Geometry of a 3D Wooden Star ★
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- Опубліковано 7 лют 2025
- Sorry it has been so long since I last posted.
This project looks hard at first, but once you have the sled and practice a few, it soon becomes intuitive, and then downright easy. I would have liked to include much more content and detail into this video, because I really loved this project. You probably understand that most people tune out pretty early, and they just want to see the punch-line. For this reason, I try to streamline videos to their most essential and relevant information. I hope that I didn't leave out too much in this case, because let's be honest, this one was difficult. It looks easy enough in the finished vid, but there was NO information on the interweb for this one; I had to develop this method entirely by my own tired and stressed brain. Please try to appreciate how difficult this video was to make- I spent a week of my spare time doing star-related geometry and trigonometry in order to come up with a somewhat simple solution to this problem. I included only what I thought were the things that I would've loved to find when I first googled "how to make a wooden star."
Anyhow, I'm done complaining. I promise that I will be making tons of vids starting early this summer. I have way more ideas than I do time presently. Please try to enjoy this one in the meantime, and as always, thank you for your time.
Music:
Deliberate Thought by Kevin MacLeod:
incompetech.com...
GREAT video and inspiration. I watched it this morning and spent a couple hours today building the sled. After a bit of frustration getting my head wrapped around how to turn each piece for cutting I made 3 flat stars, beveled ones are a project for tomorrow. I used your math to make a CAD drawing of the triangle, printed it out, and transferred it to the sandpaper. Once I cut out the paper I glued it to the sled and used it as a guide for installing the cutting blocks.
I've been watching a playlist of your videos for about 45 minutes, amazing tricks in every one. and there is always something to smile at. Thanks for sharing your workshop and knowledge.
THIS IS THE ONLY VIDEO THAT CAN EXPLAIN IN DETAIL IN MAKING 3D WOODEN STARS, THANK YOU FOR SHARING.
This is just beautiful in every respect!
From defining the 3D geometric challenge and analyzing the problem, through your clear exposition of the trigonometric solution, with a simple algebraic cancelation of sines... to the realization with that clever practical jig and using straight-grained wood that accentuates the star's geometry... Superb! There's a wondrous universe inside your Brain buddy!
As a math tutor and a wood working hobbyist, I LOVED this video. Great job showing the math to the side lengths. Pinned this to my favorites!
John Howell why not keep it simple! 3 x Tan (72) = 9.233 easy steps in Roof Carpentry.
Back before computer cad , us older tool makers would sit at our benches for hours figuring all our dimensions for making punch and die sections. Someone would walk up and ask a simple question and it was like a punch in the gut tryin to wrap your brain around what you were doing again.
I appreciate how you showed the steps to solving the math involved here. I've been driving myself nuts and burning through a lot of wood trying to figure out the correct angles. This will help a ton with my appliqués I use for my rustic furniture. Thanks!
Great. I'm glad it is helpful. This method will serve you well for a star against a flat piece, like on a piece of furniture. Once you figure it out and make the sled, it becomes super easy. Good luck, and let me know if I can help you any further.
I typically use (and recommend) a 24-tooth 7.25" Freud Diablo for general purpose. I also keep a 40-tooth handy for special purposes. The 24 is usually under $10 and it has nearly the finest kerf I have seen. Home Depot carries it; obviously it is the bright red one.
I once heard a mathematician say that he became good at it because he was lazy. I kind of agree with that. I don't know all of my times tables, and I am not good at memorizing numbers or angles, but I like to know enough math techniques so that I don't have to memorize. Carrying around the solutions to all of life's problems would be a lot heavier than just carrying around the ability to solve them ;)
Great video. Going to try and make a bigger one with a bandsaw and that jig. Thank you for breaking it down so understandable that a child could follow your instructions. This should be a project in high school wood shops, if they still exist
Thank you for making this video. I love it when someone makes a jig instead of hawking an expensive product most of us would only use once, if we bought it.
You are very welcome. I'm happy that you liked it, so thanks for letting me know. This one is one of my favorites.
this is a great video with showing how many maths is actually involved in making woodworking projects. Thanks for sharing
Mrhangerman Imagine and Inspire The maths is one sum Let’s keep it simple! 3 x Tan (72) = 9.233 that’s from an old roof carpenter
if this guy was a boy scout they would give him a merit badge for multiple reasons. who couldn't appreciate and marvel at this demonstration. ya might have view it more than once since it is loaded with information but unquestionably, a GREAT VIDEO !
A more than outstanding video! Precise and to the point with a calm approach!
I was pulling my hair on the math. I got it the first time watching this video- I know where I was going wrong.
I've been woodworking for 40 years or more and just now I decided to make 3D stars- go figure.
I kept trying to think of a way to calculate the cuts by using a miter saw. Your sled eliminates all this. Good job.
This is the best star instruction video i have seen yet, thanks.the math is a little beyond me.
PixelRick The maths is one sum Let’s keep it simple! 3 x Tan (72) = 9.233 that’s from an old roof carpenter
I found the math to be a very entertaining portion of the information and that part about getting more sure placement of parts by using math, well that is like a ray of sunshine. I will be looking to us that type of thinking in a future project. Thanks for making the sun shine, lol.
Great respect for the materials in every of Ur videos, minimizing wastes. Respect!
This is absolutely brilliant and thank you for taking the time to figure this out and explain it so eloquently. Will definitely be making this sled.
Your projects make me feel like a kid again. Thanks.
I appreciate it. It seems that we share some similar interests. I really liked the work that you did with tetrahedrons. Thanks for stopping by ;)
I made a couple of stars and they were ok, but not perfect. After watching your video I got some serious info on the technique of the angles needed. Can't wait to make that jig. Thank you very much.
Great. Let me know how it goes.
Deep. I just did 360 degrees divided by 5 = 72. Each finger has two parts so half 72 for 36... Maybe I'm too simple minded. I didn't care about the angle at the point. My only concern for angles was where they joined. Equal length took care of the points. I do like your sled though. Thanks for sharing.
On the subject of sizing the stars. A 1" clearance from the blade kerf to the alignment blocks gives a 6 1/8" star. So a 2" clearance gives a 12 1/4" star. And a ~5" clearance would produce a ~30" star. Practicality not withstanding.
Alignment block left > 1" clearance blade Kerf 1" clearance < Alignment block right
Thanks! I use mathematics a lot. I don't know why so many carpenters have such an aversion to it. It really is just like using a coping saw or a chisel- the more you do it, the better you get, and the more things you can use it for.
pocket83 The maths is one sum Let’s keep it simple! 3 x Tan (72) = 9.233 that’s from an old roof carpenter
Yep, my sister lives there, so I should probably send her one. I really liked the math part, but this is probably my favorite video. Maybe because I had to scratch my head so much to make it. There was a lot of math involved that I didn't include, because I get the feeling that it bores most viewers. Thanks for watching and commenting!
All the more reason to watch again and practice it. It becomes easy after awhile, and it makes you a better carpenter... everything in carpentry is triangles. If you do that problem ten times without looking, you will never forget how to do it.
Most of my audience is American. The numbers are really arbitrary, and it is just a simple conversion. Also, it makes little difference if you are using digital calipers. But I do agree with you, and I often use both systems.
The age old question in math class of, "when will I ever need to use this in real life?" has been answered. Shit... I should have paid more attention!
LOL! Yeah ok - so there's 1. And it's a choice. Should have spent more time on how to invest properly for retirement etc.
Doesnt matter because this video is a better teacher on the math process than any actual math teacher in school.... you can learn ANYTHING online. As long as you have the drive to seek out this knowledge, college is a waste of money
Never too late to learn! I'm 51 and studying GCSE maths in night school. Great fun!
Brandon Kitchens Let’s keep it simple! 3 x Tan (72) = 9.233
Great video inspiration! Pretty beautiful work!
Thank you very much for the express class on geometry. We get so busy with everyday tasks that sometimes we forget about these basic things we learned in school. Amazing work! Congratulations!
wowsers -- geometry - it's been soooo long. Who would have guessed how useful it can be.
I'm glad that you enjoyed it. Thank you.
I haven’t heard sine for almost 45 years, my math teacher would be proud! Nice job!
Wow you did such a good job with the grain patterns
Brilliantly explained in this crisp build video. Thanks
Beautiful 2x4's you started from!!! Seemingly straight and Not a knot in sight. The 2x4's at my local store as aee knot riddled twisted cupped and bowed, usually with some visible wane
Thank you for this. Admittedly, I just came for the angles and measurements of your jig. While I did learn your awesome process, I also get the sense that I am LOT less educated than I thought.
Planning a 12-point star for a clock. This showed me how. I can't thank you enough.
That would be beautiful. I haven't thought of that. Hope it turns out well!
Best video available ! Hands down 👍
I'm so fascinated with woodworking, trying to teach myself now that I'm retired. This video is very helpful, but I need to brush up on my math. It's been over 40 years since I've used geometry.😂😂😂. Any other tips or resources will be greatly appreciated. TFS
Thanks, MrChris. I am glad that some of us out there enjoy this stuff. I think many will find this one tedious or boring. And sorry I made the message too short (I couldn't get it either).
This gives me thoughts on how to make 3D crosses for Christmas presents. Thanks!
I love that you love it. Thanks for continuing to watch.
Great job explaining. Now Joey pay attention and you can do it like this gentleman did!
Great job. Been looking/thinking about wooden stars for a while. Thanks.
7:10 I use brad nails that are sticking out just a bit 1/16 or 1/32 and sharpen that keeps the wood of moving. A bandsaw with sharp blade for cutting small part works good too. Thanks for the great video, big help.
I agree: this method could easily be adapted to a band-saw. That would likely be less precise, but better suited to building large stars. Glad this was useful.
pocket83 Yes it would be less precise only because the most bandsaws are not setup for more precise work, like using a fine cutting blade ect. My other thought is to setup a small disc sander. Thanks again for the Great how to do video you made!
I really enjoyed this video. Not much info on the Web on how to make a 3d star. Much appreciated.
You are certainly welcome. I hope it works out for you!
Donald Toohey
Most excellent thanks, a great way to combine my favorite subjects of woodwork and maths. . Well produced and presented.
I made a small one of those by hand out of a single piece, carved and shaped it with chisels, rasps, files and sandpaper. It's about 2 inches tall when standing on two of the legs.
Thank you for uploading this tutorial plus the math lessons. I'll give you a thumbs up for your neat work. My dad would really appreciate this tutorial, being a carpenter and a math Wizard. However, I"ll pass and will go to Homesense to pick up a star to decorate my shelf.
Nobody seems to have mentioned it, but you did not need to use the law of sines to solve that problem since you have a right angled triangle. The law of sines works on any triangle, but right angled triangles are simpler. With your triangle you have tan A = a / b, therefore b = 1 / tan 18° = 1 / 0.3249 = 3.078 as you found.
I am sure that pocket83 wanted to have his information apply to any triangle (need an angle on a triangle? Ah ha! I can use the law of sines.) and that is why he included this law not narrowed down to right triangles only. Thankfully math provides us more than one way to skin a cat. Your comment contains the same reasoning.
Thanks so much for your. Response. I'm amazed at your work. All your videos are great. I'm new to wood working and really want to make this star.
You explained the math very concisely and if you didn't cover it, someone would ask how you worked out the angles.
I wouldn't be one bit concerned about the thumbs down. There's about a 10:1 ratio, one idiot to 10 non-idiots, so you are bound to get a few. Idiots like clicking that button, it's easier than thinking or writing something constructive.
I have a tip for anyone making one of these solid wood stars: Don't cut your sections before you're ready to glue them together.
I made the sections of a 36" X 1½" star and when laid out, the pieces fit perfectly. Then the pieces sat for several days, and when I went to glue them up, they had warped every which way as they continued to dry.
Good point. These are super-precise cuts, and any moisture/temperature changes can ruin even the best-laid woodworking plans. Also, whenever a board is cut, many of its internal stresses are released, and so it will slowly change as it acclimates to its new shape.
For the record, warping is no major issue to an _already glued_ star. The wooden star in this video is now over a decade old, and it's been hanging on a block wall in my basement for the last five. Still looks new.
@@pocket83squared Right. I would think the bigger it is, the more it would warp, BUT, once all pieces are fit together, it would seem that any warpage would only be in flatness, which is a lot easier to deal with.
By the way, I plan to take my warped pieces and glue them flat to ten new triangle pieces so as to make the star twice as deep, then bevel both sides on a bandsaw with a tilted table, before gluing the five sections together, using your masking tape ides. Thanks again for that.
great vid, 1. what is the distance on your jig of the following=
top kerf to edge of board (assumed equal on both sides
bottom kerf to 18 degree cut corner
length of board that has 18 degree cut on bottom
I built a jig and used your math but I missed it somewhere because I now have a jig to make great 6 pointed stars not 5 pointed stars.
fiberinspector Side edge: 3" from kerf. Edge along kerf: 9.234".This is discussed at 5:25, let me know if you still don't figure it out.
pocket83 went back and rechecked all measurment, got it right this time, as to the clamps I put a stop with a small board at the 9.234 point to stop the piece being cut from moving, this way all pieces are cut to the same length and will not slip when being cut. Thanks again for the jig!
@@fiberinspector1304 I see this is 3 years old but any chance of a pic showing the "stop with a small board at the 9.234 point"?
@@whoDatBeDare no, but it is just a piece of wood that allows the board to be placed at the same spot every time you make a cut for that Angle.
Nice!
I think the subliminal message in this one was revealed when immediately after I watched it, I did a Google search on why people put stars on their houses.
Might be just me but it looks like you only need one side. Not both to have the angled blocks. So you could cut the build complexity in half. (???) - Yes, proven in Sketchup. I have added my Sketchup version to the 3D warehouse under the same name as this video. Shared with best intentions. ( I have NOT looked at the 30° slope 3D version as yet. )
That was awesome Pocket!!, and now I can make some stars.I loved the way you matched the grain in the wood to make............I don't no like infinite little stars. It felt like that to me anyway.
Thank you, and keep up the great work that you do because people will learn a lot from watching them. I well anyway.Kevin.
you are the best ever.
love this project and really love the way you are thinking and doing
thank you very much
i loved it and learnt from you math solution fantastic i love it when the penny drops on something!
WOW... You're videos have always been good.. This is a whole new level. Great use of technology and math. It is obvious to the audience that you really know your stuff. Keep up the good work. I check out your videos on a regular basis!!!! Charlie
Thanks for the math. I like to cut to the "chase scenes" as soon as possible.
You could do that, but why bother with the extra work now that the numbers have been figured out? Also, with something this precise, the thickness of the printed lines or any minor distortion from the printer could be enough to throw it off.
Agreed. A digital protractor is best.
I love it. Not too much math. Have you ever been to Texas? State logo is this 3-D Star! Great vid - please keep them up.
Just an FYI: Harbor Freight sells an aluminum caliper that is 24 inches long. It measure in fractions of an inch down to 1/128's which is .0078125 of an inch or .198438 of a millimeter.
I'm a little late to the party but thanks for the vid and clear explanation. Thumbs up and subscribed.
You are a star 🌟. More fantastic content from an amazing channel.
DUDE!!! you just made yourself even more awesome!!! thanks for that man seriously
you've gone way beyond the layman's terms of wood working 😊😊
Ella Gilbert The maths is one sum Let’s keep it simple! 3 x Tan (72) = 9.233 that’s from an old roof carpenter
WOW. Love it, now to try it. Thanks for the info
I love these videos and all the maths.
Did you make a similar jig to what I used? If so, the placement of the block on the jig must be incorrect if you are getting 3-points. Also, try making the paper star- it seriously helps the confusion. I totally understand, but don't get frustrated... it took me a week to develop this method. The video makes it look so easy. It isn't. Give me more details if you still need help.
You are so amazing. I’m enjoying all your videos . I’m fascinated with wood works and I’m learning loads more from you, keep it up ? Thanks
Thanks. I really appreciate that. Glad you found some of it helpful.
wonderful. the ending with the cuts and music reminds me of Twin Peaks a little :)
You what thanks for the video very very interesting and helpful-I was looking for information about how to make exactly that star but but - it was very painful for me to remember the number one reason I hate math --a simple cut made my day full of pain . And bad memories
Finally! Finally! So this is an example of why I studied math …. Sin, cos, tan … never, until now, found out why it was useful in complex woodworking angles! Thank you! Sub’d and liked and will keep around in favourite folder!
I would like to see if another solids could be constructed from those 5 pieces if joined by different surfaces. Very nice though, thank you.
my brain has just exploded.
yea simple geometry haha i bet it took him days to figure this out. i tried it and have still no idea how to calculate any of that. but seeing the numbers solves it pretty good
Mr2at how to make a barley twist
steffankaizer it really is simple geometry. If you have been doing this stuff for a while you can solve this in under minute.
Good instructions my fellow carpenter it's all math and its in our carpentry tools but gotta use the brain to make it work.
Amazing video 😀 I somehow made a 3d star, ended up a Six Point star, dont ask 😀 but, what are the angles from blade to the stock, both short side and the long Cut? I am missing something 😀
You have so much skill for this I love you videos
Beautiful!! Really nice work.
Thanks, this was exactly what I was looking for. I'm going to be making some Hero of the Soviet Union medals and was a bit puzzled by how to add the bevel, carpentry teaches you geometry but geometry doesn't teach you carpentry :P
2 minutes in and I already know I’m not smart enough for this project. Looks great though
This is an awesome video. I've been trying to position these side blocks and can't seem to get it right. I know my measurements must be off somewhere. So in the example a= 1 inch and b is equal to 3.078. So then is a= 3 inches then b = 9.234?
Yes. You could also multiply both of those numbers by 2, or 4, or 5, or any other number. It's a ratio, so one side of the triangle just has to remain the same _proportionally_ to the other.*
The numbers 1 and 3.078 are a generic solution that can be multiplied to apply to any size blocks for any size sled, and it will always give you the correct angles.
The other dimensions on your sled will all have to do with the width of the stock you use, so that will take playing around on your part. I really hope I helped in some way.
*Oh, and one more confusing part: you can't _add_ a number to both of those numbers, because it will change the ratio. Preserving a ratio only works with multiplication, and not addition. Think of it this way: a triangle that's 1x2 has the same shape as a triangle that's 2x4. Now add 1 to each of those numbers instead; a 1x2 triangle is NOT the same shape as a 2x3 triangle.
Thanks again. I kinda figured the sled dimensions played a role in this as well. You really helped me thanks. It took you a week to figure this all out might take me a year. LOL.
Tangens look easier for that calculation of the jigs but anyway very well done! I everything with 18, 36, 54, 72, 108 degrees is cool (some even call it sacred geometry)
All divisible by 3. See Tesla 3 6 9.
Solved the angle problem. I made a jig for my miter saw. took a 2x4 and cut 30 degree cut in one end and a 45 degree cut on the other end and I can cut ant degree angle I want. I can cut stars 3D or 2D. But I do love your video. I did make your jig i like it but your stuck with one size star.
Great teaching.. I was nerding out on the math.. Love it
Parabéns pelo seu trabalho, e pela aula de matemática nós cálculos de ângulos.
Yep..I won’t be making any of these stars anytime soon. Thanks for the video. 👍🇺🇸
thank you, very useful and practical
like it, very useful. Thanks for sharing!👍💪
Excelente trabajo..
Thanks for doing the geometry! I have been trying to figure out how to cut a similar star, but with solid "arms", rather than made of 2 glued pieces. Have you put your brainpower to work on that approach (maybe using a jointer sled somehow?).
p.s. As good as you are, you deserve a better table saw - get a SawStop and you'll be glad you did!
A copy-cutting device comes to mind; perhaps a router-based pantograph is what you are after. An alternative might be an inclined router sled, but given the radial symmetry and precise stops necessary, you would end up with jigs more complicated than the pantograph is! Further, lumber size would quickly become problematic.
As for the table-saw, I presently have no problems with the one that I have, but my next upgrade is not very likely to be a Sawstop. So far, I'm not impressed by the hype. Please do not ask me to debate this subject.
Thanks for reply! Since you seem to be a solid geometry guru, can you tell me how to create a star maybe 3 times the size of yours? Do I need a very thick piece of wood to then rip on 30 degree angle? Also, does the geometry of this star mandate that both cut angles are 18 degrees? Or did you use your jig that way for convenience, making both cuts on same jig. I have seen "fat" stars, so could I make a second jig at a different angle to make longer, skinnier arms?
Question: In making this, which is a great solution to a making a star, there seems to be a lot of waste. What I mean is, you have to hold on to something on the sled fence, because the actual piece that is being made is on the "waste" side of the blade. Not an issue if using a 2 x 4, but if you use walnut it becomes a concern. Is there an efficient way of cutting your pieces?
briansullivan63 Sullivan I totally agree. Waste is just a simple fact of using this method. Since I used 2x4, it was little concern, but I would be interested to see an improved procedure. I'll think about it.
+briansullivan63 Sullivan I stumbled onto a solution to the waste. It is hard to describe but if you use the jig to cut off the waste and pay very close attention to its position on the kerf you get a second star from the waste. Now this is making the flat style star, I am not sure it will work with the 3D version.
So beautiful star 😍
Maybe someday I'll tackle this more challenging star. For now I usually don't add the bevel.
Very good.
Thanks for sharing