| For my blog, I decide to look some stuff up about tessellations - even though they may seem like a very elementary concept, I enjoy their artistic aspects. Thus, here's an answer to your question of "Why are there only three regular polygons that tessellate?" So, a regular tessellation is periodic (repeated translations of polygons) and uniform (same type of polygons at each vertex), composed of congruent regular polygons. Apparently only three regular tessellations exist (triangle, square, and hexagon) and that's because these polygons are the only ones that have interior angles that divide evenly into 360 degrees. To find an interior angle of a regular polygon, you use the formula: a = 180 - 360/n. Also, "of the regular polygons, only triangles, squares, hexagons, octagons, and dodecagons can be used for tiling around a common vertex because of the angel value." (http://www.beva.org/math323/asgn5/tess/regpoly.htm) |
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Speaking of the artsy side, I think it's pretty beautiful how we can apply math to things such as architectural design, not just architectural structure.     I enjoyed reading this quite a bit! http://www.ysjournal.com/article.asp?issn=0974-6102;year=2009;volume=2;issue=7;spage=35;epage=46;aulast=Khaira Apparently people are really into tessellations and origami, too.  Image sources: http://origamiblog.com/origami-tessellations-islamic-design/2009/06/08 http://vi.sualize.us/i_w_a_m_o_o_r_c_h_i_t_e_c_t_u_r_e_voussoir_wooden_art_tessellations_clouds_installation_picture_6rgT.html | |
Sunday, March 30, 2014
Tessellations
Monday, March 10, 2014
Probability Problems
Alice, Mieke, and Grace sat on the floor of Brown Hall doing homework and eating a bag of Skittles candy. For the purposes of this math problem, we will say that there were 55 skittles total in the bag and 11 skittles of each flavor. There are 5 different flavors of skittles: cherry, grape, green apple, lemon, and orange. Alice's favorite flavor is grape, Mieke's favorite flavor is green apple, and Grace's favorite flavor is orange. What is the probability that after picking 9 Skittles out of the bag, there would be at least one grape skittle, one green apple skittle, and one orange skittle?
(A very real life problem - ask them and they'll be witnesses)
A vocabulary test has 30 questions. Twenty questions have choices ABCDE as answer options, five questions are true or false, and five questions are fill in the blank with a word bank that has 10 words, which can only be used once. If you guess at every question, what is the probability of getting at least half of the questions right?
Someone's grandmother really likes to plant flowers in her garden. In a mass package of tulip bulbs, only one out of four bulbs sprout on average. She has twenty packages of tulip bulbs. What is the probability that out of the twenty packages, how many will not sprout?
Seven cards are dealt from a deck of cards that do not have any red hearts.
a) What is the probability of getting all face cards?
b) What is the probability of getting only kings?
c) What is the probability of getting only black cards?
A teacher is pondering if they should give his students a free period or not. He decides to play the silly game where he chooses a number between 29 and 72 and his students have to guess. The number he chose is an even integer. What is the probability that his students will choose the right number if they all get three tries?
Of the 1700 students at a school, 908 have pet dogs, 762 have pet cats, and 45 have both pets (even though dogs are much cuter). If a student is chosen at random, what is the probability that they have either pet?
A coin is bent so that the probability of getting tails is 0.59 instead of 0.50. This coin toss is extremely important because it chooses the sides of high school debaters in their final round. They have to choose a preset combination of heads and tails that consists of two tosses in order to call for the affirmative or the negative side.
a) Draw a tree diagram showing the probability of 3 tosses of the coins
b) Find P(HH), P(HT), P(TT), and P(TH) for the team that you like more
(A very real life problem - ask them and they'll be witnesses)
A vocabulary test has 30 questions. Twenty questions have choices ABCDE as answer options, five questions are true or false, and five questions are fill in the blank with a word bank that has 10 words, which can only be used once. If you guess at every question, what is the probability of getting at least half of the questions right?
Someone's grandmother really likes to plant flowers in her garden. In a mass package of tulip bulbs, only one out of four bulbs sprout on average. She has twenty packages of tulip bulbs. What is the probability that out of the twenty packages, how many will not sprout?
Seven cards are dealt from a deck of cards that do not have any red hearts.
a) What is the probability of getting all face cards?
b) What is the probability of getting only kings?
c) What is the probability of getting only black cards?
A teacher is pondering if they should give his students a free period or not. He decides to play the silly game where he chooses a number between 29 and 72 and his students have to guess. The number he chose is an even integer. What is the probability that his students will choose the right number if they all get three tries?
Of the 1700 students at a school, 908 have pet dogs, 762 have pet cats, and 45 have both pets (even though dogs are much cuter). If a student is chosen at random, what is the probability that they have either pet?
A coin is bent so that the probability of getting tails is 0.59 instead of 0.50. This coin toss is extremely important because it chooses the sides of high school debaters in their final round. They have to choose a preset combination of heads and tails that consists of two tosses in order to call for the affirmative or the negative side.
a) Draw a tree diagram showing the probability of 3 tosses of the coins
b) Find P(HH), P(HT), P(TT), and P(TH) for the team that you like more
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