Platonic solids

The Platonic solids (here by OptimalControl) are defined as polyhedra (three dimensional solids) comprised of regular polygonal faces, arranged such that the same number come together at every vertex. The tetrahedron, octahedron, and icosahedron, each comprised of equilateral triangles, the cube made up of squares, and the dodecahedron made of regular pentagons, are the only polyhedra that match this description. These were described by Plato in the Timaeus dialogue, hence the name. He associated the first four with the elements fire, air, water, and earth, respectively, and the dodecahedron with the heavens. BTW, I know this is a LEGO-centric blog, and I try to stick to that, but if you are interested in geometric shapes like these, you might want to check out Magformers, a building toy made up of regular polygons with magnets along the edges, so they can easily click together to make various polyhedra.



From the Timaeus:

The first will be the simplest and smallest construction, and its element is that triangle which has its hypotenuse twice the lesser side. When two such triangles are joined at the diagonal, and this is repeated three times, and the triangles rest their diagonals and shorter sides on the same point as a centre, a single equilateral triangle is formed out of six triangles ; and four equilateral triangles, if put together, make out of every three plane angles one solid angle, being that which is nearest to the most obtuse of plane angles ; and out of the combination of these four angles arises the first solid form which distributes into equal and similar parts the whole circle in which it is inscribed. The second species of solid is formed out of the same triangles, which unite as eight equilateral triangles and form one solid angle out of four plane angles, and out of six such angles the second body is completed. And the third body is made up of 120 triangular elements, forming twelve solid angles, each of them included in five plane equilateral triangles, having altogether twenty bases, each of which is an equilateral triangle. The one element [that is, the triangle which has its hypotenuse twice the lesser side] having generated these figures, generated no more ; but the isosceles triangle produced the fourth elementary figure, which is compounded of four such triangles, joining their right angles in a centre, and forming one equilateral quadrangle. Six of these united form eight solid angles, each of which is made by the combination of three plane right angles ; the figure of the body thus composed is a cube, having six plane quadrangular equilateral bases. There was yet a fifth combination which God used in the delineation of the universe.

Formaldehyde

You might have noticed that I'm making some slight changes to the look of this blog, including the graphics added to the banner at the top of this page. I tried to choose some models from a few (but by no means all) of the major disciplines covered on this blog - chemistry, math, biology and astronomy. Let's take a few blog posts to look at the models I used. Starting at the left end with one of my own, here is my model of formaldehyde (shown next to a standard organic chemistry model kit version). Formaldehyde is made up of one atom of carbon (shown in black), with a double bond to an atom of oxygen (red) and two bonds to hydrogen atoms (white). One thing that is demonstrated by this model is the shape of formaldehyde. Molecular shape is driven by VSEPR - Valence Shell Electron Pair Repulsion theory. The bonds (gray lines) are made up of negatively chaged electrons, and, since like charges repel, those bonds push each other away. VSEPR says that the best (lowest energy) arrangement of bonds will maximize the distance between the bonds. Here we have three sets of bonds around carbon, and the furthest they can get from each other is 120 degree angles (360 / 3).

Inventing Our Future of Flight

I just ran across a press release that NASA and LEGO will be sponsoring a contest along the theme of Inventing Our Future of Flight this summer. Details will be forthcoming and I'll post them here when I find them.


NASA logo by Galen Fairbanks

Colossus Mark 2

James Pegrum built the Colossus Mark 2:

1944AD 1st June, Bletchley Park, England. The improved Colossus Mark 2 starts working in time for the Normandy Landings.
The Colossus was the world's first electronic digital computer that was at all programmable. It was designed by Tommy Flowers to solve a problem posed by a mathematician, Max Newman. In December 1943 the prototype, Colossus Mark 1, was shown to work. There were ten Colossus computers in use at the end of the second world war.
The computers were used by British code breakers, giving the Allies valuable intelligence, obtained from reading many encrypted high-level telegraphic messages between the German High Command and their army commands.

Newton's cradle

I've previously described a Newton's cradle, a desktop toy that demonstrates the conservation of momentum. Derfel Cadarn has built another LEGO version.

Lunniy Korabl

The LK Moon Lander (here by Kei_Kei_Flic) was a planned Soviet landing vessel in the late 60's, roughly the equivalent of the Apollo LM. After Americans were the first to reach the moon, and following setbacks in their own space program, the Soviets decided to scrap the mission and instead to focus on orbiting space stations.

Leonardo

Leonardo da Vinci (here by Legopard) was the ultimate Renaissance man. Of course he is known for his art, but he was also a scientist. His notebooks are full of his observations of anatomy and botany, his inventions in many areas, and his writings on geometry, the formation of fossils, the flow of rivers and the reflection of light off the moon.

LEGO math fun

I spent some time doing LEGO math with my 4-year-old today. Phase 1, numbers - build stacks for each number 1-9 and put them in order. Phase 2, addition - combine stacks and see what they make. Phase 3, subtraction - take away bricks from a stack.




BTW, that's 1-year-old's hand just behind her brother in the second picture, and that's her artwork on the wall. Each kid has gone through this write-on-the-wall stage. Time to paint the kitchen again. :(

Simple machine: screw

A screw is a machine that transforms rotational motion to linear motion. When you turn a wood screw, for instance, you are adding torque, or rotational force, but the screw translates this to a forward force, pulling the screw into the wood. An Archimedes screw (known since at least the third century BC and attributed to the Greek mathematician) uses this concept to lift water. Here are two LEGO versions of Archimedes screws to move little balls up a slope, both by Akiyuky. BTW, these were built as modules in Great Ball Contraption layouts. The GBC is a collaborative LEGO project where people build different modules that move balls from point A to point B. These modules all get strung together to make huge mechanism that are fascinating to watch.

Simple machine - wedge

Another machine that is so simple that it is easy to overlook is the wedge. The idea of a wedge is that due to the angled shape, as it is pushed forward, force is exerted outward (at right angles to the path of the wedge. Think, for instance, of a log splitter - you put the log splitter in the top of the log and hit downward with a sledgehammer. You are exerting force downward on top of the log splitter, but the result pushes the two halves of the log outward. Or even just an axe is a simple example of a wedge, with really the same idea. Axe by Demonhunter.



You killed Kenny! You b... by dm_meister

Simple machine: inclined plane

I got sidetracked from my series on simple machines. The next classical machine is perhaps the simplest of all, the humble inclined plane - a flat surface set at an angle connecting levels at different heights. I can see why some might not refer to a ramp as a 'machine,' but it fits the definition of changing the direction or magnitude of some force. When you push forward on a load sitting on the inclined plane, the slope of the surface translates part of that force into upward motion. Also, as anyone who's ever moved some heavy furniture into a U-Haul knows, it takes less force to move something along a ramp than it does to move it straight upward. You don't get something for nothing, though. To get this advantage you have to move the load over a longer distance, as the ultimate amount of work (force times distance) is the same. We see this in action in a moving truck by DadventureDan.

God speed, John Glenn

BMW_Indy made this great rendition of the launch of Friendship 7, taking John Glenn aloft to be the first American to orbit the earth.

Breaking Bad, the video game

As a chemist, Breaking Bad is a pretty fun show to watch. Not only is the protagonist a chem teacher, but they sneak in little nuggets of real science here and there. Brian Anderson made this parody of a Breaking Bad video game based on the style seen in the various LEGO games.

Pulley

Our next simple machine is a pulley (here by Evilnurn). A simple pulley changes the direction of a force transmitted by a cable as that cable moves around the circumference of the pulley. For instance, you could attach a rope to a rock and loop the rope over a pulley above you. If you pull down with a force of ten pounds, the result will be an upward force of ten pounds on that rock.


If you loop back and forth between two or more pulleys, you create a block and tackle (here by Louise Dade). This gives you a mechanical advantage. For instance, if there are two parallel stretches of rope, as in the model below, if you apply ten pounds of force in pulling the rope, twenty pounds of force will be exerted to lift the load. BTW, you never get something for nothing - you have to pull the rope twice as far to get double the force.

Lever

I was going to move on to the next simple machine, but Bobofrutx just posted this great example of a lever.

Wheel and axle

Next up in our look at simple machines is the wheel and axle. As with the lever, there is a relationship between the amount of force applied along the edge and the radial distance. Therefore a large wheel can be turned with relative ease, and yet be used to lift a large weight, as seen in this medieval crane by Stephle59.

Simple machine: lever

A simple machine is a mechanical device that changes the direction or magnitude of a force. Classical and Renaissance scientists defined six different ones. A lever (here by Linda Hamilton) is a rigid rod that pivots on a point called the fulcrum. In a class 1 lever, when a downward force is applied on one side of the fulcrum, an upward force results on the opposite side.



It also makes a difference how far the point of force application is from the fulcrum, as the actual term to be considered is torque, defined as the amount of force times the distance. The longer the lever, the greater torque can be produced, so that very large objects can be moved, as shown here by Ringleader. Archimedes supposedly said he could lift the earth if he were given a long enough beam and a place to set the fulcrum.

LEGO math fun

LEGO is great for teaching kids math concepts. I've used stacks of Duplo bricks to practice addition - i.e. 'put the stack of two bricks together with the stack of three bricks, and how tall is the tower?' And I've previously noted helping my daughter learn her 2x multiplication table. Here Erin from the So you call yourself a homeschooler blog is using stacks of bricks to teach fractions.

Apollo 13

CustomBricks has a look back at the Apollo 13 service module as the astronauts leave in the command module for their return to Earth.

Gear up

A gear is a simple machine, where two or more wheels have teeth, or cogs, that fit together so that when one turns, the teeth fit together so that the other turns as well. In this way, rotational torque is transferred from one axle to another. These axles can be parallel to each other, or, as in this case by Legohaulic, at an angle. If the gears have different diameters, they will rotate at different speeds.