How to draw a regular pentagon inscribed in a circle

How to construct an 5-sided polygon inscribed in a given circle.
This KZbin channel is dedicated to teaching people how to improve their technical drawing skills. It focusses on drawing figures from the geometric plane to descriptive geometry and also different systems of technical drawing representation.
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Dubbed by Frank Shaw.
Music by Antonio Fernández Ruiz. antoniofernandez.es/
#Geometry #HowtoDraw

[@saxmam74]

Thanks for the clear explanation! It makes sense, but I'm still coming up about 5mm short. Probably cheap tools, but I love geometric art.

[@christinekaye6393]

I got better results after sharpening the protractor's pencil, but still off a tiny bit, probably due to my less than technical grade protractor.

[@chineduhillary213]

Pl

[@enoisrael7306]

Good work

[@TyPsitoTy]

This is the best and the easiest way of making pentagon! Quality stuff mate !

[@ajeesuji620]

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[@christinekaye6393]

I'm 70 years of age and remember very little of my high school geometry, but I did remember there was a way of dividing a circle into equal parts using a protractor--I just didn't remember how. Thanks for this easy-to-understand video.

[@cloroxbleach7554]

I came up with an equation to do the same thing in this video for those who don't draw well like me. You just need to identify the radius and the side of the pentagon and you're done. It also works on any polygons. Idk if it's been discovered already or what but it works well for me and saves me a lot of time.

[@bananapopproductions1292]

Heheh I thought the intro was how to draw a pentagon

[@dontmindme4466]

same lol

[@wolfboyft]

Me too-- last video skipped a lot of steps too so I got really worried haha

[@kenkelly1154]

It is a Pentagon... your probably thinking of pentaGRAM

[@honeysdiary_]

@@kenkelly1154 Heheh, yeahhh 😃😄!

[@najwa2151]

Same😂

[@wesleyduck]

Thank you for this simple and clear explanation. I learned how to do this when I was in middle school (nearly 60 years ago!). I've been looking for this method for years. Today, I Googled it and I had to wade through eight pages of methods using a protractor. Thank you again for posting this!

[@javeriianavaid3710]

Wes Duckett 60 YEARS?!!WTH HOW OLD ARE YOU

[@6List]

Wes Duckett nearly 61

[@lukala333.]

Thank you for explaining,I have an exam tomorrow,so this will help me atleast get few of the points! :D

[@ArthurGeometry]

Good luck!

[@Caramel77788]

You are the best. After trying different gurus; you were the only one i could follow without hesitation.

[@trelligan42]

This one doesn't seem to stick inside my head too well. Good thing I have such an excellent reference to fall back on.

[@janelleprincesslopez2707]

Thank you so much, it help me a lot , 🤗 , doing my homework ,

[@johnhassan2074]

Just what I've been looking for. Excellent. I will use this very accurate method to produce wooden knobs that have 5 "fingers". Thanks so much

[@averagecornenjoyer6348]

tip: when constructing the middle point of the radius you can just point in R with the compass radius OR and drawing arcs that intersect the circle with center O, and connect the intersections. this removes the steps of using a different radius and drawinng another arc.

[@FUNKINETIK]

Well spotted ; )

[@laurakeeper6133]

Thank u soooo much !😄 We had homework where we had to draw 12 of these all the same size . I couldn' figure it out until I stumbled across ur vid. And now ... I DID IT !

[@KatzeARL]

Thank you very much! I can now make my 5 pointed star for christmas decorations! :)

[@henrytjernlund]

I would suggest in physical application to go both directions from A to B and A to E. Since you already have the end of the compass point at A, then use it twice, once in each direction. Then use the compase to go from B to C and then E to D. And check the distance between C and D to confirm. By going around A to B to C to D to D you increase the chance of an additive error being more pronounced. By splitting the directions you cut any error in half. Also the audio was a bit loud on my computer.

[@artdedaj8613]

thanks bro,it helped me for the test and the homework

[@schoolie8139]

Finally…i’ve found a video explaining the same way my prof does 😭 thank you!!

[@ProphetCaleb.]

thanks alot i have exams on this tmrw and your video was simple and easy

[@rabishamoktan846]

It makes me feel easier to construct pentagon thanks for your help

[@judithvandijkhuizen8331]

Brilliant! I've often wondered how to do this, thank you! I would love a proof of why it works.

[@bigsegs]

Thank you for that, someone bought 6 downlights and wanted one in the middle and the remaining 5 equispaced around a circle, trying to figure out how to get the holes in the right place whilst MISSING ALL THE JOISTS was a real headfuck... Thanks again, amazing what you can do with a piece of string and a pencil

[@calvincengala8581]

Thankyou you have made me learn a simple and accurate step in drawing pentago

[@sivaprakashk3945]

Sir you are superb i lile your classes very very very much😘

[@danielkidane3572]

Thanks for this video. It would be simpler by ignoring line I and Point B & E can be drawn at the same time from point A.

[@Todasanita]

Cuándo tu profe de plastica no enseña nada y tienes que ver estos vídeos. PD: Thank you very much,such a great video

[@love-fb6qt]

oml tysm for real, i got an exam tomorrow and thanks to u I learnt how to do the mtf pentagon 😥

[@lakshminarayana5998]

Thank you so much bro..... Lots of love from India

[@InstintJustice000]

OMG THIS WAS SO HELPFUL

[@alterherrentspannt]

I remember doing this over 50 years ago in high school technical drawing class. It was just a procedure with no understanding of what the parts of the construction was. Nobody pointed out that the length of the diagonal from the middle of the radius to the top was the square root of 5. And then, the transfer of the length to the other side, marked a point where the length to the top was equal to what? I'm guessing that length would be the golden ratio. I don't know; I haven't done the mathematics yet. Excellent video of the drawing of a pentagon.

[@FUNKINETIK]

Yep it’s all to do with the Golden Ratio Phi. From the quadrant AOR, if that was squared off, then you are forming a golden rectangle to the point S.

[@Bekindtoeveryone2]

Thank you for your kind information.🙂

[@jenydangol2106]

Thanks, it helped me a lot.

[@trunyan5080]

This is the fourth or fifth video I watched on this procedure and the only one that explained it clearly. As a former math teacher, I noted differences in the videos. There are those who don't know what they are doing, those who know but can't explain it, and those who know what their doing and can teach it. Arthur Geometry is clearly in the latter category. Thank you.

[@ArthurGeometry]

Thank you!

[@31337flamer]

fast, simple, accurate. good video.. sound could be better :D .. ty v much

[@HappyPotatoe-he7ke]

Dayum! nice vid really made it easier for me to understand how to construct it. You earned a sub!

[@gingerhamlin2935]

Simple. Elegant. Clear. I could listen to your voice all day. :-)

[@christinesibona6553]

Me too!

[@sikhabc30]

What a easy idea todraw such a construction

[@palatianator_007]

Thank you so much for the great explanation. It overlapped perfectly :D

[@tronrevel7751]

this is spectacular 😆

[@TheMusketeers-om5ol]

You Saved me man thanks a million

[@swilliams8328]

Thank you great video!!!

[@marushke9446]

Thank you!

[@nithilakrishnan6611]

Thank you , it's very clear

[@goodguyviz]

thank you so much!

[@my-crazy-fantastic-fanatic]

Thank you so much!! We have engineering drawing this semester, and I couldn't understand a thing at classes... You're an ED messiah!! 😭

[@mgmanju2259]

Nice explanation and clear too thanks sir

[@STATUS__VIDEO554]

Thanks for a classes

[@dammyb9315]

Thanks a lot. That help me in my technical drawing class.

[@ingonemet4282]

Thank you! :)

[@loganquinn9452]

For the sake of efficiency mark points B & E at the same time and confirm DE instead of EA, also no reason to label points O & P since you're not using them. Also a square is usually used to denote a right triangle/perpendicular intersection, but that appears to be a software issue.

[@thilakkannan6580]

Thank you so much for this video

[@TomOS1971]

very simply done

[@seamusmcardle2610]

excellent video,thanks

[@StyleArrangements]

Thank u very much

[@KrakenDoesEverything]

Ty!

[@monu_bishnoii29]

Nice video and thanks

[@raheema0916]

Thank you so much.

[@aglezyerro3403]

I have a 9 on my visual arts class thanks!!

[@therealpc195]

9 out of 100 XD

[@bashbd912]

I really enjoyed your lecture, please what software is this?

[@dnpoudel3741]

Thanks it is helpful to me

[@radosawdobrowolski5984]

Thx for help

[@sigidprabowo4578]

Thank you for your video..

[@MrAuswest]

Hi Arthur, Nice explanation but you could have put in some of the maths involved such as the root (5/4) ratio (or root 5/2 ) of the scribed arc AS to the radius of the circle. My technique involves using the root 5 on 2 length and adding 1/2 to it along the horizontal axis QR such that SR = root 5+1 on 2 or Phi (approx 1.618034) Then by using this length as your compass radius and setting the needle at point R you can draw an arc that touches the circle at 2 points above and below the diameter QR forming 2 of the pentagon points. These points are + and - 30% of the circumference from point R. By resetting the compass to give root 5 - 1 on 2 (= phi or 1/Phi) by setting the compass to the length of the line SO and again placing the needle at point R you can draw a smaller arc touching the circle at 2 more points which defines the base of the pentagon. The final point being point Q the smaller arc defines 20 % of the radius, as do all other sides of the pentagon. Using your diagram and my additions the pentagon 'points' to the left of the page. This can be corrected so the pentagon points vertically by finding the midpoint of OP instead of OR and using either points Q or R to find a new S point on the vertical axis and replacing point R with P in the above paragraph. 🙂 A simple way of describing these techniques is to say that: For any given point of any circle, radius = r, a perfect pentagon is defined by points that are a straight line distance of phi.r (0.618r), Phi.r (1.618r), and 2r from the starting point. Using a 2 x 1 unit rectangle with a 1 unit diameter circle at it's centre and the diagonal of the rectangle gives a clear understanding of how Phi and phi are discovered in this very simple diagram.

[@rongerente]

thx dude..

[@easy-steps-carpentry5745]

Hello Auther, I know you mainly doing the Geometry in these videos and yes good its to see! but I would just like to ask you out of my own interest, if the diameter is divided by 1.618 will it be equal to the required length of each side?

[@bloodreaper3020]

Just saved my Geometry grade

[@mosesbwalya3191]

Thank you

[@akshaykumbhar5242]

Very nice

[@ThiongMichael]

Nice explanation

[@17hmr243]

Thanks for your time

[@mosesontheweb]

For some reason I’m always having troubles with my accuracy drawing a pentagon. The construction is clear, I even tried other ways, but the last test is always if the distance between the last two points is the same as the distance of the other 4 points. I’m always fighting with a gap of about one or two millimeter. Any hints?

[@stanrogers5613]

Better tools (a more rigid compass that stays where you set it, sharper pencils, and an actually-straight ruler) and/or more careful use of the tools you have. Any slight error you make along the way will transfer to any subsequent construction... and then the error will be multiplied by five once you've established the side length of the pentagon. Try it with dividers (a compass with two points rather than a point and a pencil/pen) and a needle scriber on a metal surface (heavy aluminum foil will do), which makes it easier to pick up your marks and makes even the tiniest mistakes quite visible. The whole key to this construction is in making an accurate right triangle with sides of 1 (half the radius of the circle), 2 (the full radius) and the square root of 5 (the hypotenuse) - which becomes the length of the pentagon's sides.

[@emilivan5350]

You are not the only one

[@dnickaroo3574]

If your compass was off, even slightly at any stage, the difference will be magnified. To double-check, walk the compass around the circle in the opposite direction. If there's any difference between the marks made in each direction, the actual points of the pentagon are found half way between them.

[@carlos19zy]

Thanks!

[@akashambrose]

Nice man

[@smallforestdweller6999]

Thank you this was very helpful!

[@holyshit922]

Construction will be clear and easy if he constructs center angle (for pentagon measure of this angle equals 72 degrees) With basics of trigonometry we conclude that golden ratio is useful to construct this angle

[@easy-steps-carpentry5745]

Hello Jacek, if the diameter is divided by 1.618 it will be equal to the length of each side ?

[@mumtasahani]

Nice explanation bro and nice video I like it 💖

[@grinda3578]

ty :)

[@douggief1367]

Love to know *WHY* this works!!!

[@ArthurGeometry]

It works because in regular pentagons, its side and its diagonal are in the golden ratio.

[@cszbmain]

Thanks nice video 😊

[@MrSvenJoli]

how do we KNOW that line segment AS has the length of a side of the pentagon?

[@GreggDevanna]

Yes. Why? This!

[@pierrechardaire8525]

Use pythagoras theorem to find the length of segment AS (assume without loss of generality the radius of the circle is 1). This happens to be equal to 2×sin(pi/5) which is the length of a pentagon segment. The way to find the exact formula for sin(pi/5) is explained at

[@bukarsadiq6625]

LOVELY

[@ajdinhigh8116]

nice ty :D

[@zyppyneoncr8062]

AMAZING video,I'm leaving like and I subscribed I love channels like this,this helps me so much, thanks!

[@johnpauladamovsky86]

This is the easiest way to construct a Regular Pentagon, while keeping everything inside the unit circle... BUT There is no explanation for why line segment 'SA' is the correct side-length of a regular pentagon. We can certainly confirm that the length of 'SA' is equal to √((5-√5)/2) via Pythagorean Theorem, and we can use the Golden Triangle and the law of cosines to calculate that the side length of a regular pentagon inscribed in the unit circle is equal to √((5-√5)/2), but there does not seem to be an intuitive way to arrive at this construction without using a brute-force trial-and-error method. Did this construction just fall from the sky?

[@kenkelly1154]

100% with you sir. Worn out several dry erase markers on this one...

[@LoganSmithtaichi]

What ratios derive a pentagon or pentagram from a typical 6 pointed star (metatrons cube) or a sphere? Ratio is just a measurement corresponding another measurement. So in other words, what is the number in degrees:degrees and mm:mm?

[@dianebenjamin9024]

thanks ,cool

[@lishanzeleke4459]

When he say radius MA the first thing that comes to my mind was young MA !

[@gauravpoojary3277]

How to draw a regular Pentagon inscribed in a circle of side 4 cm??

[@TheBetito123]

How this works???

[@pikachugirl522]

Thanks

[@amitshrestha3187]

Thank u master

[@salamquraan3070]

thanks very very very much for this video without it I would have the midterm today

[@caleblaloo6878]

Noting on this change helps me

[@tonyamechi5401]

what are you using for your geometry online pls tell us

[@marqutox]

awesome

[@lauramaniscalco9114]

Thankyou

[@author_unknown654]

at 1:10, what is the inside circles distance, measurement, and relivants ?

[@vibzrecord]

Thank You So Much

[@ebereobiezue8682]

Thanks This was the clearest I saw

[@juancarlossaavedra4505]

@ 1:12 a circle appears from nowhere !

[@maggichuang6840]

But how do u know AS is the length of the pentagon ?

[@brindaparthasarathy7344]

Thanks a zillion!!!!!!!!!!!!!!!!!!!!!

[@bozothetaco]

best method I've seen. I took drafting in high school so this relates to my way of thinking better than other vids on the same topic. elegantly simple...good job.