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It's not because of a natural law or something; it's inherent in the structure of space, and the shapes of triangles, hexagons, and squares. Your question is like asking, "why does 2 + 2 = 4?" There's not a reason, they just do because that's how things are.
Also, they aren't the only shapes that tile, just the only regular polygons that tile.
>>M.T.<<
Think it has to do with the fact that for a shape to tile the measure of the interior angle multiplied times something has to give you 360, if not the shape cannot tile
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A bag contains green and yellow tiles You pick 2 tiles without replacing the first one The probability that the first tile is yellow is 35 The probability of drawing 2 yellow tiles is 1235?
What is the probability that the second tile you pick is yellow? (didnt have enough space to finish the question)
What percentage is the second distribution sextile of a normal bell curve?
By definition, the 1st 6-tile is the point below which 1/6 of the population falls (irrespective of which distribution is involved). The 2nd 6-tile is the point below which 2/6 of the population falls. This is 100 * 1/3 ~ 33.3% of the population.
What is the probability in picking a vowel in mathematical?
Probablity of picking up 3 vowels from the word MATHEMATICS Each of the letters in the word MATHEMATICS is on a letter tile in a bag
How many combinations can be made with a b c d e and f if 5 letters are taken at a time?
The related link explains the difference between a combination (order not important) and a permutation (order is important).In a combination, the order doesn't matter. This is like drawing 5 cards for a poker hand. You can arrange them how you want once you have them. Or a lottery ball problem. You can match the balls, regardless of what order they were drawn. Or rolling 5 dice, like in Yatzee.There's another constraint called repetition. In the dice throwing, you could get all five dice to land on the number 1 (repetition allow). In the card game and lottery ball, once a card or ball is drawn, you cannot draw that one again (no repetition).In a permutation, order is important. So if you have six Scrabble tiles with your letters A through F, and you want to see how many different five letter words you can make (in this example, for permutations a lot of them would not be real English words, just the certain sequence of letters in a particular order - a permutation).Then there is permutation with repetition allowed. This is like you draw a tile, record the result, then return that tile into the pile and mix them up and draw again. The order that you recorded is important for permutations.Depending on which one that you are interested in, there is a formula to calculate. See the related link for explanation of the various formulas.So permutation with repetition, the answer is 6^5 = 7776.Permutation no repetition: 6! / (6-5)! = 6 * 5 * 4 * 3 * 2 * 1 = 720.Combination no repetition: 6! / ((6-5)! * 5!) = 6Combination with repetition: (5 + 6 -1)! / (5! * (6-1)!) = 252
Which regular polygons will not tile a surface?
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.
Can a hexagon tile with a square?
no
Which polygons will tile the plane?
If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.
How do you change a tile to a triangle?
If a tile is a square or rectangle, cut the tile from corner to corner and you will create two triangles.
Does a square and hexagon fit a tile plane?
noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Will a hexagon tile tessellate?
A regular hexagon will tessellate.
How many square feet in a 8x8 hexagon tile?
The answer depends on the dimensions used for 8x8. For example, an 8 inch x 8 inch tile will have a different area to an 8 cm x 8 cm tile.
Does a regular decagon tesselate?
No. It doesn't tessellate. (You cannot tile out an area with small decagons.) The sum of the measures of the interior angles of a polygon with n sides is (n-2)180° So the sum of all the interior angles in a decagon add up to (8x180)= 1440°. To find only ONE angle you need to divide 1440 by 10, yielding 144. 360 divided by 144 is 2.5, not an integral number. This shows that a decagon doesn't tessellate. In fact, only the regular (equilateral) triangle, the square, and the regular hexagon will tessellate. For example: The sum of all the interior angles in a triangle add up to 180. 180 divided by 3 is 60. 360 divided by 60 is 6 (an integral number). This shows that a triangle will tessellate. Try this method with a square (or hexagon) and you will see that it works (square 360/90=4 and hexagon 360/120=3).
Can Regular hexagon tile the plane?
Yes.
Can a hexagon tile the plane?
Yes.Yes.Yes.Yes.
Can a regular pentagon and regular hexagon tile together in a plane?
Yes it can tile. * * * * * No, they cannot.
Why can a hexagon tile?
This is like asking "why is pi 3.14 plus a bit"? It just is. Hexagons tile because they do.
