Level 3 – Concept 17 Exercises

Coding Exercise 1

Prerequisite Concepts 7, 12, 13
Key Concepts 16, 17

The official symbol of the Olympics (since 1915) consists of five interlocking rings. The rings represent the ve inhabited parts of the world, and the design was created by Pierre de Fredy, Baron de Coubertin.

Write a Bricklayer program that builds a LEGO artifact, similar to the Olympic rings, shown in Figure 1. Notice the rings in the LEGO artifact below are interlocking. Before building this artifact it is recommended that you complete all Vitruvia exercises for Concepts 16 and 17.

Hint: use setMyspace2D to draw portions of a ring (i.e., arcs). A good way to better understand (e.g., debug) what is being built is to differentiate the colors of the arcs from the rings they overwrite as shown in Figure 2.

17_01
Figure 1: The Olympic Ring logo.
17_01b
Figure 2: Using color to differentiate a ring from an overwriting arc.

Coding Exercise 2

Prerequisite Concepts 7, 12, 13
Key Concepts 16, 17

A Boomerang-like artifact can be made using 4 flexible sticks. The artifact is held together by tension alone (e.g. no glue is required). For those who like frozen treats, Popsicle sticks can provide suitable materials for constructing the Boomerang. For those who like coffee, the sticks provided in coffee shops to stir coffee are also suitable for constructing the Boomerang.

The figure below shows a Boomerang constructed using 4 coffee sticks. Tension is created between the sticks by placing sticks above/below one another in a particular configuration. The tension holding the Boomerang together results from a single “tension stick” that passes above two sticks and below the third stick. This construction causes the tension stick to push down on two sticks and push up on the third stick. The three affected sticks are positioned in such a way that, in turn, they also apply tension to each other in a manner that holds the artifact together.

17_02_sticks
A Boomerang constructed from coffee sticks.

The basic idea behind creating stick constructions that are held together by tension alone is as follows. Individual sticks are treated as two-dimensional artifacts. We assume that (1) it is possible to bend a stick (e.g., a rod made out of rock will not bend) so that it occupies more than one two-dimensional plane, (2) a stick can only be bent a little bit, and (3) bending a stick creates tension (e.g., unlike “bending” a piece of string the stick wants to unbend). From these assumptions it follows that, without bending, sticks can only exist in a single (two-dimensional) plane, and a stick can only be in more than one plane if it is bent.

A collection of 4 sticks (i.e., an artifact) is held together through tension when they are arranged in such a way that the resulting construction can only exist in two adjacent two-dimensional planes.

The figure below shows how a two-dimensional Boomerang can be constructed in a (single) one-dimensional plane in Bricklayer. In the Boomerang artifact, each stick is constructed using two lineXZ function calls. Creating the visual impression that a stick is below/above another stick is accomplished using two mechanisms. The above/below positioning of the tension stick is created using the function setMySpace2D, and the above/below properties for the remaining three sticks is accomplished using overwriting.

Before building this artifact it is recommended that you complete all Vitruvia exercises for Concepts 16 and 17.

17_02
A Bricklayer Boomerang constructed in the xz-plane.

Coding Exercise 3

Prerequisite Concepts 7, 12, 13
Key Concepts 16, 17

Write a Bricklayer program that uses the functions setMyspace2D and circleXZ to create the artifact shown below. Before building this artifact it is recommended that you complete all Vitruvia exercises for Concepts 16 and 17.

17_03
A four colored circle.

Coding Exercise 4

Prerequisite Concepts 7, 12, 13
Key Concepts 16, 17

Write a Bricklayer program that uses the functions setMyspace2D and ringXZ to create the artifact shown below. Before building this artifact it is recommended that you complete all Vitruvia exercises for Concepts 16 and 17.

17_04.png
A rainbow colored spiral.