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PDF Editor FAQ

How can music be represented mathematically?

It is already represented mathematically. The symbols for duration (relative length of tones) are made with variations on an oval “note”, either outlined, or solid black, with a stem adorned with flags and dots which signify the length of the note relative to one note of constant duration. Thus, 4/4 time, expressed just like a fraction, shows a whole measure of time filled up with 4 “beats” worth of time, each one a “quarter note” long. It’s like a matrix of time, as if you moved your finger along a ruler and ticked off the inches, half-inches, quarter-inches or whatever you pleased. The composer merely fills in the matrix with the appropriate symbol.This is different than a typical mathematical symbol, which is an instruction to perform a certain action upon numbers (which represent real things or events).One could actually make a simplified system of music notation by drawing lines horizontally along the x-axes of graph paper, using the vertical lines to represent the elapsed time. That would do away with having to learn all the various types of temporal notation, and the entire system of wholes, halves, quarters, 8ths, 16ths and so on. Even the staccato and other touches could be made by simply shortening the length of a line or reducing it to a dot!HOWEVER,Your score would have to be (for a pianist) 88 lines tall, to represent all the available notes, and a single octave span would be twelve lines tall, or about three inches. How would this be visually? An octave on standard score paper is somewhere around a half-inch tall. The “graph paper” would require 9 inches height just to read a regular piano score - so you see that traditional sheet music, with its line/space concept, is a marvel of compactness, suitable not just for ancient times when paper was forbiddingly expensive, but for music today.Rotating a graph-type score 90 degrees could make it more attuned to the left-right nature of a keyboard (it would look sort of like Guitar Hero), but would require an exceptional number of pages, even for a short piece of music. It might be Mathematically Correct (MC), but highly impractical. Plus - you’d have to rewrite all previous music (which could be done through digital optical rendering, but quite a zillion-digit project for the world).

What are your favorite games on paper, besides Tic Tac Toe, Battleship, Pictionary?

There’s one I love that’s remarkably simple yet surprisingly complex. I have no idea what it’s called. I call it “Burger Blocks” because it was taught to me back in high school by a guy whose last name was “Burger”. He didn’t have a name for it either. I’m sure others are aware of the game so someone can likely tell me what it’s actually called.edit: Thanks to Franciscus Alex Rebro for providing the name of this game. It’s apparently called “Dots and Boxes” and a better description than mine can be found here:Dots and Boxes - WikipediaBut it’s played on a gridded sheet or graph paper. (or by drawing dots as shown in the Wikipedia link) Each player has a different color pen. Red and Blue are most common since you can tell them apart from the black or grey lines of the grid. One player draws a line connecting one section of the grid. No diagonals allowed. Only 90° lines. The first turn for each player might look like this:…or wherever the players wish to put their lines. For the first little while of the game it might be a bit boring while you each fill up the sheet with lines; depending on how large a sheet you intend to use. Smaller sheets equal shorter games. The next turns might look like this:Okay, so the object of the game is to fill in as many squares as you can with your own color. To get to fill in a square, you have to place the final (fourth) line that defines it. So whenever there’s a three-sided box somewhere on the sheet and it’s your turn - you can place the fourth line, create a four-sided box and color it in. Players try NOT to place the third box-defining line anywhere since that will give the next player the chance to take said box. So if a player makes an error and places the third box-defining line, it might look something like this:Now Blue has taken one square and is in the lead. But as the game progresses and players are cautious of NOT placing the third box-defining line anywhere, the sheet may begin to look something like this:…and as players make mistakes the sheet begins to take shape - full of paths and shapes that contain no three-sided boxes. If a player draws a fourth box-defining line to color in a square and that line creates another three-sided box, then that player can go again and fill in the next square by adding the fourth box-defining line. Each time you color in a square you get to go again. So one small error can lead to your opponent gaining multiple boxes in one move. Like so:And so on and so forth……as errors and miscalculations compound. But often times a sacrifice will be made in order to be able to take a turn. One player might calculate the number of squares lost by placing a third box-defining line in a certain area and place it there on purpose. This can be a smart move at times. But it can also be a way out of a desperate situation.That move gave Blue four squares, but it gave Red another turn to think and find a square that he/she can use. (Bear in mind this is typically only done when the sheet begins to get filled up with lines and there are no other places to place lines that won’t result in a three-sided box.) So as the game continues the sheet gets covered with lines and filled-in squares.Typically by the end you can glance at the sheet and tell who won; but in close (and larger/longer) games it helps to keep track of the squares as you go so you know the scores by the end and don’t have to go back and count every square.So anyone who knows the name for this game, feel free to comment and let me know. It’s one of my favorites since it’s so simple and can lead to some interesting spatial observation and calculation practices.

How do I prepare for the CPT test for a CSS post at SSC CGL?

Answer is bit long but you won't need anything else… just read this answer, practice in the way described and easily clear CPT/DEST/ Typing Test in less than 2 day's time.Hacks for Typing Test -Full mistakes-If you miss a word , then no of letters in that particular word would be counted as Mistakes.--------ex. According to Constitution of India ...now if you type According to of India then it would be counted as full mistake of 12 lettersFor every substitution of word/figure- According from Constitution of India ......so mistake would be of 2 lettersFor every addition of word/figure not found in paragraph- According to the constitution of India ... 3 letters for extra theHalf Errors-wrong capitalizationwrong spellingSpacing errorImp pointsYou should give only one space after full stop. extra space would be will also lead to penalty.New paragraph should be started with Enter+ Tab space.Strategy:Keep your speed maximum right from the first para...don't be lax in first paratry to stay focused and try to keep your fingers on right placeif there is any long spelling then be little bit cautious and type it slowly so that there is no errorread sentences in parts -- till , " ( ) . or digits or end of the line / line changingSkip typing digits and all capital letter words like CO2, NH3 ...type at last if time permits but maintain accuracy elsewherecheck time at the end of each para if you think that you are getting slow but if you have used very less back spaces in 1st para or if you are going very fast then no need to check again and againif you find that very less time is remaining and and you won't be able to finish last line of the last para then you can simply write first word , last word and full stop but then you should bring your cursor after the first word and finish line as much as possible but make sure that you don't commit much mistake in haste. Also you can't apply this trick to more than one line as every line has almost 80 key depressions and if you skip more than one line you may exceed error percentage.Hacks for EXCEL -Functions-absolute difference - abssum function - sum(B10: G10)average function - average ()minimum function - min()maximum function - max()Pass/Failed - if (G23>350, "Pass", "Fail")drag formulas to copy paste themdon't compare by yourself , you are supposed to apply formula for everythingRow height ,just go to the row end and right click there and change row height optionPie charts - select the whole table and go to " insert " , there you have option of " Pie " , select 2D chart from there and now go to " design" and you can select required design of pie chartBar graph - select all table , go to "insert" there you have option of " column" for vertical bars and " Bar" for horizontal bar graph, then design select 1st oneFor linear graph, select all table , go to insert and there you have option of " scatter" for linear graph , then go to the " layout" to change axis titlesIn the insert, you have option of adding " header and footer " , in that you can put " File path " in header by the same named option given there.Strategy for EXCEL -open a workbook and the first step should be to save it as per the instruction given ( although this instruction may be given as last one )set paper size , orientation and margin so that you will get to know that what are the borders ...you will also observe one dotted line as borderset font size and font name by selecting all cells by clicking top left corner so that it selects all cells in this sheetnow read instructions one by onedon't forget to write your name and roll no and sign it even if the invigilator doesn't asktake a look at print preview and don't print without necessary adjustments ....like if some letters are getting outside etc.Check formula two three times while applying, and do the formula work before border etc.PowerPoint Basics -in layouts choose Title and Content slide option if nothing is mentioned speciallyto create sub bullet press tab and shift+tab to return to main listif you do not want auto fit option in the slides then go the edge of the slide box and right click over there and you will get format shape . In that format shape go to the text box option and in the autofit option just change to do not autofitfrom insert you can insert various shapes like rectangle etc. and you can change the background of this box by going to the format , and you can also change outline from format onlyto change the line style of the border of the box, click on the border and go to the format shape, there you can go to line style , make it double border , change its thickness etcto change background color of the slide , just right click anywhere and go to the format background , there you have option to changego to insert , there will be option of header and footer , go the footer in that and invariably write kyour name and roll no on every slideif you get a wider slide , uou can go to page set up and choose 4:3 slidefirst finish typing and then do all the formating at lastStrategy1st go the home in the 'layout ' and select title and contentthen go to the 'title ' and 'content ' and complete typing workthen go to the 'insert' and add header and footer from the same named optionthen start formatting (font size color style etc) from footer only, then do formatting of title and contentthen start with outer lining and then fill color, but if the fonts are having different than black then first change their colorgo to print and check print previewPlease upvote the answer if you find it helpful or suggest how it can be improved. It will help me in evaluting my writing style.

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