GRAPHICS
USING MINECRAFT ON YOUR TABLET AS A LEARNING TOOL.
Install either Minecraft or Worldcraft 2 on your tablet. We will use these apps to help with drawing in 3D or Isometric views.
Activity One: Phi - the golden ratio or golden rectangle. The golden rectangle was used in ancient Greece in art, design and architecture. The resulting rectangular shape was apparently pleasing to the eye. The ratio is found in plants, the human face and hands. The ratio of the length to the width of the rectangle is 1.618...similar to Pi (3.1415...) in the fact that both numbers keep on going after the decimal point without repeating. These numbers are also classified as irrational numbers because they cannot be expressed as fractions or a 'ratio' of numbers. An example of the Golden Rectangle can be found in the Parthenon in Greece. There is no formal mention of the use of the golden rectangle or ratio in the construction of the building. The first time it is mentioned in Greek literature occurs about 140 years after the Parthenon was built. However, by constructing a rectangle around the ruin one can see a close relationship of the dimensions of the Parthenon with the Golden Rectangle. The diagram below also shows that the Golden Rectangle is made up of a number of smaller (decreasing in size) rectangles.
Install either Minecraft or Worldcraft 2 on your tablet. We will use these apps to help with drawing in 3D or Isometric views.
Activity One: Phi - the golden ratio or golden rectangle. The golden rectangle was used in ancient Greece in art, design and architecture. The resulting rectangular shape was apparently pleasing to the eye. The ratio is found in plants, the human face and hands. The ratio of the length to the width of the rectangle is 1.618...similar to Pi (3.1415...) in the fact that both numbers keep on going after the decimal point without repeating. These numbers are also classified as irrational numbers because they cannot be expressed as fractions or a 'ratio' of numbers. An example of the Golden Rectangle can be found in the Parthenon in Greece. There is no formal mention of the use of the golden rectangle or ratio in the construction of the building. The first time it is mentioned in Greek literature occurs about 140 years after the Parthenon was built. However, by constructing a rectangle around the ruin one can see a close relationship of the dimensions of the Parthenon with the Golden Rectangle. The diagram below also shows that the Golden Rectangle is made up of a number of smaller (decreasing in size) rectangles.
Using Minecraft or Worldcraft2 to construct the Greek Parthenon
You can approximate the Golden Rectangle in Minecraft by constructing a model of the Parthenon using 15 blocks in width and 9 blocks in height. The half block is called a slab. This gives a ratio of 1:1.666 or 1.666...as a number, (compare that with 1.618...the real ratio). Construct 8 columns along the front separated by one block space. Use the floor plan below to help position the columns. The length of the Parthenon is 17 columns. You can make it smaller to save construction time if you like. I left out most of the columns on the inside of the Parthenon in my own construction.
You can approximate the Golden Rectangle in Minecraft by constructing a model of the Parthenon using 15 blocks in width and 9 blocks in height. The half block is called a slab. This gives a ratio of 1:1.666 or 1.666...as a number, (compare that with 1.618...the real ratio). Construct 8 columns along the front separated by one block space. Use the floor plan below to help position the columns. The length of the Parthenon is 17 columns. You can make it smaller to save construction time if you like. I left out most of the columns on the inside of the Parthenon in my own construction.
Make the columns 6 blocks in height and then join them together with blocks. Rows 7, 8 and 9 form the pitch roof of the Parthenon.
Use 13 blocks for the 7th row, 5 blocks for the 8th row, followed by 1 block on top which is the apex of the roof as shown below.
The next step is to add the half blocks or 'slabs' to complete the front of the building. Place one slab either side of the apex block and two slabs either side of the blocks in row 8. Next place one slab either side of the row 7 blocks.
The next step is to create the 3D effect of the roof by adding 'slabs' around the edge of the roof as shown below.
Complete the back of the building by copying the front. Build the inside sections and add torches for effect. The doors are made from Oak slabs. Finish by continuing the roof section until the building is completed.
Activity Two: The Pyramid of Giza.
Firstly, Pi is another one of those irrational numbers that just keeps on going after the decimal point without repeating. Pi = 3.1415... and is often introduced to high school students by the fact that the diameter of any circle will "fit" around its circumference 3.1415...times.
The pyramid at Giza is an interesting case and a good example to build using Minecraft. The height of the pyramid is about 480 feet (147m) and has a length of about 755 feet (232m). The pyramid has suffered from erosion since its construction so archaeologists and historians can't get exact measurements off it.
If you double the base length of the pyramid and then divide that by its height a very close value to pi can be obtained. e.g. (232 x 2)/147 = 3.156. (Compare that with 3.1415...). However, in Minecraft, the blocks are cubes and restrict the angles of elevation we can use for the walls of the pyramid. The Giza Pyramid has a wall slope of about 52 degrees.
For now choose a base length of 23 blocks to start your own Pyramid of Giza, working up to the last block at its apex (choosing an odd number of blocks for each level ensures there is one single block at the apex or peak).The 23 by 23 Pyramid is quite small but if you have time you can try larger numbers of blocks. The more blocks you use the more realistic the pyramid looks.
Firstly, Pi is another one of those irrational numbers that just keeps on going after the decimal point without repeating. Pi = 3.1415... and is often introduced to high school students by the fact that the diameter of any circle will "fit" around its circumference 3.1415...times.
The pyramid at Giza is an interesting case and a good example to build using Minecraft. The height of the pyramid is about 480 feet (147m) and has a length of about 755 feet (232m). The pyramid has suffered from erosion since its construction so archaeologists and historians can't get exact measurements off it.
If you double the base length of the pyramid and then divide that by its height a very close value to pi can be obtained. e.g. (232 x 2)/147 = 3.156. (Compare that with 3.1415...). However, in Minecraft, the blocks are cubes and restrict the angles of elevation we can use for the walls of the pyramid. The Giza Pyramid has a wall slope of about 52 degrees.
For now choose a base length of 23 blocks to start your own Pyramid of Giza, working up to the last block at its apex (choosing an odd number of blocks for each level ensures there is one single block at the apex or peak).The 23 by 23 Pyramid is quite small but if you have time you can try larger numbers of blocks. The more blocks you use the more realistic the pyramid looks.
You can also create a tomb inside your pyramid and store treasure there. As an example here is a plan for the network of tunnels used in the Pyramid of Giza. Use your imagination. Note the angle of 52 degrees used in its construction.
Before I actually began construction of another pyramid I designed it using a square grid like the one shown below I got an angle of elevation for the pyramid walls of 51.8 degrees. It has a base length of 33 blocks. The original cladding (covering layer) and apex (tip) of the pyramid have worn off over the centuries. This means that archaeologists, scientists and mathematicians have to estimate their measurements. Having said that, the results are interesting. I wonder if the relationship between the dimensions of the pyramid and Pi was a deliberate one, or could it have been done by chance? Unfortunately, I built the pyramid a few 'km' from the current location in minecraft and I have never been able to find it again!