Hope your head doesn't hurt from last night! Here's some math to help soothe the pain. I also posted some additional content to this video on my 2nd channel. Happy new year ;)
OK, I got everything except the rubber band part, which I thought was very complex and deserved a video on its own to show exactly how it was done. :D Not sure if it was intentional on your part, but this video was simplified to such an extent as to make it fairly difficult for anyone that has any woodworking experience to watch comfortably. I kept wanting to swat that utility knife out of your hand and march you over to the table saw :)
pocket83 The audience likes being fucked with occasionally. :) I doubt I lost any subscribers worth keeping - if they can't take a little ribbing (or are too dense to see it for what it was), then they can step off. For every one that gets jettisoned, 100 more climb on to take their place. I think we all have that same segment of the audience that doesn't have the tools or experience, but like to watch someone make something.
pocket83 I bet the followers of people like Chris Schwarz and Frank Howarth are captivated by your work. What you do is tactile and thought provoking. Woodworkers who care about proportions would do well to pay attention.
Pocket I do more "woodworking" projects, granted that I don't have too many tools. I think I was drawn to you by your "woodworking" projects, but your true audience is just entertained by your personality, creativity, and originality. I just hope that you don't steer away from woodworking projects because you don't think it fits your audience anymore. It fits your audience as long as you bring your values into that project.
@@pocket83 Just stumbling on this now. I'm slightly over the 25 demographic but since I'm a beginner, I really appreciated the simplification! :) Thank you!
i never expected to learn something from a woodworking video about something i am really interested in, but the assembled icosahedron really amazed me. i'm probably going to dive into the maths behind this, thanks for the inspiration :)
your projects are lots of fun to watch and build. some channels are fun to watch, some channels are only for building ideas. Pocket is good for both. thank you for taking the time to make these.
Nice video, very entertaining! This is why I love both woodworking and math so much - together they can bring you loads of fun and some nice projects to do in your freetime. Greetigs from germany, Paul
I absolutely love your stuff pocket, thanks again for the upload. I can't quite tell you exactly what it is, but your videos are extremely satisfying to watch. Cheers mate!
i guess the number 1.732 approximates to √3, as the rectangle is made of two right angled triangles following the pythagorean triplet 1,2,and √3, not related to the golden section, but the six petal diagram can be worked out for 1.68..., in fact there is a paper on this link based on floral geometry.
If you really want to, you can make the ratio using a compass, a pencil, and a straightedge. Use the pythagorean theorem with sides of 2 and 1, and you'll get sqrt (5) as a hypotenuse. With that, just add the length to the 1 and halve that total. length.
Your presentation skills have really improved this last year, and in this video especially. Although I kind of thought the awkwardness in your old videos was sort of endearing, this is probably better.
Isn't the platonic dodecahedron based on the silver rectangle the way a platonic icosahedron is based on the golden rectangle? I wonder what polyhedra are based off the bronze mean and other metallic means. en.wikipedia.org/wiki/Metallic_mean
Actually, you can construct a perfect golden rectangle using a compass since φ is constructible (you can get root 5 by constructing the hypotenuse of a 2 x 1 right triangle). In fact, you can add, subtract, multiply, divide and take square roots of numbers with a compass and straightedge (you can even take cube roots if you cheat a little bit).
You're kinda right, and I knew that word would get scrutinized. But my point still stands on two technicalities: 1) the construction of an actual Fibonacci rectangle that's representative of the entire number would require infinite space and time, while we don't know if those variables are available to us, and 2) variation in any and every drawing implement yet devised introduces some random error, which prohibits perfection. I love that mathematics creates these ideals for us to use as models, but it's important to remember that they can never be realized in the world in which we live. Political and economic theories are also tools that suffer the same limitations. This, in part, is why Plato considered his realm of 'forms' to be more substantive -and real- than our world. One more interesting thing to consider: the arbitrary nature of irrational numbers. If our numerical system were based on a hypotenuse, rather than on a leg, root(2) would be a rational integer, and one would become an infinite decimal. In spite of Bertrand Russell's Principia Mathematica, it is nevertheless an assumption to consider one as a fundamental truth sufficient to build a mathematics predictive of all possible states of the universe. It may be that "perfect" eludes us because for us, perfect must be in terms of one, while the universe does not necessarily adhere to such a precept.
I love building things out of that 5 mm underlayment! I keep a steady supply of it in my shop. I actually built my first delta style 3d printer from that exact stuff!
Very nice work Pocket83! Excellent! However: You may obtain a perfect Golden Rectangle by drawing a circle whose origin is the lower center of a square's lower edge, and whose radius is from the origin on through to the upper corner of the square. It is the point where the circle extends beyond the lower edge of the square that will define a perfect Golden Rectangle, being VOID of any approximations whatsoever. Have fun.
I should've kept my mouth shut there. I expected somebody to pick at that. Please don't take the following as an evasion, or as being smart-assed. My point was more abstract than any approximate construction. "Perfect" is a theoretical ideal. Just like it's impossible to draw a perfect circle, the Golden rectangle can't be constructed because of its irrational nature. Even IF we had the ability to produce sides of zero thickness in the real world, the figure would still require an infinite space in which to draw it. I have come to understand all irrational numbers as being descriptions of things that can't actually be defined within any numerical system that still assumes one as its fundamental. I have yet to be shown evidence to the contrary, but I certainly invite it. Our mathematics, much like the brains that invented it, are unfortunately quite limited. For example, we can make a symbol for infinity, so that we can use it operationally, but we can't know if infinity can even exist in reality. Such would be a (T)ruth claim, and those arguments are outside of the present scientific/philosophical purview. Sorry if that all sounds fuzzy, but I would just admit it if I had misspoke in the video. I really _meant_ it when I said that drawing a perfect figure is impossible. Even deeper: The "perfect" description of infinity would be the set of all sets, even the set of all sets not possible, and of course, the set of all sets not possible become possible. In this place, I can't cease to exist, because my conscious experience reasserts its continuity immediately following my demise, because all cases are present. Whoa, is this the ontological argument? I'm not sure, but if infinity exists, we all come back again and again: we have to, because all sets, cases, scenarios, experiences, and meanings will exist an infinite number of times and in an infinite number of variations. Even the case where we can draw perfect figures will exist, which requires additional infinities. Thus, I don't think infinity exists, and by extension, neither does perfect.
I really like how you should the 3 planes that makes the shape. I did a project to make a 20 sided die to be 3D printed and came across this during research and thought it was remarkable.
I just finished mine. Hope you might check it out. Setting up for the cut going through the center of each piece took way longer than I thought it would.
very cool. I usually hear my art history professors refer to the Golden Number/Ratio as Phi. is there any difference there, between Phi and the Golden Number?
Ah platonic solids. I really enjoy these video's. Thanks for putting in the time and effort to build these. The copper one was beautiful top watch you make as well. Makes me want to build some rolling ball sculptures (namedropping David Morrell, specifically, his 66th build, the sphere), and add some wood elements to it. Quick question; I seem to remember there being a system where you could use chopsticks and rubber bands alone to build stable solids, but it would only stay together once the tension was equal after adding the last rubber band. Something like "tensors"? It's kind of eluding me atm, and my google-fu is getting me nowhere.. Maybe you can shed some light on it? Also, Those are some nice gears. Have you been hanging out with Izzy? :) Also also, happy new year dude! Well wishings to you and your friends and family!
It's possible to make a "Hexastix" from pencils, which is a self-contained form that's pretty stable, if I remember correctly. That "stand-up math" guy made a video about it, I think (if you can tolerate his sarcastic anti-Americanism). That shape could probably scratch the itch for you, but nothing else like that comes to mind right now. Thanks!
Hexastix, ah yeah I saw the video, but that wasn't what I meant. The rubber bands are not optional. I'm talking about making almost entirely hollow solids, but using rubber bands to pull the sticks through the center, or toward it, or into eachother's vertexes. No glue, no friction, just tension. I remember this one guy who was able to make stuff like rhombic cuboctahedrons, and icosahedrons, ,all the way down to simple cubes and tetrahedrons. It would be putty in his hands until he had the last string on. A very elegant form of tension based balance. I don't mind the stand up maths guy though. I'm Dutch, so my tolerance for language based banter and patriotic jabs is quite up there :) But yeah, I learned to read, write and speak english from SKY Channel, when they still ran series like GI Joe, Mask, and transformers, so that might explain a thing or two :) Cheers man, thanks for replying and thinking along!
Okay, okay, not 10 seconds after i posted above reply, I found it. Tensegrity Structures/Models. YES! Wow, that's 10 years ago, and I (well, you and me both actually) had to dig deep to remember that. Wow. Okay, well anyway, I'd love to see you build some stuff with this technique. There's a lot of disciplines and methodology there that reminded me of you. Damn I love it when a plan comes together! /watch?v=8gtvxYZ0GIg
pocket83 This is great, especially making it accessible to people without power tools. Also, phi pops up in the construction of a regular pentagon, which is my favorite way to get to it. (Also: ironically enough, I'd be more likely to let my six year old use a carefully set table saw instead of a box cutter on this project. It's a lot less likely to maim him. But not all parents are reasonable like that.)
Sure. I'll get started on it right away. In the meantime, send the retainer to my PO box. No need to discuss a price; I'm not really interested in the details, so just keep sending payments until I've finished. You'll find that I'm quite easy to work with! Talk to you around spring.
Rather than a retainer, you might do better by taking a share of the profits. I recommend splitting things 38.196601125010515179541316563436 61.803398874989484820458683436564
Apologies. Didn't mean it that way. Just seeing earlier comments made me wanna help clear things abit. Deleted my thoughtless comments. A very informative video actually. Thanks.
so I did the math too, except I used some trigonometry instead. I got b = a/tan(30 degrees), which, when we set a to 1, means b = 1.732050808..., which is the same as your answer. 1/tan (30) is equal to sqrt (3), which doesn't look that similar to (1 + sqrt (5))/2. so yeah, it's just a coincidence that they look about the same.
Amazing!!! Listening to you was like listening to Isaac Newton! If I was Bill Gates I will hire you right away! I 've created a board game buy yours made my jaw drop to the floor!
Re. the rectangle inscribed in the circle. You may appreciate how I saw the ratio "at a glance". The construction is simple. imgur.com/a/qZcJK Connect every corner of the rectangle to the center of the circle. Now all the short lines (red) are equal; They all equal the radius of the circle, r. So we have two equilateral triangles. The height of an equilateral triangle is root3 / 2 of the side. So the sum of the heights of both triangles is r*root3. And that is also the length of the rectangles longer side.
I had that same bag of rubber bands. It took over 10 years for my house to use all of them. It probably takes you like 10 minutes on a project to do the same.
Not at all. I go through lots of effort to give you that "feel like you're there" feel. I zoom in on stuff like that, and I appreciate that you notice!
The single greatest toy ever invented, except for that dry-rot problem. I once had a buddy that worked at the bike shop, where every shipment had a bunch of those big fat noodly ones. His was the size of a basketball, and it was heavy enough to knock the wind out of you when you caught it!
I built a robot with the front, top and side views all using the eye-pleasing golden ratio in some manner. Then it turned out I screwed up measuring the batteries, and it needed a different set of sensors in front, and... sigh.
The digits of the sequence are not exactly representative of the golden number. Kind of like how pi is not 3. As you add more digits, you get closer to it. Just because two numbers belong to the sequence, that doesn't mean that they alone can define the golden number. Remember that it's irrational, so any definition of it that only uses integers will be an approximation.
Nice find. Messy, though. It requires that the calculator be set to Deg, not Rad. It's also conceptually tough; irrationality is not always easy to internalize, so removing it by more than one degree geometrically makes the expression become quite opaque to curiosity. I mean, I'm getting philosophical here, but what is 'cos θ,' really? It's just too arcane for me to understand. The Golden number here is being defined as something like, two of the quantity that's the ratio of two side lengths of the triangle that has an angle that's 1/10 of the circle. Whatever. Thanks for getting me to think this morning ;)
Yh ermm wow I really love the Golden but I struggle getting my head around the maths (yeah I am English I say maths it just doesn't sound right without the s)
Dissatisfied comment: "Just under an eighth" should be said as "An eighth minus a blonde one." You can use other hair colors depending on how much over or under the measurement is. Sometimes you can use half widths (ie half a blonde one), but now we're splitting hairs. Happy new year. Hahahaha.
Hope your head doesn't hurt from last night!
Here's some math to help soothe the pain. I also posted some additional content to this video on my 2nd channel. Happy new year ;)
pocket83² What's with the random nature of the 'dropped in' frames - I can see no pattern or correlation.
Can you use card instead?? doing it for school project
pocket83² where did you get '2a=a' and '2b=b'?
OK, I got everything except the rubber band part, which I thought was very complex and deserved a video on its own to show exactly how it was done.
:D
Not sure if it was intentional on your part, but this video was simplified to such an extent as to make it fairly difficult for anyone that has any woodworking experience to watch comfortably. I kept wanting to swat that utility knife out of your hand and march you over to the table saw :)
I think I lost all of the "woodworker" viewers. They don't take me seriously for some reason. But I do get lots of the
pocket83 The audience likes being fucked with occasionally. :)
I doubt I lost any subscribers worth keeping - if they can't take a little ribbing (or are too dense to see it for what it was), then they can step off. For every one that gets jettisoned, 100 more climb on to take their place.
I think we all have that same segment of the audience that doesn't have the tools or experience, but like to watch someone make something.
pocket83 I bet the followers of people like Chris Schwarz and Frank Howarth are captivated by your work. What you do is tactile and thought provoking. Woodworkers who care about proportions would do well to pay attention.
Pocket I do more "woodworking" projects, granted that I don't have too many tools. I think I was drawn to you by your "woodworking" projects, but your true audience is just entertained by your personality, creativity, and originality. I just hope that you don't steer away from woodworking projects because you don't think it fits your audience anymore. It fits your audience as long as you bring your values into that project.
@@pocket83 Just stumbling on this now. I'm slightly over the 25 demographic but since I'm a beginner, I really appreciated the simplification! :) Thank you!
i never expected to learn something from a woodworking video about something i am really interested in, but the assembled icosahedron really amazed me. i'm probably going to dive into the maths behind this, thanks for the inspiration :)
Ahhh Geometry, the one thing in this world that can't be corrupted.
bill baggins
bill baggins tell that to Salvador Dalí
Ahhh Art. One of the most commonly corrupted things around.
bill baggins who corrupts them all? kicked out of every country multiple times. the that's the real puzzle. U know hew
House of Leaves
your projects are lots of fun to watch and build. some channels are fun to watch, some channels are only for building ideas. Pocket is good for both. thank you for taking the time to make these.
I highly appreciated you walking me through your reasoning and mathematical analysis to just arrive at "less than 1/8" " I am really satisfied!
Nice video, very entertaining!
This is why I love both woodworking and math so much - together they can bring you loads of fun and some nice projects to do in your freetime.
Greetigs from germany,
Paul
great video! i've been building icosahedrons big and small for over two years now. i did not realize they contained golden rectangles.
Why do you add a sublim in the videos? And why didn't you complete the model with the band that would follow a wooden line?
I absolutely love your stuff pocket, thanks again for the upload. I can't quite tell you exactly what it is, but your videos are extremely satisfying to watch. Cheers mate!
Love the flower of life relationship. Perfectly fits when the lines are the proper width...
2017 starts with a bang! Thanks for the great video. I'll be cutting those pieces out tonight to take into my classroom later this week.
Dissatisfied comment
I really enjoyed this video happy new year
i guess the number 1.732 approximates to √3, as the rectangle is made of two right angled triangles following the pythagorean triplet 1,2,and √3, not related to the golden section, but the six petal diagram can be worked out for 1.68...,
in fact there is a paper on this link based on floral geometry.
Sometimes, you make me wish I had paid attention in geometry. I love it.
Pocket, I think you would be interested in "le modulor", it the golden ratio based on the human. Measurement which are comfortable for people.
If you had access to a milling machine or router, could you possibly cut the slots in the middle out with a small enough bit?
Yes.
I gave this one a like just for the narrative in your description. Well done.
If you really want to, you can make the ratio using a compass, a pencil, and a straightedge. Use the pythagorean theorem with sides of 2 and 1, and you'll get sqrt (5) as a hypotenuse. With that, just add the length to the 1 and halve that total. length.
Your presentation skills have really improved this last year, and in this video especially. Although I kind of thought the awkwardness in your old videos was sort of endearing, this is probably better.
What brand of thumb tack are you using??
hi which table saw do you use in the video. many thanks
Pocket 83, you're such a cool guy and it's fun to hang out with you during your videos
Isn't the platonic dodecahedron based on the silver rectangle the way a platonic icosahedron is based on the golden rectangle?
I wonder what polyhedra are based off the bronze mean and other metallic means.
en.wikipedia.org/wiki/Metallic_mean
No Pocket 83, what are you looking for in making these excellent videos?
Pocket! You're back!!!
Actually, you can construct a perfect golden rectangle using a compass since φ is constructible (you can get root 5 by constructing the hypotenuse of a 2 x 1 right triangle).
In fact, you can add, subtract, multiply, divide and take square roots of numbers with a compass and straightedge (you can even take cube roots if you cheat a little bit).
You're kinda right, and I knew that word would get scrutinized. But my point still stands on two technicalities: 1) the construction of an actual Fibonacci rectangle that's representative of the entire number would require infinite space and time, while we don't know if those variables are available to us, and 2) variation in any and every drawing implement yet devised introduces some random error, which prohibits perfection.
I love that mathematics creates these ideals for us to use as models, but it's important to remember that they can never be realized in the world in which we live. Political and economic theories are also tools that suffer the same limitations. This, in part, is why Plato considered his realm of 'forms' to be more substantive -and real- than our world.
One more interesting thing to consider: the arbitrary nature of irrational numbers. If our numerical system were based on a hypotenuse, rather than on a leg, root(2) would be a rational integer, and one would become an infinite decimal. In spite of Bertrand Russell's Principia Mathematica, it is nevertheless an assumption to consider one as a fundamental truth sufficient to build a mathematics predictive of all possible states of the universe. It may be that "perfect" eludes us because for us, perfect must be in terms of one, while the universe does not necessarily adhere to such a precept.
I love building things out of that 5 mm underlayment! I keep a steady supply of it in my shop. I actually built my first delta style 3d printer from that exact stuff!
Very nice work Pocket83! Excellent! However:
You may obtain a perfect Golden Rectangle by drawing a circle whose origin is the lower center of a square's lower edge, and whose radius is from the origin on through to the upper corner of the square. It is the point where the circle extends beyond the lower edge of the square that will define a perfect Golden Rectangle, being VOID of any approximations whatsoever. Have fun.
I should've kept my mouth shut there. I expected somebody to pick at that. Please don't take the following as an evasion, or as being smart-assed.
My point was more abstract than any approximate construction. "Perfect" is a theoretical ideal. Just like it's impossible to draw a perfect circle, the Golden rectangle can't be constructed because of its irrational nature. Even IF we had the ability to produce sides of zero thickness in the real world, the figure would still require an infinite space in which to draw it.
I have come to understand all irrational numbers as being descriptions of things that can't actually be defined within any numerical system that still assumes one as its fundamental. I have yet to be shown evidence to the contrary, but I certainly invite it. Our mathematics, much like the brains that invented it, are unfortunately quite limited. For example, we can make a symbol for infinity, so that we can use it operationally, but we can't know if infinity can even exist in reality. Such would be a (T)ruth claim, and those arguments are outside of the present scientific/philosophical purview.
Sorry if that all sounds fuzzy, but I would just admit it if I had misspoke in the video. I really _meant_ it when I said that drawing a perfect figure is impossible.
Even deeper:
The "perfect" description of infinity would be the set of all sets, even the set of all sets not possible, and of course, the set of all sets not possible become possible. In this place, I can't cease to exist, because my conscious experience reasserts its continuity immediately following my demise, because all cases are present. Whoa, is this the ontological argument? I'm not sure, but if infinity exists, we all come back again and again: we have to, because all sets, cases, scenarios, experiences, and meanings will exist an infinite number of times and in an infinite number of variations. Even the case where we can draw perfect figures will exist, which requires additional infinities.
Thus, I don't think infinity exists, and by extension, neither does perfect.
Your videos are always so dope dude, love your channel
I really like how you should the 3 planes that makes the shape. I did a project to make a 20 sided die to be 3D printed and came across this during research and thought it was remarkable.
I just finished mine. Hope you might check it out. Setting up for the cut going through the center of each piece took way longer than I thought it would.
Nice video. Clear, entertaining (for those of a geometric mindset), and educational. An easier way to generate the Golden Number is Phi = 2 cos 36.
N914TJ Radian, or Degree?
The Dark_Speed_Ninja/ShadikkuX degree i belive
Your videos are always amazing and truly interesting
very cool. I usually hear my art history professors refer to the Golden Number/Ratio as Phi. is there any difference there, between Phi and the Golden Number?
Nope. It's just a Greek letter, like Pi.
It just stands for the golden number.
You always make the nicest projects. Keep it up 👍👍
Ah platonic solids. I really enjoy these video's. Thanks for putting in the time and effort to build these. The copper one was beautiful top watch you make as well. Makes me want to build some rolling ball sculptures (namedropping David Morrell, specifically, his 66th build, the sphere), and add some wood elements to it.
Quick question; I seem to remember there being a system where you could use chopsticks and rubber bands alone to build stable solids, but it would only stay together once the tension was equal after adding the last rubber band. Something like "tensors"? It's kind of eluding me atm, and my google-fu is getting me nowhere.. Maybe you can shed some light on it?
Also, Those are some nice gears. Have you been hanging out with Izzy? :)
Also also, happy new year dude! Well wishings to you and your friends and family!
It's possible to make a "Hexastix" from pencils, which is a self-contained form that's pretty stable, if I remember correctly. That "stand-up math" guy made a video about it, I think (if you can tolerate his sarcastic anti-Americanism).
That shape could probably scratch the itch for you, but nothing else like that comes to mind right now. Thanks!
Hexastix, ah yeah I saw the video, but that wasn't what I meant. The rubber bands are not optional. I'm talking about making almost entirely hollow solids, but using rubber bands to pull the sticks through the center, or toward it, or into eachother's vertexes. No glue, no friction, just tension. I remember this one guy who was able to make stuff like rhombic cuboctahedrons, and icosahedrons, ,all the way down to simple cubes and tetrahedrons. It would be putty in his hands until he had the last string on. A very elegant form of tension based balance.
I don't mind the stand up maths guy though. I'm Dutch, so my tolerance for language based banter and patriotic jabs is quite up there :) But yeah, I learned to read, write and speak english from SKY Channel, when they still ran series like GI Joe, Mask, and transformers, so that might explain a thing or two :)
Cheers man, thanks for replying and thinking along!
Okay, okay, not 10 seconds after i posted above reply, I found it.
Tensegrity Structures/Models. YES! Wow, that's 10 years ago, and I (well, you and me both actually) had to dig deep to remember that. Wow.
Okay, well anyway, I'd love to see you build some stuff with this technique. There's a lot of disciplines and methodology there that reminded me of you. Damn I love it when a plan comes together!
/watch?v=8gtvxYZ0GIg
Who is going to have not one but two combination squares, but not a saw?
A kid who is not allowed to use the power tools in the garage. Not that it matters: you can make a marking gauge from a stick, so use two of those.
1 i dont have a garage or any tools.
pocket83 This is great, especially making it accessible to people without power tools. Also, phi pops up in the construction of a regular pentagon, which is my favorite way to get to it. (Also: ironically enough, I'd be more likely to let my six year old use a carefully set table saw instead of a box cutter on this project. It's a lot less likely to maim him. But not all parents are reasonable like that.)
Excellent. Math made fun! Thanks for the effort to put this together.
Do you Instagram?
Thank You for sharing your hardwork.
What is the unit..? Cm ?
imagine the bottom line of a golden spiral as a movie timeline. would it mean that the best part of the movie is in the point where the spiral ends?
great video,very interesting subject and idea and uncommon,you have the admiration from a science teacher from Greece,!!!
What _am_ I looking for?
also a great project for the lasercutter, thanks to the template!
Thanks for the book showing :) Just ordered
hope your holidays went perfectly.
I enjoy what some people might see as an "over-explanation". It's kind of the only reason I got through Algebra 3.
best d20 i've seen this week
You could also use foamcore instead of plywood
Definitely.
RawSauce338 or some mat board, like what thy use in picture frames. that stuff is great for architectural models
The number you found at 11:20 is the square root of 3.
I found what I was looking for.
Congrats on 100k subs!
I love how he has like 6 other ones in the background
The ratio you obtained with the 6-point flower (1.7320508076) is actually sqrt(3) by the way.
Nice catch! I never recognized that!
Dear, i wanna start a company and for that i need a logo. Could you please design a golden ratio based logo for me. thanks
Sure. I'll get started on it right away. In the meantime, send the retainer to my PO box. No need to discuss a price; I'm not really interested in the details, so just keep sending payments until I've finished. You'll find that I'm quite easy to work with! Talk to you around spring.
Rather than a retainer, you might do better by taking a share of the profits. I recommend splitting things 38.196601125010515179541316563436 61.803398874989484820458683436564
That damned square root of 5 mucking things up.
Is it coincidence that the 1.732 you came up with is so close to sqrt(3)?
I hadn't put two and two together at the time. nice catch.
Two and two together is fou---, yeah I see what you did there ;o)
tiny, baby rubber bands on the ends of wires. then you can unfold flat pieces and put the rubber loops over tacks and make an antenna.
You really seem to like that sandpaper-on-a-stick.
Apologies. Didn't mean it that way. Just seeing earlier comments made me wanna help clear things abit. Deleted my thoughtless comments. A very informative video actually. Thanks.
I can't believe you went through all that trouble just to find out it was just under 1/8"
so I did the math too, except I used some trigonometry instead.
I got b = a/tan(30 degrees), which, when we set a to 1, means b = 1.732050808..., which is the same as your answer.
1/tan (30) is equal to sqrt (3), which doesn't look that similar to (1 + sqrt (5))/2.
so yeah, it's just a coincidence that they look about the same.
5/64th is closer still. If you want to really get into it, 11/128th is wishing 6thiusandths of an inch
Amazing!!! Listening to you was like listening to Isaac Newton! If I was Bill Gates I will hire you right away! I 've created a board game buy yours made my jaw drop to the floor!
This is pretty great to be honest.
Re. the rectangle inscribed in the circle. You may appreciate how I saw the ratio "at a glance". The construction is simple.
imgur.com/a/qZcJK
Connect every corner of the rectangle to the center of the circle. Now all the short lines (red) are equal; They all equal the radius of the circle, r. So we have two equilateral triangles. The height of an equilateral triangle is root3 / 2 of the side. So the sum of the heights of both triangles is r*root3. And that is also the length of the rectangles longer side.
Luan is 3 ply underlayment.
4:54 that is 3/16. Not 3/32.
You are incorrect. Look again.
I had that same bag of rubber bands. It took over 10 years for my house to use all of them. It probably takes you like 10 minutes on a project to do the same.
I love the sound of the tack being inserted into the wood. Is there something wrong with me?
Not at all. I go through lots of effort to give you that "feel like you're there" feel. I zoom in on stuff like that, and I appreciate that you notice!
Very cool stuff.
neat the video duration is 12:34
should have been 16:18
the most badass rubber band ball in the world
Dissatisfied comment: I appreciate your attention to detail and take offense to the suggestion that I wouldn't.
;-D
Hahaha :) loled at "What are you looking for" :)
Pocket, what do you think of rubber band balls?
The single greatest toy ever invented, except for that dry-rot problem.
I once had a buddy that worked at the bike shop, where every shipment had a bunch of those big fat noodly ones. His was the size of a basketball, and it was heavy enough to knock the wind out of you when you caught it!
That's awesome! Mine is the size of a small cantaloupe! Do you have one, Pocket?
I built a robot with the front, top and side views all using the eye-pleasing golden ratio in some manner. Then it turned out I screwed up measuring the batteries, and it needed a different set of sensors in front, and... sigh.
Its actually 8 and not 8.09... You can check it out in Fibo acci's Sequence.
The digits of the sequence are not exactly representative of the golden number. Kind of like how pi is not 3. As you add more digits, you get closer to it.
Just because two numbers belong to the sequence, that doesn't mean that they alone can define the golden number. Remember that it's irrational, so any definition of it that only uses integers will be an approximation.
Please use dark color rubber band
9/10 IGN would be dissatisfied again
I'm looking for spicy Easter eggs
Those are nice things that you bought
Cool video, you could have constructed the golden ratio geometrical too to save on mathing
Satisfied comment.
The Golden Number, Phi, is also equal to 2 cos 36°.
Nice find. Messy, though. It requires that the calculator be set to Deg, not Rad. It's also conceptually tough; irrationality is not always easy to internalize, so removing it by more than one degree geometrically makes the expression become quite opaque to curiosity. I mean, I'm getting philosophical here, but what is 'cos θ,' really? It's just too arcane for me to understand. The Golden number here is being defined as something like, two of the quantity that's the ratio of two side lengths of the triangle that has an angle that's 1/10 of the circle. Whatever. Thanks for getting me to think this morning ;)
a project that doesn't require a saw?
new year's resolution make something on pocket83's channel complete
maybe you've heard this before, but I think you would enjoy the "standupmaths" channel. he often makes weird geometrical thigngs.
Super video, thank you.
Yh ermm wow I really love the Golden but I struggle getting my head around the maths (yeah I am English I say maths it just doesn't sound right without the s)
are u a math teacher with ocd obsession???
some how i feel very intrigue with all your videos... lols
new subs incoming. Have a nice day
I sense autistic vibes but idrk
That underlayment crap is 5 ply, 2 paper thin faces.
Great! Tnaks for teaching and sharing.
Woo! Math!!!
Ummm... atoms are a lot smaller than you think. A lot smaller than 1*10^-9
Oh! I made one of these on a 3D printer, so I guess I made one without using a saw.
lovely
Always interesting
Wow!
Dissatisfied comment: "Just under an eighth" should be said as "An eighth minus a blonde one." You can use other hair colors depending on how much over or under the measurement is. Sometimes you can use half widths (ie half a blonde one), but now we're splitting hairs. Happy new year.
Hahahaha.