TIP: Quickly Divide a Circle

all right hello YouTube uh I wanted to show you guys a real quick tip um I'm going to try and make this a fast video um you'll be able to stop watching before the end of the video if you don't actually care about the math involved here you just want to see or just want to be able to use the quick tip um so the the tip relates to finding um some arbitrary number of uh points around the outside of a circle so you know dividing a circle in half is easy enough or in quarters but if you need to find like nine points even points around the outside uh circumference of of a circle um that can get to be a little bit tricky you can do it with a protractor you can do it with a compass um I usually do with the compass just you know guesstimating and then making small adjustments until I get it right not a great way to do it uh very error prone uh Plus getting that last little bit of precision is a real pain doing with the protractor again it's kind of a pain it takes a little while um and there's a high uh error rate only in that there's a stacking tolerance issue okay so like if you if you're you know some very small percentage off here by the time you make you know nine uh angle um you know lines around the outside of the circle here you're going to end up with potentially nine times the eror that you started with so I'm going to show you is a way to do it the first time every single time incredibly accurately um just with a set of calipers and a compass you can do it without calipers um if you have a calculator that'll spit out fractionals you can do it with a ruler um but I recommend use Cal calipers um it's going to be far more accurate if you do need a calculator that will spit out fractional values um I recommend power 1 SL it's a uh scientific calculator program for your smartphone um it's available for free in the Android and Apple Store but onto the actual trick um so the other day I was watching a video by Jack howling and he was measuring around a circle to make a uh a lazy Susan and he needed to divide it by five and he just kind of threw this number out uh 1.18 um and he multiplied uh the radius of the circle by 1.18 um set his um or you know set his cpers um and subsequently set his compass and then measured around and it was bang on dead accurate uh first time um no problem he didn't explain how he did it though so that's what I'm about to do um I posted the in the comments how he did it as well um because his comments uh were just flooded with people asking about that 1.18 value and where it came from and how he got it um it's actually just a little bit of really simple um like high school geometry um so uh let's Jump Right In um I'm just going to just pick you can pick any number you want the the formula is going to work all the time and I'm going to show you the formula really fast and don't let this scare you off because you don't need this I've pre-calculated all of the uh multipliers for you from like 3 to 20 and there'll be in the comments below um so you never actually have to type this provided you're dividing by you know an even number you know like 3 20 you know whatever if you want um a number I didn't provide then that's where the formula will come in so what you really need to know is s of however many degrees you want to cover divided by two times two okay and degrees is just going to be 360 divided by however many slices you want to make the the circle cut up into okay so for our example here we're going to use seven um I'm going to wedge my calculator a little bit so hopefully the glare doesn't uh come off the my overhead light here so in the event um that we want to divide um this circle and this is a 4in circle so 2in radius 4in diameter um if we want to divide this into seven again without a protractor without making much of fiddly adjustments with a uh Compass um the easiest way to do it is to take this formula um to get a multiplier so and again you don't have to do this you'll be able to just start with the multiplier if you just look in the comments but if you need to figure it out for yourself um for any particular value this is how you'll be able to do it so I'll go through the whole process uh doing doing the math which again you won't have to do but I'm going to do with the math and just so you can see how fast it is to actually do it okay so first we need to find our degrees so 360 divid 7 and now we get get into our formula okay so 51.4 28 that's our degrees divided by two takes care of that the sign 43388 y y y times 2 okay that's our multiplier so our multiplier for seven is going to [Music] be 8 6 7 7 yada yada yada let call that 8 in fact I'm just going to store that value on my calculator now we take our radius in this case it's two and we're going to multiply it by a recall value which is going to give us um a value of um 17355 um Etc so this is what we need to set our calipers to well really this is what we need to set our Compass to um we're going to use our calipers to set our Compass just because it's the most accurate way to do it at least the most accurate way I have really spending more time than I need to on this um generally in Geometry you only go to the second decimal place and that's close enough all right and we will set our Compass using our caliper value your caliper distance all right so we're going to use this is our starting point and I'm not going to make marks on this pass I'm just going to walk the circle um so we're just going to go one two three four five six and I'll I'll Zoom this in so you can see really close seven okay it's literally dead on okay it's right on the mark okay you're not going to ask for a a a a more precise way of doing this okay and it to work with any value just using this formula so if you want to uh stick around and see kind of what this math is actually doing um as opposed to just using the values out of the comments um by all means stick around and really quickly I'll show you what what's actually happening here so let's draw Mark here um and let's measure this out or not measure this but so ultimately what we're after of course is this distance right we want the straight line distance between two points on the outer circumference of a circle now the easiest way to get that at least the easiest way I know of and there may be an easier way I'm no mathematician is to turn this angle which in this case you know this is the entire spance that we're trying to get um you know this is our 360 divided 7 that's that's how we're getting this angle uh is simply to divide it in half divide the the degrees and half and that's going to turn this into a right triangle or rather two right triangles okay now that we have a right triangle we can just use our regular U you know sign function on our calculator so here we have our hypotenuse we have our adjacent and we have our opposite um the we don't need this at all right now uh the sign is literally just the opposite angle the distance here divided by uh the hypotenuse um we have a button for that on any scientific calculator called s sinin um so in this case so we're dividing this in half here that's this divide by two so degrees divided by two that's turning this into the two right triangles we're using the sign function which is this divided by this which is going to give us a ratio okay that's going to tell us um what percentage of this line this line is okay then we're so that's our sign function then we need to double it multiply it by two to get from here all the way to here so we're not just getting the distance um to here that's it that's all the math if you ever need to figure this out for a value that's not provided in the comments that's all you need to do and that's that's how it works and why it works um so hope you like this if you did please like And subscribe and if you're one of my existing subscribers or not one of my existing subscribers um there are very few of you right now um let me know if you actually like these kind of tips and trick videos um normally you know lately at least I've been doing a lot of build videos um instead of like reviews and things like that um so uh let me know if uh you want to see more of this kind of stuff in the future I've got loads of them um not necessarily math based but just tips and tricks around the shop um and I'll talk to you later and I'll bring you some more videos soon

Channel: TabLeft Workshop

Views: 108,972

Keywords: math, Perfect, papercraft, Tricks, howto, raymond, woodcraft, pie, trick, metalwork machining, metal, wood, Tips, geometry, lesson, paper, mowder, woodwork, tutorial, pi, trigonometry, tip, ray, circle, Chords of a circle, chord, chords, coord, cord

Id: 8Rg2DT7BOE0

Length: 10min 38sec (638 seconds)

Published: Tue Nov 04 2014