Volumes of Tori and Pyramids

The volume of some solids can be found intuitively (e.g. for a right rectangular prism, V = lbh). However, some more exotic solids will require calculus for their volumes to be found.

Two such solids are the torus (donut) and rectangular pyramid. The former's volume can be found, possibly among others, using the technique of volume by rotation, and the latter's with volume by cross-section. These techniques will be used for deriving the formulae for the volumes of the respective solids. In summary:

• Volume of torus = 2cπ²r²
• Volume of rectangular pyramid = ¹/₃abh

The Stuff of Sensations

With the senses of sight and hearing, a person can see colour and hear sound, respectively. So many hues and timbres exist, yet both are composed of basic elements and can be constructed by combining them in special ways.

Colour

• Sensing body part: Eyes. The lens and cornea focus light to fall on a surface of rods and cones, the pattern of which is sent to the brain as electrical impulses.
• Element: Primary colour
• Medium: Colourants (usually ink) on a white surface, or light on a black surface
• Types of element: For colourants, cyan (reflected blue and green light), magenta (reflected red and blue light) and yellow (reflected green and red light) (practical implementations also use black), although the fine arts has traditionally used blue, red and yellow (which alone cannot theoretically produce black). For light, red (long-wavelength visible light), green (mid-wavelength visible light) and blue (short-wavelength visible light).

Halian Geometry

The Halion encounter in the Ruby Sanctum requires careful positioning and movement in order to conquer it. Certain principles of geometry can help greatly with this endeavour, so it helps to be acquainted with them! Even if they will not be used in actually formulating strategies (since strategies will conveniently be recommended here), it is good to see how they were derived.

Circles and their radii
A circle is a (plane) shape where all points on its perimeter (the circumference) are the same distance from a single point (the centre). A radius is any straight line drawn from the centre to the circumference. Because of the definition of a circle, all radii are of the same length.

Vision’s Incentive Systems: A Case Study

Every World of Warcraft raiding guild aspires to progress through raid content in a timely pace. Most members of the raiding corps focus on attaining gear and other goals, and so cannot be expected to directly satisfy the guild’s purpose. Thus, the guild must facilitate this indirectly by setting compatible goals, and then motivate raiding members to achieve them.

Human Resources (HR) departments of real-life companies handle these issues regularly, and the officerships of ingame guilds are no more exempt. I will introduce the theories associated with incentive systems, then apply them to analyse the incentive systems of my current guild, Vision of Frostmourne US.

Direct Costing (with Defects)

In the ideal world, every bit of material and labour allocated to a product is used, and no waste is generated. Unfortunately, materials can have defects and precious labour is spent on dealing with it. This means that more input than ideally required is actually used.

In developing standard costs for products, management accountants must take defects into account. To do so, they need to have a good grasp of division and multiplication.

If C is the theoretical amount of material or labour and r is its defect rate, the total amount of material/labour actually used (T) is:

T = ^C/_{1 - r}

WoW Mathematics: Breach of Contract

Ever signed a contract later regretted? Unfortunately, they are all too common during the Blood-Queen Lana'thel encounter, as she regularly binds raid members into Pacts of the Darkfallen. The law in Icecrown Citadel cares not of requirements of intention and genuine consent, so surely it will not mind a breach? What is the most expedient and mathematically sensible way to do so?

Summary:

• To remove Pact of the Darkfallen the quickest way possible in the 10-man Blood-Queen Lana'thel Encounter, the raid members should run to the midpoint of the interval they form.
• To remove Pact of the Darkfallen in the quickest way possible in the 25-man Blood-Queen Lana'thel encounter:
• If the raid members trace an acute triangle, they should run to its circumcentre.
• If the raid members trace a right-angled or obtuse triangle, they should run to the midpoint of the longest side.

Compress Your Waveform

Many World of Warcraft raiding guilds use Ventrilo (Vent) to allow raid members to communicate more easily. However, it may be frustrating to find a large variation in volume between others' voices. Fortunately, Vent has a function to alleviate that.

The Compressor module can be used for reducing the such. It works by changing the shape of the envelope, or outline, of the waveform. It can be activated by going to Setup | Voice | SFX and adding Compressor under Sound Effects. To be able to configure these settings without a recommended configuration, one needs to know some of the basics of sound synthesis, in particular the ADSR envelope.