About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. Welcome to my own little slice of the Internet, which is shared freely with anyone who is interested.

The viewpoints and opinions expressed on this website are my own, except for the relatively small number of clearly-identified works of others. Nothing here should be confused with the views of my current, nor past, employers, nor any other organization, of any kind.

I am, by profession, a high school teacher of many subjects — mostly mathematics and the mathematical sciences — over a career of more than two decades. I live, and work, in the USA.

55 thoughts on “About RobertLovesPi”

  1. As a teacher, perhaps your class might be interested in a problem that’s been vexing me for a while now…
    The problem started with the fact that

    (3^3)+(4^3)+(5^3)=(6^3)

    …this has led some puzzle-minded people to ask…
    “What’s the smallest number of parts that can assemble into a size_6 cube, in such a way that they can also assemble into a trio of cubes, sized 3, 4, & 5?

    It’s simple to prove that 8 is the lowest possible answer.
    Since a cube has 8 corners, if a 7-piece solution WAS possible, then one of the pieces would have 2 of the corners, which would make it 6 blocks long, which is too long to fit inside any of the smaller cubes.

    An internet search will reveal at least 2 basically different 8-piece solutions. In one case, the size-4 cube is kept intact, & the other 7 pieces assemble into the cubes of sizes 3 & 5. In the other case, the size-3 cube is intact, 2 other pieces build the size-4, & the remaining 5 pieces build the size-5 cube.

    With this background established, here is my current problem:

    “Is there an 8-piece solution to this puzzle if we’re forced to keep the size-5 cube intact, & if not, how do we prove that it’s impossible?

    For a classroom experiment, I’d use 91 blocks:
    36 would form a 6*6 “floor”.
    05 would be stacked in one corner, for a total of 6 blocks tall.
    The remaining 50 blocks are then divided in half, & form a 5*5 “wall” on either side of the stack.

    The resulting shape is what a 6*6 cube looks like, after a 5*5 cube has been removed.

    So, how would you break this shape into 7 parts, if you want to rebuild them into the cubes of sizes 3 & 4?

    I’d welcome any thoughts you could offer, whether it’s a solution or a “proof of impossibility”.

    I hope you enjoy this notion, Good Sir!
    Cheers!

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  2. Robert, I randomly found your website when I was looking for tools to build polyhedrons (for myself and with my kids). Something easily accessible, affordable and user friendly. I was going to buy generic magnetic sticks and balls. But then I learned that many people use Zometools. But Zometools has distinct pegs and lengths which I think may complicate things. I also learned about Polydron and Geometiles but I rather have sticks and balls. I’d be happy to hear your recommendations? Perhaps Zometools is the best. Thanks.

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      • Really just looking for a comprehensive listing of near misses. After more than a dozen hours searching im still not deeing this.. which i think must be a fluke since it is so simple. My first model was paper (which appears perfectly regular), then folded and welded sheet metal (which required force and face distortion to get sides to align).. now setting up to machine a solid die from billet.. a bit tricky getting all the angles perfect on the indexing head and bridgeport. So interesting how the models from sheets have regular polygons with some warped faces while the machined solid will have flat, slightly-non-regular faces. If there is any official catalog of near misses that you could recommend it would be much appreciated. I very much love your work in this area btw! 

        Sent from Yahoo Mail on Android

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  5. Hi Robert, who do you think you are?

    I’m a lot like you, teach matematics and love Pi. Or PiSquare as my alias is.

    Do you like punk music? There is an artist who answers the question that I started this reply with. He then kicks in/out a door and “comes out” to 50 000 People.

    My mail is Jonsson812@hotmail.com if that sounds interesting

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  6. Hi Robert, my name is Shana Marsh and I believe we are family members. I came across one of your articles digging into some family history/trauma. I’d love to speak more in depth with you about your father. My email is shanamarsh.biz@gmail.com. I would understand if I didnt receive an email as Im sure his memory is hard to bare when reliving.

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  8. Came here in the search on 3D uniform honeycomb information for video game design. It’s so calming to see unique souls posting about what they like on internet.

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  9. I am doing more basic geometry as @gmtrcply on insta.

    I never heard of Zometools. I do realize that it is a vertex and edge model, where the vertices offer certain angles, and the edges are available at certain lengths. But it looks a bit complicated to handle, while still being limited?

    So what’s so special about it to get yet another modeling tool?

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