Good, we have an octagon in a square - but how good is it? Let's find out! Clearly all the angles are equal, and the lengths of sides 1-2, 3-4, 5-6, and 7-8 are all the same, as are the lengths of sides 2-3, 4-5, 6-7, and 8-1. But are these two groups of sides all the same length? I'll calculate one first, then the other, and see how they compare. You gave a length of 180mm as the length of your square's sides, but for the sake of the argument I will call that value N. Now, when you draw the arcs, the length from the center of the arc to any point on the arc is N*sqrt(2)/2. So the amount outside the arc is N*(1-sqrt(2)/2). Removing the two sections on either side of side 1-2, then, gives us a length of N - N*(2-sqrt(2)), or N*(sqrt(2)-1). Meanwhile, the triangles cut off are right isosceles triangles. The legs are both length N*(1-sqrt(2)/2), meaning the hypotentuse, side 2-3, is N*sqrt(2)*(1-sqrt(2)/2), or N*(sqrt(2)-1). So we have a regular octagon after all! To be honest, I'm actually kind of relieved - I've seen quite a few videos claiming to offer compass-and-straightedge ways for an arbitrary regular polygon to be inscribed in a circle, or to be drawn given a known side - never mind the fact that it's been proved that only certain regular polygons can even be constructed PERIOD using only those two tools!
My son and I just did this with simalar method ... For a homeschooling exam ... Then built a fire safety platform for a kerosene heater to show the applied mathematics at work .
Wow thanks alot didn't know how i would construct a regular octagon starting with a square....thanks
Thank you! I've been looking for a simple way to make an octagon from a square, and knew there must be a simple way. And here it is.
Thank-you! This made it very simple. To the point, no annoying music or chatter.
- Another great geometry lesson w/o the excessive numbers & lines & "stuff." Thanx.
Wow this is actually really simple. Thanks!
Neat and good presentation 👏
Brilliant, well done, thank you, I knew there must be a way.
I'm trying to handcraft a wooden ring and I gotta say, centring that shape over a hole is incredibly difficult.
TOO GOOD . THANKS A LOT. IT WAS OF GREAT HELP TO ME
good job mate
Short and sweet😀
if you don't have a compass, just use the measurement from center to corner and mark from the corners.
wow man thanks u so much
it does help me on my work
Thank u it is so easy to draw
ur saving my exams dude
Tom Hardy sameeee
FINALLY THANKS DUDE
Thank you for this
Thanks very much. But why do you cross out your seven?
Huge help thank you
Good, we have an octagon in a square - but how good is it? Let's find out! Clearly all the angles are equal, and the lengths of sides 1-2, 3-4, 5-6, and 7-8 are all the same, as are the lengths of sides 2-3, 4-5, 6-7, and 8-1. But are these two groups of sides all the same length? I'll calculate one first, then the other, and see how they compare.
You gave a length of 180mm as the length of your square's sides, but for the sake of the argument I will call that value N. Now, when you draw the arcs, the length from the center of the arc to any point on the arc is N*sqrt(2)/2. So the amount outside the arc is N*(1-sqrt(2)/2). Removing the two sections on either side of side 1-2, then, gives us a length of N - N*(2-sqrt(2)), or N*(sqrt(2)-1).
Meanwhile, the triangles cut off are right isosceles triangles. The legs are both length N*(1-sqrt(2)/2), meaning the hypotentuse, side 2-3, is N*sqrt(2)*(1-sqrt(2)/2), or N*(sqrt(2)-1).
So we have a regular octagon after all! To be honest, I'm actually kind of relieved - I've seen quite a few videos claiming to offer compass-and-straightedge ways for an arbitrary regular polygon to be inscribed in a circle, or to be drawn given a known side - never mind the fact that it's been proved that only certain regular polygons can even be constructed PERIOD using only those two tools!
MustardPipeLibrary You're just a bag of wind.
nice sir ji
when youtube teaches better than school ✨
I love your corpse display and I totally agree with this comment 😂💖
Live saver i passed my DT test 🎉
Wish I had a compass
Cool merci
This is great thanks
I hated you
good
Are all sides equal?
thank u so much u help me pass my exams :D
Hey im jack and im here to tell you about the Word octagon
Hello Creagh College Tech Dept,
It is unnecessary to indicate the length of the square, it can be any size..
My son and I just did this with simalar method ... For a homeschooling exam ... Then built a fire safety platform for a kerosene heater to show the applied mathematics at work .
in this course we have to be stronger enough
Chuck Norris saw this....
Tomorrow is my test !!!!!!
than u so much😭
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CNM Technology Department is better, I'm sorry but it's the truth.