How to Build a Clay Igloo (/How to Present Igloo Mathematically

Blocks are labeled as follows. The Number of Blocks decreases as the igloo reaches the rooftop

b = Distance Between the center to the layer, H = Triangle's Height, Theta = Angle of that block
Green = Hypotenuse of the Triangle, Pink = Height of the Triangle

1) Measure the distance formed between the center of the igloo to the edge of the layer (b)
2) Measure the Height that forms perpendicular with Base (h)
3) Solve the angle of the that specific angle of the ramp (theta)
- Arctangent( Height / Base) = angle of the trapezoidal block (in degrees)
Determining the Dimensions of the Block (Circular Layer):
- 1) Measure the Radius of specific layer
- 2) Calculate its Circumference ( C = 2 x pi x radius)
- 3) Divide it by measured external length of a block
- 4) If the number of the blocks match with the calculation, then igloo's layer can be formed accurately without any shortage of materials
Determining the Dimensions of the Block (Vertical/Height):

H (with subscript I) = Height of the igloo, H (with subscript #) = Height of the Individual Block, x = Calculation of proportional relationship with the igloo's height and one particular block

1) Measure the height of the igloo as a whole
2) Using the proportions, calculate the 'X' for each layer's specific block
- Make sure the blocks are positioned on top of each other
3) Set Base Layer's block to be 13/5 of the igloo's height
4) Set Second and Third Layers' blocks to be 52/15 of the igloo's height
5) Set Fourth and Fifth Layers' blocks to be 1/7 of the igloo's height
6) Set Sixth Layer's blocks to be 1/8 of the igloo's height
7) The Roof should be height of the igloo as a whole

Ramp formed when one layer is stretched out into one trapezoidal block
x = Circumference of the Layer/Base Length of the Trapezoidal Ramp, y = Height of the Ramp from Dashed Lines to its peak, theta = Angle of the Ramp

1) The length should be the circumference of the layer's circle(X)
2) Measure the Height that forms perpendicular with the dashed lines (Y)
3) Solve the angle of the that specific angle of the ramp (theta)
- Arctangent( Height / Base) = angle of the trapezoidal block (in degrees)

If the Igloo is built correctly:
- The angle of the blocks in that particular layer should have an increasing trend from lowest to highest degrees
- The Base is the radius of that specific radius; in other words, it should be the constant
- Height should increase from lowest block to tallest block

What Not To Do

Presenting the Igloo into single equation:
- y = -ax^2 + b; x = from a vertical point of view, the block number; b = height of the igloo
Problems Regarding Single Equation:
- Inaccurate display = it doesn't necessarily show every single block in the 3-Dimensional plain
- Symmetrically, the length of the block doesn't equal to each other side's block
- Symmetrically, the height should be similar, if not the same, because of quadratic's concept. However, that's not true for the spiral igloo
Calculating the Volume:
- Integrate 2pix(-ax^2 + b)dx [0, radius of one layer]
  - This doesn't answer the question...
  - Don't act smart by calculating unnecessary quantity or value if it doesn't calculate the shape of the block or the ramp of an igloo

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