SCALING PATTERNS
ok hello everyone! today we're going to talk about things you can do with algebra in your real life.
under a cut because pictures and long
that little squiggly equals sign mean congruent, which means these triangles are to scale with each other. (i think that's right????? i hope i'm not making any algebra teachers out there cringe) anyways what's important is those triangles are to scale. so how do you find x? to do it you need at least two values of the first triangle, one of which needs to be the corresponding side that you're trying to find. then you set up the equation like this:
so in this case, the 8 side and the 12 side are corresponding sides, and the 3 and x sides are also corresponding. SO the 3 and the x are on the top of the fractions, and the 8 and 12 are on the bottom. and since the 3 and 8 are on the same triangle, they're in the same fraction.
SO YOU'VE GOT YOUR EQUATION SET UP. now you have to solve it. you do that by multiplying the two diagonal values that you have, and dividing your answer by the remaining value, and that's how you get x.
sorry i'm not a super math whiz, so i can't go into WHY exactly you set up and solve the equation like that, but it's because of algebra reasons. i assume if you go through the steps to solve any x type equation you get that. (the answer to this one is 4.5 if anyone was wondering.)
anyways, what does this have to do with scaling patterns? EVERYTHING!! think of that little triangle as the pattern you have, and the big triangle as the pattern you want to get. you know how big the pattern you have now is, and you know what percent it's at (100%), and you know how big you want your other pattern to be, you just don't know what percent to scale it to. that's x.
so say you drew up a pattern that you want to make big. you make a pattern dummy and find that it's all fitting together right, all you need to do is scale it up, first you measure how tall it is now.
so your pattern as it is now, at 100%, makes a plush that is 6.5 inches tall. you want it to be 16 inches tall. so set up the equation:
6.5 is the pattern height value you already have, and 100% is the percentage you already have, so they go in the same fraction, size on top, percent on bottom. then in the next fraction you know the height of the bigger pattern, so you put it on top next to the other height, and the percentage, which you don't know, is on the bottom. solve for x. (246.2%)
now you take your pattern to a copy store, or scan it into your computer, and get it printed at 246.2 percent.
NOW. say you started with your pattern in photoshop or something, you printed it out, and you made your pattern dummy. then you do all the math things and you go to print it out, and you realise that you printed your original test pattern at 87% instead of 100%!!! crap!!!
well, do the equation again, but instead of putting the original pattern size at 100%, just put it at whatever percent you started out with, 87% in this case. then solve for x.
then print that pattern out!
note that that last half with the 87% only applies to patterns that you are printing from an existing file. so like... you draw a pattern in photoshop and print it for a 6 inch plush, then you want to use the same file to print for a 16 inch plush. if you're just working from physical paper to begin with, and THEN you're scaling it, you're always starting at 100%.