I tried to see if the ratio of the square grid would be 4 and found that it would be. If the radius was 3, the diameter would be 6 and the circumference would be 24. 24:6 is equal to 4. The grid with the triangles has a ratio of 3. This is because the circumference is 12 and the diameter is 4 (12:4 is 3). After reading Trevor's blog I became confused. A triangle has a ratio of 3. A square has a ratio of 4. But other than that finding a pattern would be ridiculously hard.
The reason that only triangles, squares, and hexagons can tessalate has to do with the interior angles. The interior angles are respectively 60, 90, and 120. All three of these are factors of 360. If you look at a pentagon, the interior angle is 108 degrees which does not divide into 360. An octagon has an interior angle of 135 degrees which also does not divide into 360.
I think that the Polyhedra tessellations are very similar to regular tessellations. You could glue pyramids, cubes, and hexagonal prisms together but not a pentagonal prism.
http://solmentes.blogspot.com/2010/01/italian-floor-tiles-and-euclid.html
I did find this weird thing called a rhombic dodecahedron. Based on the wikipedia page it looks like it can tessellate. Based on this link i got the impression that it could tessellate (but i'm not sure).
http://en.wikipedia.org/wiki/Rhombic_dodecahedron
Thursday, April 3, 2014
Sunday, March 9, 2014
Probability
To answer the question on the most likely inconsiderate lumber man i would say the chances of the man entering the lane right next to you at that exact time are very low. Since there are 16 lanes and you chose a middle lane, there is a 1/8 chance the man would jump in a lane directly next to you. Usually people want to be further away from strangers so i find it strange that the man chose a lane right by you (this decision is probably a factor in the probability but i don't know how to calculate it). Finally, it takes you 45 seconds to swim 50 meters. During 7 of those seconds you are at the side of the pool where the lumpy man is getting ready to jump. So the probability of the man jumping in the pool while you are at the same side of the pool is 7/45. The answer of your question would be 1/8 x 7/45 = 7/360. This probability would be even less if you factored in that he could have gone to the pool at any time of the day. I think the man was trying to be rude based on this data...
One time my brother and i played a fun game with chips. My brother got out 2 sea salt and vinegar kettle cooked chip and 8 normal kettle cooked chips (the chips look the same). I absolutely loathe vinegar and the game was i had to eat 3 out of the 10 chips. It was a really fun game and i did end up having to eat a vinegar chip along with 2 normal chips. The probability that i would get a vinegar chip would be (8C2 x 2C1)/(10C3)= 7/15 probability
One time my brother and i played a fun game with chips. My brother got out 2 sea salt and vinegar kettle cooked chip and 8 normal kettle cooked chips (the chips look the same). I absolutely loathe vinegar and the game was i had to eat 3 out of the 10 chips. It was a really fun game and i did end up having to eat a vinegar chip along with 2 normal chips. The probability that i would get a vinegar chip would be (8C2 x 2C1)/(10C3)= 7/15 probability
Wednesday, February 19, 2014
Pascal
In Pascals triangle, the sum of each row is a power of 2. The first row is considered row 0. And 2 to the 0 power is 1 (this is how Pascals triangle begins). Row 1 sums up to 2 because 2 to the 1st power is 2. Row 2 sums up to 4 because 2 to the 2nd power is 4.
There are many other cool and interesting things about Pascals triangle. Pascals triangle is very interesting if you look at it diagonally. In one diagonal row the numbers increase by 1. In the next diagonal row there is a pattern such as 1, 3, 6, 10, 15. One of the coolest part of pascals triangle however is the powers of eleven. If you are in row 4, you find that 11 to the 4th power is equal to the numbers in the 4th row.
Blaise Pascal was born in 1623 and died in 1662. He was very influential because he invented an early calculator named the Pascaline. He published books on probability and theology which laid the foundation of Pascals triangle. Blaise Pascal got started on his work at a very young age. Some sources say he was involved with math meetings at the age of 12. Pascal started the "mystic hexagram" theorem which changed the view on geometry for the whole world.
There are many other cool and interesting things about Pascals triangle. Pascals triangle is very interesting if you look at it diagonally. In one diagonal row the numbers increase by 1. In the next diagonal row there is a pattern such as 1, 3, 6, 10, 15. One of the coolest part of pascals triangle however is the powers of eleven. If you are in row 4, you find that 11 to the 4th power is equal to the numbers in the 4th row.
Blaise Pascal was born in 1623 and died in 1662. He was very influential because he invented an early calculator named the Pascaline. He published books on probability and theology which laid the foundation of Pascals triangle. Blaise Pascal got started on his work at a very young age. Some sources say he was involved with math meetings at the age of 12. Pascal started the "mystic hexagram" theorem which changed the view on geometry for the whole world.
Wednesday, January 15, 2014
Math humor
Here is an attempt to be humorous:
Q: What did Ethan say to the piece of pie?
A: I don't know, probably something irrational!
i and pi got in an argument... i said to pi "get rational." Pi said to i "get real."
(not me)
Q: What did Jeremy say to Ethan?
A: you must be half a person cause im twice as cool as you.
because .5 x 2 = 1 (im one person)
Q: why did Ms. Mariners math class all get fat?
A: She told us the pie would never end!
Q: what did the bank tell Ethan?
A: If your looking for interest your at the wrong place...cause we have none for you!
That's about all i can come up with (sorry Ethan). There are plenty of other good jokes out in the internet. This is one i particularly liked...
http://www.edudemic.com/is-this-the-root-of-all-evil-math-humor/
http://images4.fanpop.com/image/photos/20700000/Math-Jokes-math-20787076-550-400.jpg
http://katharinefrank.files.wordpress.com/2011/09/algebra.jpg
And my favorite:
http://media-cache-ec0.pinimg.com/236x/c0/61/2d/c0612dd212f70bd39c317e09e402d6ca.jpg
Q: What did Ethan say to the piece of pie?
A: I don't know, probably something irrational!
i and pi got in an argument... i said to pi "get rational." Pi said to i "get real."
(not me)
Q: What did Jeremy say to Ethan?
A: you must be half a person cause im twice as cool as you.
because .5 x 2 = 1 (im one person)
Q: why did Ms. Mariners math class all get fat?
A: She told us the pie would never end!
Q: what did the bank tell Ethan?
A: If your looking for interest your at the wrong place...cause we have none for you!
That's about all i can come up with (sorry Ethan). There are plenty of other good jokes out in the internet. This is one i particularly liked...
http://www.edudemic.com/is-this-the-root-of-all-evil-math-humor/
http://images4.fanpop.com/image/photos/20700000/Math-Jokes-math-20787076-550-400.jpg
http://katharinefrank.files.wordpress.com/2011/09/algebra.jpg
And my favorite:
http://media-cache-ec0.pinimg.com/236x/c0/61/2d/c0612dd212f70bd39c317e09e402d6ca.jpg
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