38 chapters long.

Yeah. To say I'm unenthusiastic about this textbook would be an understatement.

EDIT: Passed the test. It was actually really easy (and I

*still*haven't read more than five chapters in this book). Not sure what all the fuss was about, but have a feeling I'm going to be tutoring several of the guys over the next few weeks.
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Date: 2011-06-16 02:22 pm (UTC)nagasvoiceAnd yeah, those kind of calculations are helpful on other things of scale, I think I end up rethinking it every time instead of remembering what it was!

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Date: 2011-06-16 05:52 pm (UTC)kiyakotariwith the highest score so far in our entire department. Seriously. It was 100 questions long, and we had 75 minutes to take it. I finished it in less than 25 minutes, then spent about 10 minutes sitting there waiting for my boss to come back so I could submit it and get my approval to leave.I have a sneaky suspicion I'm going to end up playing "tutor" to several of the guys over the next couple of weeks.

And I've always just kind of guesstimated the scale, but last night I decided to figure out exactly what the numbers were for this group, so that I can get their stuff right. (I hate math. My decision to do this is evidence of much MORE I hates this textbook. Really, it just needed a copy-editor, and it would have been fine. But it was full of contradictions and typos and just...crap.)

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Date: 2011-06-16 08:48 pm (UTC)greenjudyThose sure look like useful numbers to me. MMmmmm....scaaaaale....

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Date: 2011-06-20 11:51 pm (UTC)kiyakotari## no subject

Date: 2011-06-17 10:04 pm (UTC)shipwreck_lightAlso, your math. It's incredible. Alas, according to it, my various doll couches... not so much.

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Date: 2011-06-20 11:54 pm (UTC)kiyakotarifartoo large for it.