Chapter 1: Understanding LEGO Geometry

Chapter 1 in the LEGO MINDSTORMS deals with the basic building material we use to build our robots with. LEGO bricks are usually represented in three numbers, representing Length, widt and height. The standard way to use LEGO bricks is "studs up". The width and lenght are expressed in terms of studs, also called LEGO units.
The LEGO system includes a class of components whose height is one-third of a brick. The most important element of this class is the plate. If you stack three plates, you get the height of a standard brick. It takes 9plates to make 3 bricks.
In 1977, LEGO decided to introduce a new line of products which targetted older audiences. It was called LEGO TECHNIC. It turned the 1xN brick holes into what we call a TECHNIC brick or beam. THese holes allow axels to pass through them, and permit the beams to be connected to each other via pegs.
If you want to construct a robot that needs to be strong but light, you would have to use a number of beams, plates, and pins to create the frame, and potentially you would need to cross-brace it. You should create a strong chassis. Building a strong and light chassis is pretty straightforward.
We shold not have everything in right angles because of the advent of studless parts, diagonal connections are mainstream now, makinf our world a bit more varied abd interesting and giving usanother tool for problem solving.
There is a question some people will ask. How would you bace a stack of beams with a diagonal beam?
First you must look at the diagonal bea as though it were te hypotenuse of a right-angled triangle. Then proceed to measure its sides, remembering not to count the first holes, because we measure lengths in terms of distances from them. The base of the triangle is 8 holes. Its height is six holes . Remember that in a standardized grid, every horizontal beam is at a distance of two holes from those immediately below and above it. It counts 10 holes in lenght. For people who have never been introducedto Pythagoras theorem, it is this.
Pythagoras Theorem is a theorem which is used in right angled triangles. The sides of the right angled triangle are called opposite, hypotenuse and adjacent. Lets call opposite and adjacent A and B and lets call the hypotenuse C. The equation is this:
(AxA)+(BxB)=(CxC)
(8x8)+(6x6)=(10x10)
64+36=100
100=100.