User:RDBury/Sandbox

Notes:
 * ANKoS p231 ff.
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Polytonic Greek
Rules:
 * Upper only at beginning of word.
 * Accute, Grave, Circumflex only on vowels, last vowel of syllable
 * Asper, Lenis only on central vowel of syllables at beginning of word that begin with a vowel (or rho at the beginning or a word or part of double rho).
 * Diaeresis only on iota and upsilon not at beginning of word.
 * Subscript only on alpha, eta and omega
 * Diacritic for diphthong of three vowels appears over central vowel
 * Apostrophe allowed at end of word

&#x1f58;&#x1f5c;&#x1f5a;&#x1f1e;&#x1f16;&#x1f4e;&#x1f46;&#x1f1f;&#x1f17;&#x1f4f;&#x1f47;&#x1f5e; b &#x1fb0; &#x1fb1; &#x1fb5; &#x1fb8; &#x1fb9; &#x1fbd; &#x1fbe; &#x1fbf; c &#x1fc0; &#x1fc1; &#x1fc5; &#x1fcd; &#x1fce; &#x1fcf; d &#x1fd0; &#x1fd1; &#x1fd2; &#x1fd3; &#x1fd4; &#x1fd5; &#x1fd7; &#x1fd8; &#x1fd9; &#x1fdc; &#x1fdd; &#x1fde; &#x1fdf; e &#x1fe0; &#x1fe1; &#x1fe3; &#x1fe2; &#x1fe4; &#x1fe5; &#x1fe7; &#x1fe8; &#x1fe9; &#x1fec; &#x1fed; &#x1fee; &#x1fef; f &#x1ff0; &#x1ff1; &#x1ff5; &#x1ffd; &#x1ffe; &#x1fff;

Compounds
e&#x0300; E&#x0300; e&#x0301; E&#x0301; e&#x0302; E&#x0302; e&#x0303; E&#x0303; e&#x0304; E&#x0304; e&#x0305; E&#x0305; e&#x0306; E&#x0306; e&#x0307; E&#x0307; e&#x0308; E&#x0308; e&#x0309; E&#x0309; e&#x030a; E&#x030a; e&#x030b; E&#x030b; e&#x030c; E&#x030c; e&#x030d; E&#x030d; e&#x030e; E&#x030e; e&#x030f; E&#x030f;

e&#x0310; E&#x0310; e&#x0311; E&#x0311; e&#x0312; E&#x0312; e&#x0313; E&#x0313; e&#x0314; E&#x0314; e&#x0315; E&#x0315; e&#x0316; E&#x0316; e&#x0317; E&#x0317; e&#x0318; E&#x0318; e&#x0319; E&#x0319; e&#x031a; E&#x031a; e&#x031b; E&#x031b; e&#x031c; E&#x031c; e&#x031d; E&#x031d; e&#x031e; E&#x031e; e&#x031f; E&#x031f;

e&#x0320; E&#x0320; e&#x0321; E&#x0321; e&#x0322; E&#x0322; e&#x0323; E&#x0323; e&#x0324; E&#x0324; e&#x0325; E&#x0325; e&#x0326; E&#x0326; e&#x0327; E&#x0327; e&#x0328; E&#x0328; e&#x0329; E&#x0329; e&#x032a; E&#x032a; e&#x032b; E&#x032b; e&#x032c; E&#x032c; e&#x032d; E&#x032d; e&#x032e; E&#x032e; e&#x032f; E&#x032f;

e&#x0330; E&#x0330; e&#x0331; E&#x0331; e&#x0332; E&#x0332; e&#x0333; E&#x0333; e&#x0334; E&#x0334; e&#x0335; E&#x0335; e&#x0336; E&#x0336; e&#x0337; E&#x0337; e&#x0338; E&#x0338; e&#x0339; E&#x0339; e&#x033a; E&#x033a; e&#x033b; E&#x033b; e&#x033c; E&#x033c; e&#x033d; E&#x033d; e&#x033e; E&#x033e; e&#x033f; E&#x033f;

0&#x0307; 1&#x0307; 2&#x0307; 3&#x0307; 4&#x0307; 5&#x0307; 6&#x0307; 7&#x0307; 8&#x0307; 9&#x0307; n&#x0307; 0̇ 1̇ 2̇ 3̇ 4̇ 5̇ 6̇ 7̇ 8̇

0, 1, 2, 3, 4, 5, 6, 7, 8 $$\dot{0}, \dot{1}, \dot{2}, \dot{3}, \dot{4}, \dot{5}, \dot{6}, \dot{7}, \dot{8}$$ $$\textstyle\dot{0}, \dot{1}, \dot{2}, \dot{3}, \dot{4}, \dot{5}, \dot{6}, \dot{7}, \dot{8}$$ $$\scriptstyle\dot{0}, \dot{1}, \dot{2}, \dot{3}, \dot{4}, \dot{5}, \dot{6}, \dot{7}, \dot{8}$$

ĖėĠġİıŻż ė Ė ë Ë

Math Symbols
∈∉⊆∪∩∅←→≤≥≠⋅

Image Playground
Rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble Greek rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble rubble.

Meander curve
A Meander curve is one of a family of curves used to model several phenomena including river meanders.

PTA notes

 * Greenhill (Radial angle)
 * Williamson
 * Love
 * Edwards
 * Osgood
 * Todhunter
 * Shikin

RPG
A role-playing video game (RPG) is one of a loosely defined genre of computer and video games with origins in pencil and paper role-playing games such as Dungeons & Dragons, borrowing much of their terminology, settings and game mechanics.

Characteristics of the genre
While no single feature or characteristic of a video game can be used to identify it as an RPG, there are several characteristics of the genre as a whole.

non-player characters (NPCs) run shops with equipment and supplies, ask the player to complete quests in return for a reward, give advice and information about playing the game, or simply provide additional color.
 * Players usually control a small number of characters called a party. This is in contrast to the wargame genre where players control large groups of identical units, as well as non-humanoid units such as tanks and airplanes. This is also in contrast to adventure games where the player controls a single character.
 * Characters gradually grow in power and abilities, usually by defeating various hostile creatures through the mechanism of experience points. These can be extremely in-depth and complicated and many games give the player some degree of latitude in determining which abilities will be improved. Most RPGs, in common with paper based games, use level as a broad measure of the character's strength.
 * The game world is inhabited by many computer controlled characters with which the player's character can interact. These
 * There is a highly developed story which unfolds as the game progresses.
 * The game world is large and diverse. In some cases the exploration of new areas is limited by the ability of characters to survive attacks by their inhabitants. In others, the player must reach a specific point in the story before a new area is accessible.
 * The game depends very little the player's physical skills such as timing and aim . Often the player controls the characters actions by issuing commands though a system of menus. The effectiveness of these actions determined by the character's numeric attributes.
 * The game depends correspondingly more on the player's strategy, tactics and knowledge of the game. For example, the outcome of a battle may depend on players exploiting a weakness to a specific type of weapon.
 * In the past, most RPGs entered a separate "battle mode" when enemies were encountered. Recently there is a trend toward incorporating battles seamlessly into the rest of the game. This can be seen in the Final Fantasy series where Final Fantasy X and earlier have a battle mode while Final Fantasy XI and later use a seamless approach.
 * The game often has a fantasy setting with primitive technology enhanced by magic.
 * The games usually feature a rich collection of items to collect and manage. Success in the game is strongly affected by whether characters have the proper armor, weapons and other equipment.
 * The different members of the party play different roles in battle according to their specific abilities and weaknesses. For example a party will usually have a character that specializes in doing physical damage to enemies and another that specializes in healing other members of the party.

Euclid's Elements
Book 1 Definitions 1: Point 2: Line 3: Extremities of lines 4: Straight line 5: Surface 6: Extremities of Surfaces 7: Plane surface 8: Plane angle 9: Rectilineal angle 10: Right angles 11: Obtuse angle 12: Acute angle 13: Boundary 14: Figure 15: Circle 16: Circle center 17: Circle diameter 18: Semicircle 19: Rectilineal figure 20: Equilateral, isosceles, scalene triangles 21: Right, obtuse, acute angled triangles 22: Square, oblong, rhombus, rhomboid, trapezia 23: Parallel lines Postulates 1: Draw a straight line on two points 2: Produce a finite straight line 3: Draw a circle with given center and distance 4: All right angles are equal 5: Intersection of two straight lines on a third straight lines so the included angles are less than two right angles Common Notions 1: Things equal to the same thing are equal 2: Equals added to equals are equal 3: Equals subtracted from equals are equal 4: Things which coincide are equal 5: A whole is greater than a part Propositions 1: Construct an equilateral triangle 2: Mark a segment on a given straight line equal to a given straight line segment 3: Cut from a straight line segment a segment equal to a given shorter line segment 4: Side-Angle-Side 5: Isosceles triangle theorem (Pons asinurum) 6: Isosceles triangle theorem converse. 7: Length of sides of a triangle on a given base determine the triangle. 8: Side-Side-Side. 9: Construct an angle bisector. 10: Construct a bisector of a line segment. 11: Construct a line perpendicular to a given line at a given point on the line. 12: Construct a line perpendicular to a given line through given point not on the line. 13: Adjacent angles on a line equal two right angles. 14: Converse to 13. 15: Opposite angles 16: Exterior angle theorem 17: Two angles in a triangle are less than two right angles. 18: Greater side subtends greater angle 19: Greater angle subtended by greater side 20: Two sides of a triangle greater than the remaining side (triangle inequality) 21: Triangle within another triangle on the same base has smaller sides and greater angle. 22: Construct triangle with sides equal to given segments. 23: On a given line, construct an angle equal to a given angle at a given point. 24: Given two triangles with two equal sides, the triangle with the greater angle will have the greater base. 25: Converse of 24 26: Angle-Side-Angle, Side-Angle-Angle 27: If alternate angles are equal then the lines are parallel 28: In interior angles equal two right angles then the lines are parallel 29: Converse to 27 and 28 30: Lines parallel to the same line are parallel 31: Construct a line parallel to a given line through a given point. 32: Angles in a triangle are two right angles. 33: Lines joining equal and parallel segments are equal and parallel 34: In a parallelogram, opposite sides and angles are equal, a diameter bisects the areas. 35: Parallelograms having the same base and equal parallels are equal 36: Parallelograms having the equal bases and the same parallels are equal 37: Triangles on the same base and in the same parallels are equal 38: Triangles on equal bases and in the same parallels are equal 39: Equal triangles on the same base are in the same parallels 40: Equal triangles on equal bases are in the same parallels 41: Parallelogram is double a triangle on the same base and the same parallels 42: Construct a parallelogram in a given angle equal to a given triangle. 43: In a parallelogram, the complements of parallelogram about a diameter are equal. 44: Construct a parallelogram on a given line equal to a given triangle. 45: Construct a parallelogram in a given angle equal to a given figure 46: Construct a square on a given line. 47: Pythagorean theorem 48: Converse of 47

The first few and selected larger members of the sequence of factorials. The values specified in scientific notation are rounded to the displayed precision.

The first few amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368).

Missing EoM articles

 * L-algebra
 * L-group (group with lattice structure)
 * L-matrix
 * L-space (statistics, not Terry Pratchett)
 * L-variety (see L-group)

LaTex scratchpad
Use the notation $$P=[\mathbf{v}]$$ to indicate that $$P$$ is a point in $$R(V)$$ represented by the vector $$\mathbf{v}$$.