Been a bit obsessed playing with my CNC software.

Tend to fill bored moments with new patterns for small coasters.

Here are a few.   More on my blog:https://4dfurniture.blogspot.com/2023/08/coaster-everywhere-i-look-i-see-coasters.html

 

If you see a pattern you want to use and are using Vcarve or Aspire from Vectric.com, let me know in a personal message. I can email you the file.

4D

WOW!!!

 Some nice patterns for chip carving.

If you're interested, I can export the vector files to a PDF file you can print and use to chip carve DuckSoup.

My interest in this pattern work started many years back when at a local woodworkers show (associated with a pancake feed) and one display was filled with chip carved lathe spun plates and bowls and wall art, etc..

4D

I keep adding variations to my blog post.  As aspire remembers my job settings it is easy to crank out another one if I've got a few minutes to kill.  I've been starting with simple polygons, then chopping parts out of them before spinning them to see what the final pattern will look like..   I also experiment with the rotation point I use as that can make a big different in the final pattern. 

4D  

I like it!

Thanks KevTN.    After doing several I started to notice some recognizable shapes generated, a bit Escher like.  Now I've been playing with simplistic animal shapes to see what I can come up with.  When I stumble upon a pattern I like I'll add it to the blog post.    Right now I'm momentarily possessed with finding a way to make a heptagon with just circles/arcs or lines.  Google insists it is impossible, but my brain keeps nagging me to prove it can be done. 

4D

With new technology is allowing shapes to be created that once thought impossible.

Finally cracked it last night.  So far no matter how far I zoom in I can't find any near misses unless I was careless where I clicked when starting a line or arc or circle. 

Math sites and other assorted google links insist it has been proven that you can't draw a true regular heptagon using compass and straight edge. Something about 360/7 not being a whole number.   Despite that I have proven it can be done.  Thinking about setting up a drafting table and digging out my t-square, compass, and triangles just to prove you don't even need a computer to draw one.  

https://4dfurniture.blogspot.com/2023/08/proof-you-can-construct-regular.html

Even uploaded a crappy screen grab of me stepping through the process using Aspire.  Finally got some sleep after posting the blog last night. Woke up with a dull headache. That is consistent with other times when I've done a slow long mental burn  to create an impossible thing.  Brain feels wounded a bit. Some breakfast should help. 

4D  

Creativity hangover huh? The link you left isn't working for me. It's cool it worked! Hope you feel better

I turned it back into a draft so I could work on the screen shots and video a little more.   I have a sister with a husband and daughter-in law who both teach geometry at a school they founded.  The Lucy School, named for our grandmother.  Also two other sisters who taught math before retiring and are interested. With growing interest I figured with a little time I could make it a bit more professional. Add some audio to the video, etc..

 

As for the brain drain hangover some meat lover's pizza for breakfast pretty much took care of that.    

4D

That's pretty cool and I am sure it is helpful too. 

 

Pizza always fixes those things...

11 hours ago, 4DThinker said:

I turned it back into a draft

 

Let us know when it's available.  About a 99+% chance it will be over my head... but I will check it out

I may now know why math pros claim creating a heptagon using just compass and straight edge it impossible.  Made the mistake of zooming in on all the intersections of the lines and arcs in my solution(s) and keep finding near misses.   By near I mean .0002" or such.  Unnoticeable when zoomed back to see the whole drawing or video, but proof that my assumptions of alignment and intersection can't rely on the pixel resolution of my PC screen.  While there are several perfect vector intersections (that still intersect when zoomed all the way in), so far I haven't found one that lead to a solution. 

Finding all the sides only requires starting with/finding any two sides, adjacent or not, or any three corners.  It is easy to start out knowing one side (two corners) and create arcs/circles/lines that pass through all the other corners/sides.  What is hard is knowing where on those vectors the heptagon sides intersect.  I can find several points that land on a side with two or more vectors passing through to verify, but at least two on the same side are needed to deduce the direction of the side they lay on.  That can lead to the needed corners that will let you find all the other sides/corners.    

 

Not giving up as (usually late at night) I've come extremely close several times.  Reality always strikes the next morning when I realize I used unknown info or inaccurate intersections. Getting into the habit of using layers to mark any confirmed or potential intersections in a different color than all the construction lines I've created and the heptagon shape I'm after. Nice to be able to turn off a layer or two on occasion to remove clutter which can reveal new potential directions to pursue.

4D

 

 

Math used to keep me awake at night too. Probably because I blew off homework to do something more funner

Retracting my last Post.  Proof below that starting with just the top side of a heptagon you can find all the other corners and sides between them. 

1.   The side length I started with is 4" long.  From the ends draw 4" diameter, 8" diameter, and 16" diameter circles.

     The 8" circles pass through the top 4 corners, although we still don't know where on them the lower set of the top 4 are. 

 2. Draw lines straight down from the outer edges of the two 4" circles.  Where these intersect the outer 16" circles is a location on the heptagon side.

 3. Draw a line between the two intersection points found in step 2 above. The center of that line is a critical point where lines from the upper side corners to the opposing lower side corner will cross.  The crossing lines also intersect vertical lines projected down from the end of the starting side. 

 4. You know know where all the corners are but the bottom corner.   Draw two 4" circles centered on the lower side corners and they will intersect at the lower corner. 

 5.  Such is a graphic connection between the initial known side and all the other sides/corners.  The image above has a few extra unneeded lines that weren't  required to find the heptagon shape.  I'll clean the unneeded away before I post this on my blog with a step by step set of directions.  

I'm researching who I should submit this to for publishing so that may take awhile.   I leave it here to end the story that evolved from a fun pursuit of coaster patterns. 

 

4D

 

 

Edited September 2, 20232 yr by 4DThinker

32 minutes ago, Grandpadave52 said:

Math used to keep me awake at night too. Probably because I blew off homework to do something more funner

Solutions to math challenges, as well as how to solve challenging wood joinery problems, never kept me awake.  Evening contemplation usually helped me fall asleep, and my creative subconsciousness would find the solutions to wake me up energized knowing them in the morning. 

That last sketch reminds me of the old technical drawings for bicycles and airplanes. LOL

22 hours ago, KevTN said:

That last sketch reminds me of the old technical drawings for bicycles and airplanes. LOL

I'm old, so any technical drawing I do is also an old technical drawing. Related story comes from graduate school (Product Design @ N.C. State)).  I'd been teaching as an instructor for 4 years or so before I went to graduate school. In one class the teacher asked all the students to go up to the chalk board and sketch out how they might design a bicycle that would only be used for riding up steep hills.  My drawing was large enough so it could be easily seen by anyone sitting in the back of the room.  Every other student drew their ideas no larger than a notepad sheet.   When we were all done and sat down the instructor remarked "Can anyone tell who's drawing might have been drawn by someone who's taught classes before?.  As I already knew the answer I just sat there amused and wait for the discussion of the ideas on the board. 

4D

Thgat's above my pay grade!!