Rithmatics

Rithmatics is a magic system that uses chalk. It was discovered by King Gregory III, Monarch in Exile of Britannia. Accordingly the practice of Rithmatics is heavily associated with the Church of the Monarch, as the inception ceremony by which ordinary people become Rithmatists take place in Monarchical churches..
__TOC__
== Rithmatic Lines ==
There were four known Rithmatic lines at the start of The Rithmatist; however, two new lines were discovered over the course of the novel (the Line of Silencing and the Line of Revocation). 
=== Line of Warding ===
The strength of a Line of Warding is determined by its evenness and its curvature. The steeper the curve, the stronger the line. This is a moot point in circles as their curvature is equal around its entirety. In ellipses however the strength is variable; peaking at its bindpoints and reaching its lowest point on the sides.
A larger Line of Warding is weaker, however, it takes more strength for chalklings/Lines of Vigor/Lines of Revocation to destroy 1/6 of a large circle than 1/6 of a smaller one; the strength of all circles is not the same. A typical Line of Warding can take about 6 hits from a Line of Vigor.
=== Line of Forbiddance ===
A Line of Forbiddance is a defensive line that projects an impenetrable plane perpendicular to the surface it is drawn on. Not even the Rithmatist who drew it is able to cross it. The strength of a Line of Forbiddance is determined by its straightness; the straighter the line is, the stronger it is. The line's thickness determines the height of the invisible plane it produces above it. A well-drawn Line of Forbiddance can stop bullets and, in some cases, cannonballs.
Since Lines of Forbiddance are resistant to being moved by Lines of Vigor, they are useful in anchoring Lines of Warding against being moved. Often a Rithmatist will use a Line of Forbiddance to connect two of a circle's bindpoints.
It takes about four seconds for a Rithmatist to dismiss a Line of Forbiddance they drew themselves.
A "Mark's Cross" is a set of perpendicular Lines of Forbiddance in a four-point circle. It can be attached to a bindpoint of a larger circle for support.
A Line of Vigor will bounce off of a Line of Forbiddance. However, a Line of Forbiddance can only sustain about 10 Line of Vigor hits before it is destroyed.
The material that a Line of Forbiddance is drawn on can affect its stability (e.g., more durable surfaces form stronger lines).
Lines of Forbiddance are weakest at the corners if they are joined together.
=== Line of Vigor ===
Lines of Vigor are one of the main offensive Rithmatic lines. It is drawn in the shape of a sine wave, from the outside in. As long as it completes two intervals it will shoot out until it reaches an obstacle. Most chalklings are easily destroyed by Lines of Vigor. If it reaches a Line of Warding it will create a pockmark, if enough hit the same point then the line could be breached. Lines of Vigor reflect off of Lines of Forbiddance. The strength of a Line of Vigor is based on how large the curve of their wave is. A tighter curve, that puts the same amount of lines in a smaller area is harder to draw, but stronger, than one that has a longer wave.
Lines of Vigor generally behave like light waves: they will reflect off of Lines of Forbiddance and refract upon change of medium. Higher frequency Lines are better at penetrating, while lower frequency Lines are better at energy transfer (i.e. displacing Lines of Warding).
=== Line of Making ===
Lines of Making are used to create chalklings. The strength of a Line of Making is determined by the "complexity and aesthetic beauty" of the chalkling it creates.
Chalklings made with a Line of Making are unable to affect anything that isn't made of chalk unless the Glyph of Rending is added to their instructions.
=== Line of Silencing ===
The Line of Silencing has the ability to absorb sound waves. The louder a sound is, the more it is dampened, a whisper is essentially immune. It can only absorb a sound if the sound wave is powerful enough to reach it, and it will run out of power after a given time and stop working.
The shape of this line was discovered by Trent Saxon, a chalkmaker. The effect was unknown until Joel Saxon discovered the use from the Scribbler.
===Line of Revocation===
The Line of Revocation is described as being a cross between a Line of Forbiddance and a Line of Vigor. It is able to interact with things not made of chalk. It is slightly more powerful than a Line of Vigor.
This line was first demonstrated by the Scribbler, but was later used by Fitch, Joel, and Melody.
== Teaching Rithmatics ==
=== Rithmatic Schools ===
There were eight schools that taught Rithmatics in the United Isles of America.
*Armedius Academy in Jamestown on New Britannia 
*Valendar Academy on the California Archipelago
*Calgarius Academy on Albert
*Denver Academy on Denver
*Maineford Academy on Maineford
*Académie de Montréal on Canadia
*Our Lady of the Circle Academy on Kokomo
*Academia de la Rueda Divina on New Espania
It is mentioned that there was a movement on some of the Isles to open smaller schools on every Isle. The Rithmatic academies felt that this would lead to disunity and widely varied teaching styles, which would be detrimental to unity in Nebrask.
=== Rithmatic Professors ===
Professors of Rithmatics wear different color coats depending on their rank. A professor of lower rank can challenge one of a higher rank to a duel, if the challenger wins then the two professors trade ranks.
*Tenured Professors wear red.
*Non-tenured Professors wear blue.
*Assistant Professors wear green.
*Tutoring Professors wear grey.
=== Rithmatic Students ===
Rithmatic students wear grey sweaters. Boys wear white slacks and girls wear white skirts. Kneepads are often worn for they need to kneel and draw chalks.
== Rithmatic Defenses ==
=== Four-Point Circles ===
File: Four-Point Circle.svg|The four-point circle
; Ballintain Defense: A basic and easy to set up defense, that however lacks much internal support. This defense features two Lines of Forbiddance, each connecting two adjacent bind points. There are also two circular Lines of Warding at two of the bindpoints opposite of each other. Finally there is a defensive chalkling bound to one of the remaining bindpoints. A popular defense based on the four-point circle, it is ideal for more offensive Rithmatists.
File: Ballintain Defense Diagram.svg|The Ballintain Defense
; Sumsion Defense: A defense characterized by a long Line of Forbiddance that lies tangent to its front bindpoint. A circle with a Mark's Cross is also bound to this bindpoint opposite of the main Line of Warding. Defensive chalklings can be bound to the two bindpoints on either side. The rear bindpoint has a line running across it, perpendicular to the curve, to help anchor it.
File: Sumsion Defense Diagram.svg|The Sumsion Defense
=== Six-Point Circles ===
File: Six-Point Circle.svg|The six-point circle
The six-point circle has bindpoints based on a regular hexagon whose vertices are equidistant around the circle's circumference. While it is difficult to determine where the bindpoints are without actually seeing the hexagon, Rithmatists are taught how to intuit their positions. Six-point circles have a greater inherent versatility and defensibility that two- and four-point circles lack.
; Eskridge Defense: One of the most difficult of the defenses taught to Rithmatic students. It features three internal Lines of Forbiddance, each connecting two adjacent bindpoints, leaving three openings for the Rithmatist to draw. The top and bottom bindpoints have defensive chalklings bound to them while the remainder have circular Lines of Warding. Each of the outer circles have an interior Line of Forbiddance that points towards an opponent, to help defend against Lines of Vigor.
File: Eskridge Defense Diagram.svg|The Eskridge Defense
; Matson Defense: A defense that relies heavily on defensive chalklings. Features two parallel Lines of Forbiddance, each connecting two adjacent bindpoints. The remaining two bindpoints, opposite of each other, have circular Lines of Warding bound to them each with a Mark's Cross. Defensive chalklings are bound to every bind point of the three circles, except where the smaller circles are bound to the larger one, making ten in total.
File: Matson Defense Diagram.svg|The Matson Defense
=== Nine-Point Circles ===
File: Nine-Point Circle Diagram.svg|A nine-point circle
The nine-point circle has bindpoints based on a non-obtuse triangle. The bindpoints are located at the midpoint of each side and at the points where the triangle's altitude lines intersect the circle. They require a great deal of practice in order to successfully determine where each of the bindpoints are located. Due to this difficulty many Rithmatists do not choose to spend the time required to master it.
; Easton Defense: A defense that is suited for multiple opponents. It has circular Lines of Warding at each of its bindpoints and Lines of Forbiddance that form a nine-sided figure with three lines missing which act as support for the mine circle. Drawbacks to the defense are the difficulty of nine-point circles and the restriction created by the Lines of Forbiddance. There are a number of variations on this defense, such as adding defensive chalklings to the outer circles. A more advanced iteration of this defense adds a Mark's Cross to each of the outer circles and decreases the internal Lines of Forbiddance from six to three. Defensive chalklings are also bound to a number of the outer circles' bindpoints.
File: Easton.svg|The Easton Defense
; Hill Defense: A defense that uses Lines of Forbidding, though it can be modified to work without them.
; Shoaff Defense: A defense characterized by its use of elliptical Lines of Warding at each of its bindpoints. A defensive chalkling is then bound at each of the ellipses opposite bindpoint. It only uses two, quite short, Lines of Forbiddance as anchors and is so quite susceptible to Lines of Vigor. It is however ideal against an offense of chalklings. This defense is best for those who specialize in Lines of Vigor
File: Shoaff Defense.svg|The Shoaff Defense
; Taylor Defense: A defense characterized by a pair of concentric, circular Lines of Warding. Lines of Forbiddance radiate outward from the bindpoints of the innermost Line of Warding, though the bindpoints of the larger concentric circle, and then through two smaller circles. Each of the smaller circles have a Mark's Cross. There are Lines of Forbiddance that connect two outer circles that are adjacent to each other, lying parallel to one of the Lines radiating out which are used to reflect Lines of Vigor. Defensive Chalklings are bound to many of the remaining bindpoints. The Taylor Defense is commonly held to be the strongest Rithmatic Defense though it requires great speed and accuracy from its user. It's use is somewhat controversial in duels but if the outer concentric circle is breached then it counts as a defeat.
File: Taylor Defense.svg|The Taylor Defense
=== Ellipses ===
File: Two-Point Ellipse.svg|The ellipse
Lines of Warding in the shape of an ellipse only have two bindpoints. They are strong at the ends (near the bindpoints) but weak along the sides. 
; Jordan Defense:
Invented by Matthew Jordan, it is a defense characterized by the large cage of Lines of Forbiddance drawn around it. Large numbers of offensive chalklings are drawn inside the cage and are released in waves by dismissing the front Line of Forbiddance, which is then redrawn after the chalklings have moved forward. At each of the two bindpoints have a line running through them to serve as an anchor. It requires a great deal of skill in making sure the chalklings wait until the Line is dismissed before moving forward. It is an unconventional defense and some teachers are reluctant to teach it.
File: Jordan Defense Diagram.svg|The Jordan Defense
; Osborn Defense:
The only basic defense based off of an ellipse. A defensive chalkling is bound to the upper bindpoint. The rear bindpoint has a line running through it to serve as the only anchor for the defense. On either side the Rithmatist my choose to add two circular Lines of Warding with a Mark's Cross to aid in defense. It is important though that they do not touch the main ellipse as they would not be touching a bindpoint.
File: Osborn Defense Diagram.svg|The Osborn Defense
=== Unknown Configuration ===
; Blad Defense: A defense that uses Lines of Warding "non-traditionally" by combining four ellipsoid segments. The configuration is strong enough that some believe it should be banned from official competitions such as duels and the Melee.
; Keblin Defense: A defense that is weak against the Easton Defense in most cases.
; Miyabi Defense: A defense with a "convoluted history".
== Trivia ==
* The Miyabi Defense is named after Miyabi, a longstanding member of Brandon's fan community.
== External Link ==
* The Rithmatist internal art on Brandon's website
== Notes ==
Category: Magic