Even though I know a true regular heptagon is not constructable in the classic sense this approximation is so impressive. Your eyes tell you it is a real regular heptagon, but my mind knows it cannot be exact. It's still impressive.
My Maths teacher at high school was a a droning Scot who's only use was as a cure for insomnia. :-/ Consequently I learned next to nothing, which forever blighted my career in Aerospace. I picked up some basic competence late as required. I now need to make a bespoke tool for removing a part on my Ovlov - which I won't buy from 'them' for £75! If I can transcribe your method (I only need the 'point 2' dimension really) I can modify my £2 plumbing part to do the job. Many thanks for your instruction.
that is just FANTASTIC!!! thank you so much for this explanation!!!!!! :) it was EXACTLY what I was looking for, I imagined that using the diagonal line to project the division in parallels onto the circle could be the way you would do that, but I had no clue how to actually do it! this is beyond awesome!!! thank you again!!!
I loved geometry as a kid and it has been a long time since I have used any trig but as of late I found myself in need of doing some trig to solve some building designs I was facing and it was great to play with numbers again. For a long time, I have used other methods of constructing multi-sided buildings and furniture using math and other techniques known to carpenters but these mentioned you have shown here are really quick and easy to learn. Thank You for the time and lessons they will be used by me for sure. I have subscribed.
In the decagon construction, once you have the pentagon drawn, AF is already the perpendicular bisector of side EG, so you can just set the compass to length EF for the side length of the decagon.
22:00 - It has been proved by Gauss that a regular haptagon cannot be made by compass-and-straightedge, because 7 is not a Fermat Number. The way you draw a haptagon is firstly found by Albrecht Dürer, which has 0.2% error.
This is great - all comes flooding back. Does anyone have a good tip for not leaving a hole in the paper from the compasses? Thought of using a bit of card under it, but how to stop it moving and not leave a mark?
In the first construction where you use the division of the vertical diameter into 10 equal parts, the obtained decagon is not regular because the sides that start from point P are not equal to the others, they have a shorter length
The polygons are done so cleanly and so very neat and so precise like, even though they are still not perfect. The program you are using is very impressive. Can it make lines even thinner?
Excuse me but in drawing the decagon from the pentagon you did not have to draw a perpendicular bisector because you already have one at the bottom of your pentagon: the original perpendicular diameter is the perpendicular bisector of side EG of the pentagon!
I was excited to learn that you have a method for making a heptagon... but when I tried it in autocad there was a slight difference... I tried calculating the angle of your method and it gave me 51.31781 degrees... 2*arcsin(sqrt(3)/4)=51.31781deg ... and then compared with 360 /7=51.42857 deg it was a nice approximation though... I really thought you discovered a way to disprove mathologers claim that this is not possible using compass and straight edge... 😞
A regular 11-gon is not constructable (11 is not a Fermat prime) using only the Euclidean tools ( an UNMARKED straight edge and a compass). Any such construction of the regular 11-gon gives an approximation like the regular heptagon that was done where a length of (1/2)sqrt(3) was used as an estimate of a side of the heptagon. The result was impressive but it is NOT AN EXACT construction.The other alternative is to bring additional tools into the construction if you want an exact regular 11-gon. I have found on the internet 2 mathematicians(I believe) as recent as 2014 discovered by using a neusis construction(meaning they used something other than the Eucllidean tools) a way to construct the exact 11-gon. In 1796 Gauss at the age of 19, discovered how to construct, with Euclidean tools only, an exact 17-gon!! The number 17 is a Fermat prime. Someone has figured out how to construct an exact 257-gon!!
Самое первое построение некорректно с "условной" параллельностью таких линий, фактически проведенных "на глазок". Из правильного пятиугольника - другое дело.
Первое построение позволяет построить любой многоугольник со сторонами отличающимисяот сторон правильного многоугольника на пару процентов. Единственное, там все вершины надо получать проецированием, а не только первую.
I dont understand why you only used Q and 2 and not any of the other 8 points that you marked for no reason. If Q and 2 got you B and all the other sides are equal the other 8 marks were useless
i want to know who figured it out and how they figured it out: how to find 1/5th of the circumference of a circle using only a straight edge and compass.
To answer your question: The ancient Greeks over 2000 years ago knew how to construct a regular pentagon! No one knows who exactly was the first to discover how. Euclid the father of axiomatic and formal geometry was born circa 300BC. So the Greeks were dallying in geometric construction of polygons at least 2 centuries before Christ ( not to presume on your religion, if any). Who knows, someone may have discovered how to construct a regular pentagon in ancient Egypt 2500 BC!! The ancient Greeks are not the only race with minds and could think! So much knowledge has been lost and there is undoubtedly FAR MORE ancient peoples knew and discovered that would completely trash our history books today!!
A regular 9-gon has no exact construction using only the classic Euclidean tools, which are an UNMARKED straight edge and a compass. 9 is the product of two equal Fermat primes, namely 3. Gauss showed that such regular polygons are NOT constructable. For this same reason a regular 18 and 25 gon are not constructable: 18 = 2×3×3 and 25=5×5, since 5 is a Fermat prime.
Even though I know a true regular heptagon is not constructable in the classic sense this approximation is so impressive. Your eyes tell you it is a real regular heptagon, but my mind knows it cannot be exact. It's still impressive.
My Maths teacher at high school was a a droning Scot who's only use was as a cure for insomnia. :-/ Consequently I learned next to nothing, which forever blighted my career in Aerospace. I picked up some basic competence late as required. I now need to make a bespoke tool for removing a part on my Ovlov - which I won't buy from 'them' for £75! If I can transcribe your method (I only need the 'point 2' dimension really) I can modify my £2 plumbing part to do the job. Many thanks for your instruction.
that is just FANTASTIC!!! thank you so much for this explanation!!!!!! :)
it was EXACTLY what I was looking for, I imagined that using the diagonal line to project the division in parallels onto the circle could be the way you would do that, but I had no clue how to actually do it! this is beyond awesome!!! thank you again!!!
Beautiful sharing friend😃✌️.....
I loved geometry as a kid and it has been a long time since I have used any trig but as of late I found myself in need of doing some trig to solve some building designs I was facing and it was great to play with numbers again. For a long time, I have used other methods of constructing multi-sided buildings and furniture using math and other techniques known to carpenters but these mentioned you have shown here are really quick and easy to learn. Thank You for the time and lessons they will be used by me for sure. I have subscribed.
Terima kasih sudah berbagi dengan kami... akhirnya aku menemukan teknik ini
Thanks a lot🙏👍
In the decagon construction, once you have the pentagon drawn, AF is already the perpendicular bisector of side EG, so you can just set the compass to length EF for the side length of the decagon.
13:28 Pentagon
18:56 Hexagon
Your videos are outstanding, I draw a lot of optical art by hand and you have helped me understand shapes better.
22:00 - It has been proved by Gauss that a regular haptagon cannot be made by compass-and-straightedge, because 7 is not a Fermat Number. The way you draw a haptagon is firstly found by Albrecht Dürer, which has 0.2% error.
It helped me in my assignment thanks a lot
Seeing it 1 day b4 architectural drawing exam and it's very helpful 👍
This is great - all comes flooding back. Does anyone have a good tip for not leaving a hole in the paper from the compasses? Thought of using a bit of card under it, but how to stop it moving and not leave a mark?
In the first construction where you use the division of the vertical diameter into 10 equal parts, the obtained decagon is not regular because the sides that start from point P are not equal to the others, they have a shorter length
Thanks so much for sharing this skill.
Tnx for this vedio dude😉😃😃😊😊This vedio help me to know and study this polygons because this is our lesson.
The polygons are done so cleanly and so very neat and so precise like, even though they are still not perfect. The program you are using is very impressive. Can it make lines even thinner?
I’m gonna use those techniques for my artwork.
thank you, what is the pcd of the five hole flange?
How can you divide a semi circle into a number of equal arcs?
This reminds me my secundary school "Technical Draw" course. We used the Bronislao Yurksas text book. Mid 80's.
Thank you very much teacher
Tysm ❤❤❤
Excelente didática.
What size is each side and what size is the radius?
Nice one 😊
Excuse me but in drawing the decagon from the pentagon you did not have to draw a perpendicular bisector because you already have one at the bottom of your pentagon: the original perpendicular diameter is the perpendicular bisector of side EG of the pentagon!
Thank you🙏🙏🙏🙏🙏❤️
Wow surprise for me.keep it up!
Thank you very much, this is a great help for my lesson.
О! Геометрия, ты вечна ---гордись прекрасная собой .
what is the reason behind the point 2?
Thanks. I am very happy.
Хороший транспортир с треугольником и параллельными линиями.
Thanks sir I really need this Thanku so much🥰
I learnt a much simpler way in my high school for drawing a polygon within a circle.
You should have learned that (learnt) is not a word.
@@mikeeldridge637 it is they are both acceptable spellings
Super video sirji
How do you do the parallel lines?
ua-cam.com/video/C-Wu7gOSpHM/v-deo.html
Wonder whether there is a mathematical prove for the method?
I am also looking for the video showing those kind of proofs
I was excited to learn that you have a method for making a heptagon... but when I tried it in autocad there was a slight difference...
I tried calculating the angle of your method and it gave me 51.31781 degrees...
2*arcsin(sqrt(3)/4)=51.31781deg
... and then compared with
360 /7=51.42857 deg
it was a nice approximation though... I really thought you discovered a way to disprove mathologers claim that this is not possible using compass and straight edge... 😞
В какой программе это выполняется?
decagon does not need other point than point 2 on diameter right?
so why?
For the decagon: once we have the vertices of the pentagon we find their symmetrical points with respect to the center of the circle.
What's the size of the first circles because it's the where am making the mistakes
I recomend you a radius=5cm.
@@ArthurGeometry ohh me iwas using 8 thank you teacher🙏🙏
Good job
Excelente
So there it is. The true "Gearsmith's Friend" is the humble compass!
You are just after our teacher in school.
I mean could you share the video. How to draw 11 side on circle with acurate.
A regular 11-gon is not constructable (11 is not a Fermat prime) using only the Euclidean tools ( an UNMARKED straight edge and a compass). Any such construction of the regular 11-gon gives an approximation like the regular heptagon that was done where a length of (1/2)sqrt(3) was used as an estimate of a side of the heptagon. The result was impressive but it is NOT AN EXACT construction.The other alternative is to bring additional tools into the construction if you want an exact regular 11-gon. I have found on the internet 2 mathematicians(I believe) as recent as 2014 discovered by using a neusis construction(meaning they used something other than the Eucllidean tools) a way to construct the exact 11-gon. In 1796 Gauss at the age of 19, discovered how to construct, with Euclidean tools only, an exact 17-gon!! The number 17 is a Fermat prime. Someone has figured out how to construct an exact 257-gon!!
but why? proof?
Самое первое построение некорректно с "условной" параллельностью таких линий, фактически проведенных "на глазок". Из правильного пятиугольника - другое дело.
Первое построение позволяет построить любой многоугольник со сторонами отличающимисяот сторон правильного многоугольника на пару процентов. Единственное, там все вершины надо получать проецированием, а не только первую.
I dont understand why you only used Q and 2 and not any of the other 8 points that you marked for no reason. If Q and 2 got you B and all the other sides are equal the other 8 marks were useless
i want to know who figured it out and how they figured it out: how to find 1/5th of the circumference of a circle using only a straight edge and compass.
To answer your question: The ancient Greeks over 2000 years ago knew how to construct a regular pentagon! No one knows who exactly was the first to discover how. Euclid the father of axiomatic and formal geometry was born circa 300BC. So the Greeks were dallying in geometric construction of polygons at least 2 centuries before Christ ( not to presume on your religion, if any). Who knows, someone may have discovered how to construct a regular pentagon in ancient Egypt 2500 BC!!
The ancient Greeks are not the only race with minds and could think! So much knowledge has been lost and there is undoubtedly FAR MORE ancient peoples knew and discovered that would completely trash our history books today!!
According to CAD the Nonagon is not exact, please comment.
A regular 9-gon has no exact construction using only the classic Euclidean tools, which are an UNMARKED straight edge and a compass. 9 is the product of two equal Fermat primes, namely 3. Gauss showed that such regular polygons are NOT constructable. For this same reason a regular 18 and 25 gon are not constructable:
18 = 2×3×3 and 25=5×5, since 5 is a Fermat prime.
I never understood why people draw a circle first, instead of a line first.
Yu elp andestending area civile
Uso lui
Upes 💀💀💀
Hell for those who want to believe that ❤️🥴
GG
that is not a very even heptagon
That is because 7 is not a Fermat prime.
@@Diamondblade2008 ik
Need an answer please 🙏 a
11 sided polygon hendecagon
ua-cam.com/video/LWBuWFSPLtg/v-deo.html
U
um i think i like it but not so much
Habla un poco en español
Help
But y'all ain't invited anyways.
GG. is. Look. You
Shown = Shaun