The Beauty of the Resultant


The nice thing about geometry (aside from sitting next to Cris Titsworth) is that you can perform some operations that look difficult with surprising ease.

For example, let’s look at my “wireframe” model for my next project. With needlenose pliers I can adjust the rake and splay of the legs, which are made from 12-gauge wire, until I’m pleased with how the legs look from all directions.

This is the "grasshopper" method.

This is the “grasshopper” method.

Then, using some formulas picked up from old books (see above, I can’t believe I am showing you this)…. I can dial in my angles.


Then it’s a cinch to knock out the finished piece:


Of course, I can adjust the legs to produce these simple variants.


Or, by simply changing the value of X, produce this:


— Christopher Schwarz

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Publisher of woodworking books and videos specializing in hand tool techniques.
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22 Responses to The Beauty of the Resultant

  1. Hmmm, looking at the first illustration, I can see how Cris Titsworth was a large influence on your designs.

  2. There is a great article on ellipses in pop wood written by me on how to lay out all this.


  3. joeyb5 says:

    The glue has asked me to ask you to refrain from sniffing it.

  4. Now you are just showing off
    very best

  5. misterlinn says:

    One can get help, you know, Chris. In Britain psychiatrists are free on the NHS…

  6. Brian Clites says:

    Chris, what would it take to convince you to take a vacation?

    Your posts the last few weeks have been riddled with what appears to be a volatile cut of siliness and negativity. Some of the posts are really funny (Titsworth!), but they also read like a paste wax polishing the pessimism and self-loathing that have dominated the other posts about how difficult and unpleasant your job has been of late.

    Please forgive me for saying so, but I’ve been there (I might still be there), and I’d encourage you to take some time for yourself. Your change of e-mail policy really surprised me, but upon reflection it seems like it could be the first of several large steps you might take to lighten your burden and return to the things about your job that you love.

    Sending you happy thoughts during this winter. And don’t feel obligated to post so often to this blog, at least not for the likes of me.

    • Brian,

      Thanks for your concern, but it is unnecessary.

      If you look at this blog over the long term, there are times when I experiment with different modes of writing, as well as different kinds of woodworking.

      I also do not like to say: This is satire. This is mockery. This is profound. This is a zeugma.

      These last few bits of writing are part of a very long arc planned for the year. I’m not saying it will all be disjointed like the last few posts. Far from it. I am building a case for something. And doing it slowly.

      And if I stopped writing or stopped experimenting with writing, then I would really get grumpy.

      All best,


      • Brian says:

        Thanks Chris. So glad to hear it! Then, by all means, write on!

        I want to apologize for jumping from avid-reader to creepy-pop-psychologist. It is clear me how very much you care about your readers, and I just wanted to remind you that many of us care deeply in return for you. (And not just because of your amazing wood 😉

        Cheers to a great 2015, and to learning about the furniture we all need!

  7. Rachael Boyd says:

    I’ll have what he’s having.

  8. graemebaird says:

    I thought not answering emails was supposed to HELP with your sanity issues?

  9. rpbell says:

    I hope you are planning a dvd or 2 day course on this. My geometry skills were sadly lacking even when I was in student mode. Now there is no chance to get this without intensive tutoring. Regards

  10. Folks, I’m fairly sure these are jokes about the differences between the Furniture of Necessity and the highly ornamented styles that Chris has said on many occasions he finds less appealing. You can make beautiful furniture simply. And that’s why Furniture of Necessity is the book I’m looking forward to most.

  11. jenohdit says:

    Chris is showing off just a bit here. Sure it’s as simple as just changing x but what he’s not telling you is that you have to do that in the 5th dimension, project into 4, from there to 3, and finally to the flat drawing.

    Absinthe or a simple “spirit varnish” was traditionally used to get as high as the 6th dimension. Modern ales are only good for up to 4. Schwarz obviously has a good Jenever in his Dutch tool chest. A kopstoot or 2 of that will get you to 5 in a flash.

    For those who are rusty on the math, this will have you knocking out some legs in the man cave as soon as you get home from the daily drudgery.

  12. diondubbeld says:

    Well spoke Timothy.

  13. Sean Hughto says:

    “Martha, until this rain let’s up and the field dry out so I I can get on them, I only have 11 hours of work a day to do round the farm, so I’ll try to use that extra 5 hours for the next couple days to go out to the barn and make us those chairs you been askin fer. Now, don’t worry, as I won’t be fartin around with no wire models and fancy mathmaticle figurin. I’ll use my eyes and my hands ….”

  14. npc29 says:

    Peter Titsworth wears the tube top in the world of site lines and resultant angles.

    That said I would prefer to learn my geometry using Cris as the example.

  15. In the movie “Spaceballs”, there is a scene where two adversaries face off against each other. Each one is holding a light saber with their hands in front of their lower abdominal area. One said to the other: “Ah, I see your Schwarz is a big as mine!”
    This has little or nothing to do with geometry, but I thought it was an interesting tidbit of information that fit in with the general tone of the conversation here.

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