Bridges and the Curvature of the Earth

Because of the curvature of the Earth, the biggest bridges are a tiny bit wider at the top. What I mean is the architects had to take that into account. The bridge with the longest span in the world is the Akashi-Kaikyō Bridge in Kobe, Japan. It’s 3 inches wider at the top. It’s easy to figure this out.

Wider = Span * Height / Earth Radius

These measurements are in feet. So to get an answer in inches, multiply by 12. The radius of the Earth is 20,925,197 feet. You don’t have to be that accurate. Even if you rounded to 21 million feet, the answer would be less than 100th of an inch off.

Anal Netflix

Netflix just gives me another reason to get anal retentive. I can’t keep from trying to pick the perfect queue order. I finally put all my selections in a spreadsheet. That was easy enough. In Excel, choose Get External From Web from the Data menu and enter the web address of your queue, which is http://www.netflix.com/Queue. I decided the only important variables are the year (1980 – 2010) and the Rotten Tomatoes rating (50 – 100). So I added those. That was the hard part. Then I needed a formula. The top of the list is the dot in the upper right-hand corner. That’s easy. But what about the rest? I prefer the formula that uses arc tangent. For either formula, the higher the number the higher in the list.

The Rhombic Dodecahedron

If you took a big box full of tennis balls and squished it until there was no space between the balls, what would the shape of the balls be? This makes an object I’ve been fascinated about for some time. I would use up all my kids Magz toys making it. I also made it from paper and from dowels. Each side of this object is made out of the same shape and all the edges are the same length. That makes it sound like a fundamental shape or Platonic Solid like a cube or tetrahedron. But no. There’s something irregular about it. It’s hard to tell because sometimes it looks like a cube and sometimes it looks like an octahedron. It’s the vertices. Sometimes 3 sides touch and sometimes 4 sides touch.
 
Each face has some interesting properties. The faces are all rhombuses. The right triangles in each rhombus are √1 by √2 with a diagonal of √3. (a²+b²=c² and 1+2=3)

If you fold the corners of an A4 piece of paper like this you get this same rhombus. This works with any ISO standard size paper.

But the best of all is that these objects can be stacked together without any space in between. There aren’t many shapes like that. (See Space-Filling Polyhedron.) What’s funny is Wolfram makes no connection between the Rhombic Dodecahedron and sphere packing.

When will you be half your father’s age?

Click to download Times Older.

I like to keep a calendar of strange dates like that. last week, my sister was exactly 5 times older than my daughter. I wrote a Word document that figures all that out for me. Give it a try and tell me what you think.

Integration for Programmers

Calculus can be very useful for improving the performance of a function. Resently, I saw patrickJMT’s YouTube video on Calculating a Definite Integral Using Riemann Sums. Now, I’m no math teacher. But I thought it’d be fun to demonstrate how integration works using Visual Basic code instead of the Greek used in math class. I chose VB since many people can open Excel, Word or others and try it out for themselves. I have instructions for that as well.

http://www.youtube.com/watch?v=b-lXoWf6VCs