I'm FAAARRRRR SMARTER than you! (game)

[Tellos Athenaios]

In the simplest terms air is only dielectric (non conductive) because its intrinsic resistance (probably the wrong term, soortelijke weerstand, what is for electric resistance in ohm what density is for mass in kg) is so high. However the resistance increases (or decreases) linearly with the distance in the medium which must be crossed, as a result if the gap is small enough your resistance nears to small enough that the potential on the circuit is large enough for current to pass through this resistance.

Additionally, the circuit generates an electric field (on all parts of the circuit, that is what happens when electric charge is shifted and also why CAT cables often employ a twisted pair design to negate the effects of the electric field on signal reception at the other side) which may be sufficiently strong to generate “static electricity” as the coils become “charged”.

Depending on the potential on the circuit and distance between the coils either one is the likely explanation. (At relatively low voltages/large gaps the coils act as a capacitor and the electric field explanation applies, or at very small distances or high voltages the air is not sufficiently resistant to block the electric current.)

EDIT: I am assuming the circuit looks like this in my poor ASCII art representation:

---| :---
|       |
|--C C--|

| : is the source of potential (i.e. a wall socket), the - and | are bits of wiring, and the C's are coils.

[Skullheadhq]

In the simplest terms air is only dielectric (non conductive) because its intrinsic resistance (probably the wrong term, soortelijke weerstand, what is for electric resistance in ohm what density is for mass in kg) is so high. However the distance increases (or decreases) linearly with the distance in the medium which must be crossed, as a result if the gap is small enough your distance nears to small enough that the potential on the circuit is large enough for current to pass through this resistance.

Additionally, the circuit generates an electric field (on all parts of the circuit, that is what happens when electric charge is shifted and also why CAT cables often employ a twisted pair design to negate the effects of the electric field on signal reception at the other side) which may be sufficiently strong to generate “static electricity” as the coils become “charged”.

Depending on the potential on the circuit and distance between the coils either one is the likely explanation. (At relatively low voltages/large gaps the coils act as a capacitor and the electric field explanation applies, or at very small distances or high voltages the air is not sufficiently resistant to block the electric current.)

EDIT: I am assuming the circuit looks like this in my poor ASCII art representation:

---| :---
|       |
|--C C--|

| : is the source of potential (i.e. a wall socket), the - and | are bits of wiring, and the C's are coils.

correct
now, you're next

[Tellos Athenaios]

This one is looking for an algorithm that could conceivably be used to plot a bisector on a screen.
Below some rules for answers to make sure we can understand what we come up with:

Suppose you a have a 2d coordinate system. Points are defined through the function point which takes an x and y coordinate and returns a point. Then there is a function y which takes a point and returns its y coordinate, likewise there is a function x which take as a point an returns its x coordinate. There is a function d() to compute distance between two points and a function sqrt() to compute the square root of real number. (E.g.: d(K,L) is 5 if the distance between points K and L is 5.) You can use the following comparison operators, where a and b are variables used for explaining how they work:

-- test if a is less than or equal to b
a <= b 
-- test if a is greater than or equal to b
a >= b
-- test if a is equal to b
a == b
-- test if a is not equal to b
a != b
-- test if a is less than b
a < b
-- test is a is greater than b
a > b

These operators will also work to compare variables with values, e.g. you could write something like a == 0 to test if variable a is 0.
You also get two boolean operators to combine multiple comparisons && for logical and, and || for logical (inclusive) or.

Additionally, you can use the following arithmetic operators: × (multiplication of two real numbers), ÷ (division of two real numbers), + (sum of two real numbers), - (subtracts one real number from another real number).

You are able to define branches in your algorithm using if-else syntax, where if takes an expression which must evaluate to a boolean (true or false). E.g. to test if a variable div is 0:

if div == 0
  -- proceed with one branch
else 
  -- proceed with another.

The operator precedence (the mechanism which determines how an expression like 5 - 3 * 4 is evaluated) for the defined operators is (from highest to lowest):

1. ×, ÷ (they have equal precedence values)
2. +, -
3. &&, ||
4. == , != , <=, >=, >, <
5. , (the comma operator)

You can use parentheses to group expressions. Thus: ((5-3) * 4) != (5 - 3 * 4) returns true.

Finally you are able to define new variables using <name> = <value> notation. E.g. to define a variable z as the distance between two points P and Q you would write:

z = d(P,Q)

Names must not be numeric constants the names of operators, existing functions or existing variables. Note that this means you are not able to redefine variables, so the following will NOT work:

z = d(P,Q)
z = z + 1 -- this will not work, because z already exists and is defined to d(P,Q).

You can define functions using shortened form of lambda notation (where \ denotes the lambda symbol), which works like this:

-- define a variable called sum to be a function which computes the sum of two given values:
sum = (\x y -> x + y)

And use functions like this:

-- define a variable called ten to be the result of sum() applied to 5 and 5.
ten  = sum(5, 5)

If you call functions with fewer arguments than that they require the result will be a function which takes as many arguments as needed to compute the original function's result. The arguments you supply are ordered from left to right, i.e the left most argument is the first one supplied. For example:

-- define a variable to be the result of calling sum() with only one argument (the first)
plus5 = sum(5)
-- define a variable to be the result of calling plus5() on 7 which is then the last (second) argument to sum():
result = plus5(7) 
-- result == 12.

You end a branch of your algorithm using the keyword return and the name of the variable or a constant you want to return. This is so I know where to look for your actual computed answer. To clarify, since you will be calculating a new point, the return lines should either look like:

return point(my-x-coordinate,my-y-coordinate)

, or:

return my-result

Suppose now you are given three points, let's call them A, B, C. The three make an angle ACB which is not 180°. Additionally, d(A,B) is nonzero, d(B,C) is non zero and d(A,C) is non zero as well. The algorithm I am looking for will compute a fourth point named D which lies on the bisector of this angle ACB. I am not looking for a name, I am looking for an actual implementation which we can use to compute it.

This is purely about reasoning, it requires only a minimal amount of math knowledge. It is not actually very difficult, but it should hopefully prove quite satisfying to come up with a solution that works. I suggest keeping the answers in spoilers ([spoil]) tags until we find one which does the trick.

[drone]

Is this what you wanted?

Spoiler Alert, click show to read: 

if (d(A,C) < d(B,C))

shortLegPoint = A
longLegPoint = B

else

shortLegPoint = B
longLegPoint = A

normalizeRatio = d(shortLegPoint,C) / d(longLegPoint,C)
normalizePoint = point( ( (x(longLegPoint) - x(C) ) X normalizeRatio) + x(C), ( (y(longLegPoint) - y(C)) X normalizeRatio) + y(C) )
D = point( ( (x(normalizePoint) + x(shortLegPoint) ) / 2), ( (x(normalizePoint) + x(shortLegPoint) ) / 2) )
return(D)

[Tellos Athenaios]

Almost. Your approach is sound, but you made a typo which renders your calculations a bit worthless.

[drone]

Not a typo, a cut/paste error. I find I'm doing that a lot lately when coding...

Spoiler Alert, click show to read: 

if (d(A,C) < d(B,C))

shortLegPoint = A
longLegPoint = B

else

shortLegPoint = B
longLegPoint = A

normalizeRatio = d(shortLegPoint,C) / d(longLegPoint,C)
normalizePoint = point( ( (x(longLegPoint) - x(C) ) X normalizeRatio) + x(C), ( (y(longLegPoint) - y(C)) X normalizeRatio) + y(C) )
D = point( ( (x(normalizePoint) + x(shortLegPoint) ) / 2), ( (y(normalizePoint) + y(shortLegPoint) ) / 2) )
return(D)

[Tellos Athenaios]

Your turn, then.

[drone]

The Delta Tau Chi Deathmobile is heading full steam at the mayor's grandstand during the Homecoming parade. As they approach, the Deltas yell "Ramming Speeeeeed", tailing off with a pitch of C5 (523.25 Hz). If Dean Wormer hears the pitch as D5, how fast is the Deathmobile traveling?

Assume a dry fall day in Faber (roughly sea level) with no wind and a temperature of 15C.