Parabolas

Parabolas are very commonly used in the real world. They are used to construct many of our everyday buildings. Another example would be bridges. More specifically, the Golden Gate Bridge uses parabolas to make sure the bridge is sturdy enough. The suspension cables on the bridge are parabolas. The parabolic shape of the suspension cables actually do a lot to keep the bridge up. Their shape helps relieve the tension on the bridge from all the weight, and instead distributes it elsewhere through the cables. These cables are constantly being pulled on by the weight of both the bridge itself and the cars that pass by on it everyday. Parabolas are actually very important and they are very useful for many other things besides math class.

What If...

Thinking over the question of why there are only three regular polygons that tessellate I began visualizing a picture in my head. The reason the hexagon, triangle, and square are the only regular polygons to tessellate is because of their angles. 360 is divisible by the angles of all three of these polygons. The polygons all tessellate at one point which means for them to tessellate the polygons need to be able to go around the certain point enough times that there are no spaces in between them. A regular triangle has angles of 60 degrees, therefore it will go around a certain point six times and repeat at different points. A square with angles of 90 degrees will only go around 4 times and a hexagon with angles of 120 degrees will only go around 3 times. All equaling 360.

Pascal's Triangle

The sum of the rows in Pascal's triangle are equal to 2 raised to the power of each of the rows. The 1st row is 2 raised to 0 power and so on. The sum of the rows are 1, 2, 4, 8, 16, 32...and so on.
In order to find 11 raised to the 7th power by using Pascals triangle we need to add the numbers first:

1

                                                                              1   1

                                                                            1   2   1

                                                                          1   3   3   1

                                                                        1   4   6   4   1

                                                                      1   5  10  10  5  1

                                                                    1   6  15  20  15 6  1

                                                                  1   7  21  35  35  21 7 1

Then you start with the first numbers:

17

To get the numbers in the middle you just add them as if you were adding numbers by moving the tens digit over:

19487171

Math Puns