WoW Mathematics: Heavy Breathing

When Valiona breathes fire, she breathes lots of it. Not only does it reach the very edges of the room she is in, it also has a 180° angular spread.

Given that most fires tend to be bad, it is usually prudent to run out of it. There are, of course, a multitude of possible directions to run, which leave the player roasting for different amounts of time. Which path is the quickest?

Summary:

• The quickest path out of Devouring Flames is a straight line perpendicular (at right angles) to the boundary of the cone.
• If Valiona is facing the player, the quickest path out is through Valiona.
• Given a Cartesian coordinate system, the starting position (x₁,y₁) and the equation of the boundary ax + by + c = 0 ,the distance d to run is:

Doomsday: Extreme Weather

Earth is humanity’s cradle, but by no means can it completely harbour us from harm. Many risks threaten individual lives, but there are some catastrophic enough to wipe out entire species. Is it possible for the prolific human species to face extinction?

Earth's climate is a complicated system, one which climatologists are still studying. Like in a car or computer, a minor change in one component can cause more major effects throughout. Although volcanoes can disrupt this delicate machinery, there are other factors which can plunge Earth into an ice age, some of which built in, others brought about by humans.

History
150 000 years ago, Earth orbited a little further from the Sun than normal. It went through a particularly severe ice age, where the human population dropped to as low as 2000 people.