## Posts

### Triangle wave gyroid

A gyroid is a fascinating geometric structure. It's a three-dimensionally-tileable unit that creates an infinitely connected surface. The surface is triply-periodic, meaning it repeats in all three dimensions. Gyroids also occur naturally in polymer science and biology. For 3D printing, a gyroid is a useful infill pattern. Not only does it fill volume without using much material, but it also provides strength to the final part in all three dimensions. As an added bonus, a gyroid pattern can be built using a toolpath that never crosses itself. In this article I present the traditional gyroid and a couple of alternatives that might work better for 3D printing. Traditional gyroid The gyroid surface can be approximated with trigonometric functions. It's a rather simple equation: $$\sin x\cos y+\sin y\cos z+\sin z\cos x=0$$ That is, at every (x,y,z) coordinate value where that equation is zero, that point is on the surface of the gyroid. There isn't any closed-form

### Metachronal waves of legs

Have a look at this centipede walking. You can clearly see waves of legs propagating forward along the body, from back to front, as the centipede walks forward. The motion of the legs is known as a metachronal rhythm , appearing as traveling waves caused by actions happening in squence. It's even more obvious with a millipede. In each case, a leg in back leads the one in front. Is this universal? Four-legged creatures walk this way too. A horse leads with the hind legs when walking or galloping. When trotting, however, a horse moves diagonally-opposite legs in unison and the footfalls are balanced with no leg leading, as can be seen in this video: Try crawling on your hands and knees. When crawling at a comfortably brisk pace, you may notice your legs leading the arms. If you try to lift up an arm before lifting up a leg on the same side, you can certainly do it, but it feels unnatural. Oddly, six-legged insects and spiders don't walk this way. Inse

### Something that mattered

I recently joined a Toastmasters club local to me, to improve my public speaking skills. In the educational pathways available, the first formal speech one gives is the "icebreaker", in which you speak for 4–6 minutes about a comfortable personal topic. Here is my icebreaker speech, which I accompanied with a slideshow of pictures as I spoke. Something that mattered Thank you, Mr Toastmaster, for the privilege of letting me introduce myself to this group. I'm going to share with you just one of many childhood interests that have played a large part in shaping who I am. That interest is flying. Flight in any form. It started when I was two years old, terrified of the monsters flying over our house who would eat me. Or so my parents told me; I don't remember it. We lived near the flight path of McClellan Air Force Base. My mother took me to the base to face my fears. She showed me that airplanes were machines that fly like birds, and that people fly them.

You don't see aircraft with elliptical wings anymore. The most famous aircfaft with such wings is probably the Supermarine Spitfire fighter aircraft from World War II. Elliptical wings have the most uniform theoretical distribution of lift and therefore the least induced drag. In the case of the Spitfire, the gentle taper of the ellipse near the wing root also provided more room to mount weapons internally than a straight-taper wing, while providing an overall thinner, low-drag cross-section. However, with all curved edges, elliptical wings are expensive to construct. Of all the kinds of drag that a wing or propeller blade experiences, induced drag is an unavoidable price for lift. Induced drag has nothing to do with the drag created by surface area, surface roughness, or thickness of the airfoil. Induced drag depends on the planform shape of the wing. It is also inversely proportional to aspect ratio (the ratio of wing length to airfoil average chord length). The optimal and

### Whose hands are biggest? You may be surprised.

A recent project to create an ergonomic handle for 3D printing led me down a path that introduced me to anthropometric measurements of the human hand, which in turn revealed some interesting facts about hand sizes. I had no idea that hand size is dependent on nationality, but I found a number of research articles on this topic. For those who don't want to read further, the answer to the title question is: Based on the data found, Filipino males have the biggest hands, by a significant margin. In fact, the margin is large enough that this population may be considered an outlier from the general human population with respect to hand size. Even Filipina females have larger hands than most males of other nationalities. On the other end of the spectrum, Vietnamese females and Indian females have the smallest hands. Now you can read on for the whole story, or you can skip down to the chart at the end. Idea for a toy My unintentional investigation into hand sizes started while de