![]() If you ask Google to translate "parallel minor" to German, you will get "parallel moll" – which is dead wrong! WRONG translation by Google Translate If you have never heard of Tp or functional harmony before, you might want to read up on it here (article not yet published). Below I want to point out the peculiarity of Tp (or "Tonikaparallele") symbolizing "relative minor". To learn about the basics of relative and parallel keys, you might want to read my article Relative Minor and Parallel Minor EXPLAINED first. Why is Tp the symbol for "tonic relative"? And what is the difference between parallel and relative minor? The Pythagorean theorem provides that the sum of the squares on the legs of a right triangle is equal to the hypotenuse, and is normally written as: a 2 +b 2 =c 2. In two dimensions, you can find the vector norm using the Pythagorean theorem. It has a length, known as the magnitude or norm, and a direction. A vector is a mathematical object that looks like an arrow. Vector norms specify the length of a vector. It is used in pairs on either side of the value of the vector norm, for example || X ||. The double bar symbol is reserved for vector norms. The norm of a mathematical object is a quantity that describes the length, size, or extent of that object. For example, AB || CD means that the line AB runs parallel to the line CD. To signify that two lines are parallel, you can place the names of the lines on either side of this symbol. Parallel planes are planes in the same three-dimensional space that never intersect. Last but not least, planes themselves can also be parallel. If they are not, they are called skew lines. Two lines that do not meet in three-dimensional space must be on the same plane in order to be parallel. In three-dimensional Euclidean geometrical spaces, two planes or a line and a plane that do not share points are also parallel. If two lines exist on the same plane without every intersecting at any point, then they are parallel.Ĭurves that don’t intersect may also be considered parallel. Parallel lines are lines in a plane that do not meet. ![]() We may also recall a variety of different formulas we were taught that helped us figure out the lengths and surface areas of those shapes.Īnother thing we may remember, is learning about parallel lines. When most of us think about geometry, we picture a series of circles, squares, and triangles. More simply, it is a way to study the sizes, shapes, positions, angles, and dimensions of things. Geometry is a branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. The norm value in between two brackets is the length of a vector. Its second use is to denote a norm when used as brackets. If AB and CD are both lines on a common plane, then “ AB || CD ” means they are parallel. The first meaning indicates parallelism in geometry. Here is a quick cheat sheet to this symbol’s two meanings. Have you come across the symbol || in a text and are unsure what it signifies? No problem. Things become more complicated, however, when we begin to talk about the branch of mathematics known as geometry, not to mention trigonometry or calculus.īut take courage! Fortune favors the brave, and you are never too old to relearn the basic meanings of different mathematical concepts. The symbols for addition, subtraction, division, and multiplication are pretty straightforward. This can be the case regardless of whether we learned them twenty years ago or yesterday. For those among us who are not particularly mathematically inclined, it can be difficult to remember the meanings of mathematical symbols.
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