Rithmatics

Rithmatics (featured in Brandon Sanderson's Rithmatist series) is a fictional magic learned by Rithmatists that makes chalk drawings have real-life properties and come to life. Rithmatics are based on geometry, and the preciseness and detail of a drawing will determine its strength.
It was discovered and first used by King Gregory III, Monarch in Exile of Britannia. Rithmatist are incepted at the age of 8 by the Church of the Monarch.
Basic lines
Line of Warding
The Line of Warding is, essentially, a defensive circle around one. All defenses are based on this line and a duel is lost if the line is breached. The sharpness and even curve of the Line of Warding determines the strength, and can be breached easier at lopsided areas. Ellipses have variable strength, being stronger at the tips where the curve is sharpest, and weaker where it is openThe circle can have 2, 4, or 6 bind points, the latter two placed at where an inscribed square or regular hexagon touches the circle, respectively. The more complex 9-point has bind points where an obtuse triangle and its altitudes intersect the circle. These bind points are used to anchor Lines of Forbiddance, lesser circles, or chalklings to the main circle, and anything anchored to other points will form a weak bond.
Line of Forbiddance
A line of Forbiddance is a straight line that creates an impassable plane of force above the line. The height of this plane depends on the thickness of the line, and the straightness of the line determines the strength. This plane ca be so strong that it can stop bullets and even cannonballs. It is used to secured Lines of Warding, which could otherwise be shifted by a hit from a Line of Vigor or Revocation. It is also useful to reflect Lines of Vigor and Lines of Revocation. Nothing can pass it, though, not even the Rithmatist, so he must be careful where he draws it, so to not block himself from drawing. It take four second to dismiss a line of Forbiddance.
Line of Vigor
Lines of Vigor are waves that, on impact, can destroy chalklings, move Lines of Warding a few feet, and dent Lines of Forbiddance and Warding. It is not known how Lines of Silencing react. There must be at least two wavelengths drawn before the line will actually shoot out. The power of a Line of Vigor depends on the wavelength, just like in real-life light waves, where shorter wavelengths carry more energy.
Line of Making (Chalklings)
Lines of Making, also called chalklings, are creatures that make up the main offense in a duel or battle. Their power varies according to the beauty and detail they are drawn with. They are best anchored to bind points of circles by chains or ropes, and must be given specific instructions by the Rithmatist, or they will wander off. This is done by glyphs written beside the chalkling. Some Rithmatists, like Melody Muns, can directly tell their chalklings what to do. Chalklings can only affect Rithmatic lines, not the real world or even regular chalk drawings, unless drawn with the Glyph of Rending. This is useful in telling whether a line is Rithmatic or not, which aided in the discovery of the Line of Silencing.
Line of Silencing

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