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on this video we are going to solve the polygons radiation this is an a4 page

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and we are going to start with the lowest part of the page okay so you have to measure

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20 millimeters here 20 and 20 on the other side of the page this is the

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bottom part of the page okay so if we connect these two marks these two marks

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there and there we will get some horizontal line you can see okay a

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parallel line to the bottom of the page there we have to place the midpoint the

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midpoint in this case in this kind of page a4 this is 21 21 so the midpoint is going to be 10.5

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105 millimeters that's the midpoint and we are going to measure 23 to each side

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23 to one side to the left and 23 to the right be precise please this is a and that's b

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good we are going to start so this is the segment and this segment is going to be

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shared as a side with all the polygons all together okay so this is the segment and we

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are going to draw now the triangle for drawing the triangle you take with the compass the whole

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segments a b there a b and draw um the same with the same radius a b to the other side okay

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so that's the solution for the equilateral triangle i will draw it later now

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this point we are going to call six that's going to be six

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okay and now you're going to draw placing with keeping a b as a measurement okay it's a radius

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this distance now you place the compass on six and draw the circumference that that

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circumference that pass through a and b sorry about that a and b here i have a problem

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with the compass okay so that's the hexagon be careful with this kind of mistakes okay having

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some troubles with my compass on my own okay so if you can adjust the compasses

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you can make these screws tighten okay so this is harder to move good so once you have this

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you have the two arches you have the circumference so this is going to be half the hexagon we already

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did this on the polygon on the circumference division and worksheet so now you're going to

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measure a b to take this measure a b okay that's a b and from this point sorry from this point

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on you transport a b and from this other point you do the same okay so we are just transporting

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this measurement one two times three times and four times we already have a b and that

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the rest is going to complete the hexagon now we are going to connect the dots okay

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so this is the hexagon be precise connect exactly with the point okay you don't need to invent

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anything here you just connect the points you placed that's the hexagon okay so that's the

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hexagon and you are going to draw also the the equilateral triangle this is the

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equilateral triangle AB6 so equilateral triangle and hexagon now

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you're going to connect six with M okay so if you connect six with M you will

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divide the page into half okay so you will draw this vertical axis line so we

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have connected 6 with M okay great and now the point where the arc crosses that

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vertical line we are going to call 12 that's going to be 12 this is going to

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be the center of the dodecagon dodecagon okay 12 sides dodecagon and um good now we are going to

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continue with the square for placing the number four center um we are going to need the square

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okay this ruler this ruler is the square not this one okay this is the bevel we need this one

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okay so with this square you can also do this to keep the angle or even if your tip is rounded or

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not so clean or broken or whatever you can also place this ruler here on top and move the square

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till you have the 45 degrees angle placed on a so once this line is on a you can take it out

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one minute okay so you can take this out and draw the angle okay so there you have the 45

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degrees this point is going to be number four great and now once you have number four placed

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and we need number five okay so for number five we are going to draw the segment by sector of four

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six okay so the midpoint we're going to place this midpoint for placing this you need

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the compass and you're going to draw i'm going to erase this a little bit because i don't need

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this arc to be longer

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Okay

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So from six and from four

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You're going to draw a couple of arches with any radius. So from six

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with one radius and

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From six

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to the other side with the same radius

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and we are going to keep the radius from 4 oh sorry and from 4 to the right to

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the left okay again with any radius of your choosing you just draw from

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from four one and two and from six one and two so they cross each other into two points

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we are going to place those points exactly this point and this sorry about the light

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and that other point you have to be precise here and if you connect these two points you

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will place the midpoint exactly in order to keep the cleanliness we are going to

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mark only these two segments and only the midpoint that is going to be point

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five okay now is the moment to draw the square on the pentagon okay first the

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square for the square okay all the circumferences we are going to draw and

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pass through a and B so first circumference from four passing through

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a and b sorry okay so that's it okay that's a conference oh my god sorry okay sorry about that

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um the compass is really not in the best situation okay so this is a circle center four

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this one passing through a and b okay oh sorry okay sorry about that again

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um center four passing through a and b great and now we need right angles for for drawing

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right angles you need the square or the bevel square or bevel so you place on a on b for example

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passing through okay so passing and crossing this arc the arc four center four and you do the same

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with a okay you will see there is a coincidence there so here

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this arches almost pass near through these points okay these points we are going to mark

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and we are going to connect and by doing that you have the square okay that's the square

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center four passing through ab perpendicular lines and correct now the pentagon

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all the polygons the good part of all polygons is that we can use this axis to get the top point

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so first draw the circumference center five again passing through a and b

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so there center 5 sorry center 5 a and b so we draw the circumference for the pentagon okay

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okay center 5 and this is going to be the top vertex of the pentagon because it's an

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other pentagon okay and now we are going to transport a b this is a b i'm going to zoom

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in a little bit okay so we take a b there a b and transfer it to the circumference center five

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there from a so this is a b there and this is a b there okay this is really really close

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really close to the arc here okay let's see a little bit lower okay

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to the arc of the hexagon okay here is a little bit lower great so check that you have

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the top vertex and here again we have transport we have transported this distance a b again a b

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here and from b you do the same there okay so ab here ab there and now we are going to connect

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the pentagon great so we have the triangle square pentagon and hexagon good let's continue

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now we are going to draw the dodecagon for it that is the biggest one okay so don't be scared

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because this is the bigger your drawing is going to get you're going to place the compass on 12

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and pass through a and b again so you draw a very big circumference so

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that's it

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ok, so this is the idea

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you place the compass

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on 12, there

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and draw the arc around

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passing through A and B

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as always

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centre 12, passing through A and B

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that's the dodecagon 12 sides so now we are going to transport this distance okay

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on the contour of the circumference so from b you take the distance one two

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1, 2, 3, 4, and 5, and here you do the same from A to the left, so AB, 1, 2, 3, 4, 5, great,

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Here, I have, well, a mistake, okay? Normally, if you do it right, and you calculate the 12 with accuracy, and do everything right, this distance should be AB.

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you can see here mine is not okay it's shorter and okay have that in mind your polygon needs to be

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again 12 sides okay so i'm going to draw the 12 sides the 12 sides so you can see

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okay so this is me connecting the dots connecting the points for getting a blue

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dodecagon with side AB again this is wrong okay this distance should be

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longer but you have a general idea about what you should do okay okay so this is

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the dodecagon 12 sites good so this is me just i have colored everything out so you can see the

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difference between the different polygons okay this is the radiation of the polygons okay and now

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we have reached the tricky part because we now we have to place the rest of the sensors okay

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and and we are going to divide this distance from 6 to 12 into six parts so we we will get

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the centers we need for doing that we are going to apply thales theorem and pay attention because

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this is not not difficult but you have to understand so i'm going to use for example

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this beautiful green color so this distance this distance 12 6 we are going to divide into six okay

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so for dividing any any segment into equal parts we need a line in any direction it doesn't matter

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if you have an obtuse angle or acute angle okay in order to keep here cleanliness and so on we are

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going to use for example this line okay that line in any direction any direction okay and we are

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going to measure there I'm going to zoom in a little bit the same six distances

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okay you can guess that we are going to use centimeters because they are easy to

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get okay but you can use any distance so from 12 you measure one two

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two three four sorry four five and six that's it okay from 12 in any direction this line you can

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do it here too okay and that's the distance this we don't need okay we could erase it and now

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we are going to connect the sixth division with 0.6 like this like this okay so this

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we connect with six okay great and now we are going to draw parallel lines very carefully

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so the ruler doesn't move the rulers don't move i'm going to zoom out a little bit okay so i want

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to copy this line you place the ruler there and you place this other one beside okay very close

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tightly and now you are going to move this one this stays in place so move it and draw

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move it and draw be careful that the rulers doesn't move not one of them

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if they move start again please and move

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okay so you can see they are parallel and they keep the distance between each

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other the thales theorem application is based on the fact that if these

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distances are the same these distances are going to be the same too okay but we

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didn't know that ones okay so you start with these ones that we know that we

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know they are one centimeter apart and using that and connecting this with this

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this is really important the last division with six and keep the parallels

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going so you divide this into the same distance okay good once you have that

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you can name the points the centers okay so you can guess that this is going to

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be seven eight nine ten and twelve and the rest of the procedure is really

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really easy because now i think you you got it already now you are going to draw

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circumferences on each of the centers and transport ab distance into the contour of

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the circumferences okay so we are going to keep doing one well one for the moment so you can see

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For example, the heptagon, okay, is the following one, 7, heptagon, okay, I'm placing here in 7, 7, from 7 to A, or B, it doesn't matter.

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and we draw the circumference i'm zooming out we draw the circumference 7ab okay no there okay so

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7 from 7 to a and on that contour this is an odd again polygon so this is going to be the top

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vertex that point and we are going to transport three times okay so

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this is a b you transport the circumference the distance sorry the segment on the circumference

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seven one time two time oh sorry okay again so circumference center seven you take the distance

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a b a b and from b you take the distance one and two okay you have to cross the there the

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circumference forget about the phallus procedure okay focus on that point and from from a we do

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the same a and b okay a and b a and b so now we are going to mark the points and connect them okay

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so we are going to use for example another type of color so this is the

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the heptagon, seven sides, okay, that the heptagon, great, now we are doing the same with the rest of

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the polygons, okay, so this is the hexagon, sorry, the octagon, center eight, the nonagon,

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nonagon center nine nonagon nonagon and so on good so here you can see

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all the circumferences all the radiation of circumferences okay so from eight this is eight

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nine ten and eleven circumferences okay the biggest one is 12 good and now the idea is to

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transport this measurement okay having in mind that you don't have to mistake one circumference

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from another okay so something you can do is that the first arc this one you can use

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for all the circumferences

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because this center is the same for all of them

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so you can use this one

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the first one you did for the triangle

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you can continue here

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and continue there

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so you will get all the points marked

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on one direction and on another okay i'm going to zoom in a little bit so you can see

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okay so this arc you can continue this arc you can continue and you cross each other

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you cross through sorry all these

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circumferences that pass through a and b okay a and b this should be cleaner

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and here the same and and now you have to continue transporting the a b measurement

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on the contour of each of the circumferences so you have to be really really tidy you have to be

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really really clean and you shouldn't confuse one circumference from each other okay for another

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sorry and so we are going to transport a b again a b on the contour of the octagon okay so again

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from B sorry so this you already have but you have now you have to use a point and you transport

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very carefully on the contour one and two and from a you do the same from this point that one

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that one and don't mistake one circumference from another okay so again you transfer this distance

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on the circumference whose center is eight okay it's that one and you keep doing the same on nine

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this one on 10 this one and on 11 okay okay so that's the contour of the

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octagon I'm just connecting here the dots this is another dot and that's

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another dot okay okay now I'm transporting the distances on the

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different circumferences so if you are clean enough you don't mistake one

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polygon for another okay so for example in here in this console we already did

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this is the nonagon and from these points I'm going to trace the decagon

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okay and finally here I'm going to draw the undercargon 11 sides okay and we do

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the same here there this is AB all the time remember all the time AB on the

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odd polygons we can mark the top points of the undecagon on the nonagon okay the

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heptagon I already have and now I am going to draw if it's clearer for you

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we can mark the points and connect them okay so maybe it's easier for you if you

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mark the points before drawing so you don't make mistakes so that's for the

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nonagon nine sides decagon ten sides this should be longer okay and the last

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one is the undecagon 11 sides okay I'm going to connect everything out I will

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show you so here it is this is the end of the polygons radiation okay if you

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reach this point is because you did it so congratulations and if you want to or

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need to review any part you can go back you can pause or ask the teacher if you

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have any doubts okay so that's it this is the radiation of all the polygons

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that's the general view I already told you there are some minor mistakes here

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okay this should be bigger in this two especially okay but in general this is

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the the general view of the of the polygons have in mind that i get transported i insist

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the a b side into the different circumferences that pass through a and b and have centers on

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all these points all these divisions you have here okay great thanks for listening and see you soon