Pythagoras of Samos's page

15^2 + 20^2 = 25^2

For reference,

--5' height differential--
5' horizontal = 7' movement
10' horizontal = 11' movement <-- distance from Ascendant to Khaul
15' horizontal = 15' movement
20' horizontal = 20' movement
25' horizontal = 25' movement
30' horizontal = 30' movement
35' horizontal = 35' movement
40' horizontal = 40' movement

--15' height differential-- <-- use this for calculating distances from ground to Khaul
5' horizontal = 15' movement
10' horizontal = 18' movement
15' horizontal = 21' movement
20' horizontal = 25' movement
25' horizontal = 29' movement
30' horizontal = 33' movement
35' horizontal = 38' movement
40' horizontal = 42' movement

--20' height differential-- <-- use this for calculating distances from ground to the Ascendant
5' horizontal = 20' movement
10' horizontal = 22' movement
15' horizontal = 25' movement
20' horizontal = 28' movement <-- Ascendant to Farnguy and Nal
25' horizontal = 32' movement <-- Ascendant to Kang, I've been letting it slide but technically, Slow shouldn't reach
30' horizontal = 36' movement
35' horizontal = 40' movement <-- Ascendant to Mindartis
40' horizontal = 44' movement <-- Ascendant to Arfsnarf

--40' height differential-- <-- flying upward is difficult terrain
5' horizontal = 40' movement
10' horizontal = 41' movement
15' horizontal = 42' movement
20' horizontal = 44' movement
25' horizontal = 47' movement
30' horizontal = 50' movement
35' horizontal = 53' movement <-- Mialee's movement
40' horizontal = 56' movement

Weak sauce.

sqrt(15^2+20^2+20^2) = 32.0

If that's rounded down to 30', then 30' would include PBS and it'd be +1 to attack and damage. If 30' is a cutoff, then it doesn't include PBS.

sqrt(15^2+30^2) = sqrt(1125) = 33.5

3rd range increment, no PBS

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Confirmed.

10' vertical + 5' horizontal = 11.2' < 15'
10' vertical + 10' horizontal = 14.1' < 15'
10' vertical + 15' horizontal = 18.0' > 15'

Not sure if Pathfinder topology uses ROUND() or FLOOR(), but ...

15' vertical + 5' horizonal = sqrt(15^2+5^2) = 15.8' = 15'
15' vertical + 10' horizonal = sqrt(15^2+10^2) = 18.0' = 15' (?)
15' vertical + 15' horizonal = sqrt(15^2+15^2) = 21.2' = 20'

sqrt(25^2+10^2) = 27'

My name is Pythagoras and I approve this electric arc.

30' horizontal + 10' vertical = 32' distance

15' up + 20' horizontal = 25' distance

sqrt(20^2+45^2) = sqrt(25*[16+81]) = sqrt(25*97) ~ 5*10

Quinoline is 50' from the shadow demon.

With regards to vision and line of sight, I don't want to go into geometry with this.

a^2+b^2-2*a*b*cos θ=c^2

When θ = π/2, cos θ = 0, ergo, a^2+b^2=c^2.

What's so hard about that?