Driving in Boston is actually the worst. I miss the nice Midwestern drivers I’m used to.
Where did my product go?
Q:Explain to me scientifically what makes science so great
If you’re still at UMass, go to like the one of the highest floors of the library. The view is excellent. :-) Like 23 has stacks and they’re mostly Science. :-)
We haven’t gotten there yet, but we’ll have to do this tomorrow before we head into Boston!
Whenever these schools we’re visiting quote stats about how they have the biggest/best [X] east of the Mississippi I wonder how that compares to Minnesota because our campus straddles the Mississippi. We have campuses on both sides of the Mississippi so do we count as a school east or west of the Mississippi or both?
Amherst for UMass or Amherst College??
We’re touring Penn State this morning and then heading to Amherst, Mass. It’s super weird to tour Big Ten schools having just graduated from a different Big Ten school. At least Michigan and Penn State have better mascots than Minnesota. Gophers, of any color, are not actually that threatening.
Type of Spirals: A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
Different spirals follow. Most of them are produced by formulas:The radius r(t) and the angle t are proportional for the simplest spiral, the spiral of Archimedes. Therefore the equation is:
(3) Polar equation: r(t) = at [a is constant].
From this follows
(2) Parameter form: x(t) = at cos(t), y(t) = at sin(t),
(1) Central equation: x²+y² = a²[arc tan (y/x)]².
You can make a spiral by two motions of a point: There is a uniform motion in a fixed direction and a motion in a circle with constant speed. Both motions start at the same point.
(1) The uniform motion on the left moves a point to the right. - There are nine snapshots.
(2) The motion with a constant angular velocity moves the point on a spiral at the same time. - There is a point every 8th turn.
(3) A spiral as a curve comes, if you draw the point at every turn(Image).
Figure 1: (1) Archimedean spiral - (2) Equiangular Spiral (Logarithmic Spiral, Bernoulli’s Spiral).
Figure 2 : (1) Clothoide (Cornu Spiral) - (2) Golden spiral (Fibonacci number).
More Spirals: If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. There are six spirals, which you can describe with the functions f(x)=x^a [a=2,1/2,-1/2,-1] and f(x)=exp(x), f(x)=ln(x). You distinguish two groups depending on how the parameter t grows from 0.
Figure 4: If the absolute modulus of a function r(t) is increasing, the spirals run from inside to outside and go above all limits. The spiral 1 is called parabolic spiral or Fermat’s spiral.
Figure 5: If the absolute modulus of a function r(t) is decreasing, the spirals run from outside to inside. They generally run to the centre, but they don’t reach it. There is a pole. Spiral 2 is called the Lituus (crooked staff).
Figure 7: Spirals Made of Line Segments.
Source: Spirals by Jürgen Köller.
See more on Wikipedia: Spiral, Archimedean spiral, Cornu spiral, Fermat’s spiral, Hyperbolic spiral, Lituus, Logarithmic spiral,
Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral,
Hermann Heights Monument, Hermannsdenkmal.
Spiral compulsion. But this is a handy reference.