Thank you very much for the video! Any chance you could show a formal proof that the arc AB is always going to be 2*pi*r / n (where n is the number of sides of the inscribed regular polygon)?
Quite frankly, there is a 0% chance of receiving such a formal proof and having it be valid, because this is simply not the case. To prove this, look at the finished decagon construction. Now, imagine what the situation would be like had we decided to construct a pentagon instead (i.e. half the number of sides). We would have only divided the diameter into fifths, the second of which (the fourth line here) would have connected to the second point on the pentagon (the third point of the decagon). Therefore, the line connecting C to 4 must also pass through Q. By symmetry, the line connecting D to 6 must also pass through Q. Now, assuming the circle has radius 1, the length of the side of an inscribed regular decagon (or C-D) is (sqrt(5)-1)/2. The length of the line segment from 4 to 6 is clearly 2/5. Because A, P, and Q form a regular triangle, the distance from Q to the center of the circle is sqrt(3). Therefore, by proportion, the distance from side C-D to the center must be sqrt(3)*(5*sqrt(5)-9)/4. But this can't be right, since if you draw a triangle connecting the center, the midpoint of the line, and point C, it would be a right triangle, but the squares of the lengths of the sides don't add up to the square of the radius (1). Therefore, this method does not work in general.
Thank you, the posters should really mention that fact, it is deceptive and someone like me could get the wrong impression. It'd sure be nice and convenient for human beings if space worked that way though.
This is an approximation, not exact... It should not be labeled or considered as exact. As I understand it. geometrian.com/research/RegularPolygons.php
@@MustardPipeLibrary What are you on about? It works fine for a pentagon, the second pentagon point (using the diagram shown here for convenience) is Q4C the 3rd point is Q8E. As long as the vertical line AP is divided by the number of desired polygon sides, the even number points along AP will align with a vector intersecting Q and a polygon point.
Yup...I got the resulting angle of BOA = 36.356 degrees I have no idea if that's the definitive answer (because I'm no mathematician) but I think it's pretty close. The true angle should be precisely 36 degrees.
The construction is never exact owing to the inconsistent nature of physical reality, but the ideological straight lines, angles, and areas correspond to one another exactly according to the postulates you choose to accept. Not to be argumentative, but that's what I believe elevates it to the status of a pure and infallible science worthy of study. If you accept the five postulates of Euclid then everything which follows is theoretically exact (if at times cumbersome) and should produce precision below the margin of a millimeter.
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sorry bud a general method doesnt exist (very famous theorem)
Hola! estoy muy interesado en la enseñanza del Dibujo Técnico en inglés. Felicitaciones y muchas gracias por tu trabajo.
Thank you very much for the video! Any chance you could show a formal proof that the arc AB is always going to be 2*pi*r / n (where n is the number of sides of the inscribed regular polygon)?
Quite frankly, there is a 0% chance of receiving such a formal proof and having it be valid, because this is simply not the case.
To prove this, look at the finished decagon construction. Now, imagine what the situation would be like had we decided to construct a pentagon instead (i.e. half the number of sides). We would have only divided the diameter into fifths, the second of which (the fourth line here) would have connected to the second point on the pentagon (the third point of the decagon). Therefore, the line connecting C to 4 must also pass through Q. By symmetry, the line connecting D to 6 must also pass through Q.
Now, assuming the circle has radius 1, the length of the side of an inscribed regular decagon (or C-D) is (sqrt(5)-1)/2. The length of the line segment from 4 to 6 is clearly 2/5. Because A, P, and Q form a regular triangle, the distance from Q to the center of the circle is sqrt(3). Therefore, by proportion, the distance from side C-D to the center must be sqrt(3)*(5*sqrt(5)-9)/4. But this can't be right, since if you draw a triangle connecting the center, the midpoint of the line, and point C, it would be a right triangle, but the squares of the lengths of the sides don't add up to the square of the radius (1).
Therefore, this method does not work in general.
Thank you, the posters should really mention that fact, it is deceptive and someone like me could get the wrong impression. It'd sure be nice and convenient for human beings if space worked that way though.
This is an approximation, not exact... It should not be labeled or considered as exact. As I understand it.
geometrian.com/research/RegularPolygons.php
@@MustardPipeLibrary What are you on about? It works fine for a pentagon, the second pentagon point (using the diagram shown here for convenience) is Q4C the 3rd point is Q8E.
As long as the vertical line AP is divided by the number of desired polygon sides, the even number points along AP will align with a vector intersecting Q and a polygon point.
@@wizrom3046 well it does seem to work as you say if you put a ruler against the screen.... but a formal proof would be satisfying
why the connection was done between point Q and exactly point 2 ?? this is my Confusing question
My sir told me that it is a rule..
Erroni Samuel is a rule!!!
@@eugenion5340 lol yes
This construction does not produce a regular decagon
Mathematical idwalism allows it to.
Mathematical idealism would require a proof.
how do you know the measurement between the parallel lines?
it's a random length
Thank you for uploading these videos
hi dabi
@@crappy_cobalt9622 yo, what's good?
nothing special. got sent here for an art assignment
Thank you so much!!
How to draw 24 sides in a circle
Thanks dude
Tq so much sir
thanks From Bangladesh
I just loved your videos.
Very educative
Great video
thanks for giving to knowing about polygon
what r u doing over there
not exact
Nice
Grandeee
esta muy bienn
+jesus_968 Gracias! Éste es el 1º comentario del canal! ;-)
thank u you tube
Nice work
Yup...I got the resulting angle of BOA = 36.356 degrees
I have no idea if that's the definitive answer (because I'm no mathematician) but I think it's pretty close.
The true angle should be precisely 36 degrees.
Most of the inaccuracies are due to human error.
REALLY HELPFUL
This method does not work.
why point 2 ?
Because point 1 will produce a polygon with twice as many sides. Try it out for yourself; it works for all numbers 2 and above.
how do we get the fifth line to go through the center of the circle? or is it half of all the sides of our polygon?
lol i got it:)
This not exact so we can't believe this procedure.
+Online To The Brain Never is going to be exact :)
The construction is never exact owing to the inconsistent nature of physical reality, but the ideological straight lines, angles, and areas correspond to one another exactly according to the postulates you choose to accept. Not to be argumentative, but that's what I believe elevates it to the status of a pure and infallible science worthy of study. If you accept the five postulates of Euclid then everything which follows is theoretically exact (if at times cumbersome) and should produce precision below the margin of a millimeter.