On the Subject of Geometry

Who likes geometry? Definitely not me.

This module consists of a screen, a number keypad (decimal point included), and a submit and clear button.

The middle screen will cycle 3 shapes, with a small gap at the start of the sequence. The screen will also show a symbol at the top right of the display.

In order to solve the module, you need to do some calculations, apply all necessary rules and then submit the answer using the keypad. To start you need to get your starting value.

For each calculation performed, if the decimal places are longer than 6, round off the number so that it has 6 decimal places. If the integer is larger than 999999, modulo the number by 1000000.

Starting Value:

Get the sum of all digits in the serial number and then multiply it by the number of letters in the serial number.

If a lit BOB is present, add 69 to the number.

Modifying the Starting Value:

Modify your starting number based on the symbol shown on the top right part of the screen.

Symbol	Symbol Name	Operation
∡	Measured Angle	Multiply by 30
⊥	Perpendicular	Divide by 2
∥	Parallel	Add the number of batteries to your number
≅	Congruence	Take the digital root of your number
~	Similarity	Add the number of non-needy modules on the bomb
Δ	Triangle	Multiply by 2/3

Shapes Table:

Starting value is now your current value. After every calculation replace the current value with the number you get. Any variables provided are the numbers that the module will use to perform the calculation. Use the same numbers that the module uses so that there will be no deviation from the answer.

Shape	Operation	Variables
	$$a^2$$	a = current value
	$$ah \over 2$$	a = current value h = (ports + batteries + 1) × 2
	$$ah$$	a = current value h = (ports + batteries + 1) × 2
	$$(a+b)h \over 2$$	a = current value b = last digit of serial # + D batteries h = (ports + batteries + 1) × 2
	$$\pi a^2$$	a = current value $$\pi \approx 3.14159265$$
	$$3a^2 \sqrt{3} \over 2$$	a = current value $$\sqrt {3} \approx 1.73205081$$
	$${7 \over 4}a^2{\mathit cot}({\pi \over 7})$$	a = current value $${\mathit cot}({\pi \over 7}) \approx 2.07652140$$

Venn Diagram:

Once you have done all calculations, you need to submit your number according to the rule you get from the venn diagram. If your number is negative, take the absolute value. If the decimal place does not have a length of 6, add 0 to the end until the decimal length is equal to 6.

Your number is exactly 500000 or lower
There is a non-needy module on the bomb that contains a part of List Of “Math Terms” on its module name
Last digit of serial number is a prime number
Serial number contains one of the letters from the word “MATH”

P	Submit only 25% of your number
W	Submit only the integer (ignore decimal places)
I	Submit only the decimal places (remove all leading 0). If there are no decimal places, submit “0”
N	Submit your number as it is

Solving:

When you have done all calculations and applied all necessary rules, input the number using the keypad and hit check. Inputting a number will stop the module from cycling. If you strike, the module will NOT reset. You can press “<” to remove the last number (or decimal point) on your input.

List of “Math Terms”:

ADDITION, ALGEBRA, ARITHMETIC, BINARY, CALCULATOR, CALCULUS, COUNT, DERIVATIVE, DIGIT, EQUATION, EVEN, FACTOR, FUNCTION, INDICES, INTEGER, MATH, MATICS, MATRICES, MATRIX, MODULO, NOTATION, NUMBER, NUMERAL, ODD, PRIME, PROCEDURE, QUATERNION, REMAINDER, SEQUENCE, VALUE