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Now we are going to draw a regular pentagon inscribed in a circumference,

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and this is the most difficult exercise regarding polygons, okay?

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So please pay attention, stop the video all the times you need it,

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and make me questions in class if you have doubts, okay?

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The first thing we are going to do is to draw a diameter, as we usually do, okay?

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Okay, and now we are going to draw another one perpendicular to the previous one.

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Okay, so I place here the square and down below I put the cartabon and I turn the square.

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Okay, and I slide it till the center of the circumference.

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Okay, I have two perpendicular diameters.

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Yeah, I'm going to put names to the points so we can understand each other.

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The center of the circumference is going to be O and this is going to be A.

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And also it's going to be the first vertex of my pentagon.

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OK, this is going to be B. It's not going to be part of my pentagon.

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This is going to be C and this is going to be D.

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OK, C and D are not parts of my of my pentagon either.

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okay now I'm going to find the middle point of the radius OD okay so what I

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have to do is to we are going to draw kind of a sector line okay so I'm going

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to place the compass in D okay and with the same radius just the radius OD

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I'm going to make an arch that cuts the circumference okay so then I'm going to

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join these two points okay where the art cuts the circumference okay those points

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are not important for anything well just for this for the sector line that we are

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drawing but this point is not part of the circumference not neither this one

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okay and here we have the middle point M okay the distance OM is supposed to be

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the same that OD, okay? Let's check it. Let's check it with the compass, okay? DM, oops,

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here, DM, okay? It must be the same, okay? Okay, MO. This exercise, as I have said, is

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the most difficult because there are a lot of steps, okay? If you make mistakes in one

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mistake you will have more mistakes over and over okay so now what we are going

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to do is to place the middle of the compass in M and using the radius MA

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okay the pencil in A we are going to make another arch okay cutting this part

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of the diameter okay this radius and this point is going to be called N okay

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n is not in the middle of this radius anymore okay here there is a golden

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proportion okay or golden ratio but this we will talk about that in further years

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okay and the most important thing that you need to know is that a n okay a n is

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the misser of the side of the pentagon, okay? AN is the side of the pentagon, okay?

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The polygon of five sides. So what we are going to do is to take this misser, that's

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why it's important to have a very good compass, okay? And placing the needle in A,

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we are going to make an arch okay that cuts this circumference four times okay

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first time second time okay this is going to be number two and this is going

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to be number five okay the vertex of my pentagon now I'm going to place the

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compass in two okay making the point number three three okay and I'm going to

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place my compass in five okay always is the same measure okay a and yeah do you

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see the same measure and we put it here okay this is point four and just check

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it okay the same measure must be here okay between four and three oh yeah must be the same measure

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okay the distance between the five points is the same we have divided the circumference in five

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equal parts now we are going to draw joining in each point each point each vertex we will have

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our regular pentagon that is so so beautiful and so so perfect