Frisbee Angles

I came up with this when I was throwing a Frisbee with my friends.

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See if you can solve it.

This is how my Dad and I solved it:IMG_6503

We had to break it into 2 right triangles with the same height  C.

Then we found C’s value using the Pythagorean Theorem and some algebra.

Then we used the sine  inverse on the calculator to find 2 angles (19.41 and 66.o3).

This works because the sine  of an angle in a right triangle = the opposite side divided by the hypotenuse.

Finally we used our knowledge that all angles on a triangle add up to 180 degrees to find the last angle (94.56).



 

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Hypercubes and Zometools

On Tuesday, February 9, my Dad and I went to a Math Art Opening at a Denver machine shop. We’d been invited to attend by Paul Hildebrandt, one of the inventors of Zometools. We arrived at the shop to find a cute little dog named Daisy. She greeted us at the door and gave us a warm welcome. Daisy was there, but no one else. The shop had no people and was very quiet, aside from Daisy.

Paul's 6D Sculpture
Paul’s 6D Sculpture

My Dad and I went outside and around the building.  Behind the shop, we met Paul and his gang. They were building with Zometools, making cool shapes and 3d designs under a big 6d sculpture that Paul had made. I joined in, making what I call the double decker hypercube. It can  be classified as either a cube inside of a Hypercube or  a Hypercube inside of a cube.

Shadow of a Hypercube
Shadow of a Hypercube

It has interesting shadows. In fact, I tried to build a replica of what I saw out of the red Zometools. It wasn’t exact, but I found out that at a certain angle, the shadow replica and the DD Hypercube would line up to make the same image. That was cool.

Unfortunately my Dad and I had to go get dinner and go home. I was getting hungry, and I had to practice for my piano lesson the next day. It was fun to make the DD Hypercube though. I wish I could have stayed longer.

Daisy
Daisy

 

Dad’s Note:

The exhibit, “Structure of Number”, runs through Sunday, March 27.  It consists of two large sculptures outside of Denver 4-Axis Machining at 5830 Downing Street. I learned that 4-Axis Machining made the original molds for Zometools, as well as the large struts and connectors for Paul’s sculpture.  Paul even married into the 4-Axis family! 

 

THE DDhedron

The dodecadodecahedron is a dodecahedron with its faces turned into stars and the extra rhombi pushed down. My Dad made one out of Zometools at the Mosaic Fest in Nebraska with Paul Hildebrandt, one of the inventors of Zometools. Paul is interested in the shadows of shapes and this one has so many fun shadows! Check some of them out:

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Aren’t they cool? I think they look like those patterns you can make with a Spirograph kit.  Paul and I got those different shadows by holding the DDhedron in front of a projector and rotating it.

Math in Nebraska

Two weeks ago my Dad and I went to the MoSAIC Festival at the University of Nebraska-Lincoln. We drove 500 miles, from Denver, Colorado to Lincoln.

We met the Chief Visionary Officer of Zometool, Paul Hildebrandt. My Dad had a lot of fun making a very cool dodecadodecahedron from the Zometools  Paul had brought. My Dad and I also had a long conversation about the fourth to the infinite dimensions. Then we learned how to make a hexaflexagon from a Vi Hart video. It was all very very cool and fun! Here’s one of the videos made by Vi Hart  on the hexaflexagon:

I would like to try this sometime.

Ideas: Infinity

Infinity is a strange thing that has influenced my thoughts for my whole life. Have you ever looked at the pattern made by putting a mirror in front of another mirror? It looks like an infinite hallway! When I lay in bed, my mind thinks up many different patterns of infinity, some of which relate in […]

Story behind the Blog Name

My father and I were eating at our favorite Indian restaurant called Namaste, discussing the name of our new math blog. I had curry meatballs, and when I got to the last one, I did not want to run out because it was so good! I cut the meatball in half and ate one of the halves, then I cut the remaining half in half and ate one of those. I kept on like this until it was too small for the knife and ate the last piece. I told my dad I had just created a Zeno’s Meatball because it reminded me of Zeno’s Paradox, and he suggested that Zeno’s Meatball be the name of our math blog.rotated meatball