About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

“Spiders Aren’t Animals!” Well, Actually….

Posted on 3 September 2018 by RobertLovesPi

Over the years, literally hundreds of people have told me that spiders are not animals. This seems to happen the majority of the times that the topic of spiders comes up in conversation. When I reply that spiders are, in fact, animals, the usual response is “Spiders are insects!” This gives me headaches, because (1) spiders aren’t insects, and (2) insects are also animals.

Spiders happen to be my favorite animal, so this is quite confusing to me. Hopefully, this screenshot from my Google-search for “animal definition” will help spread the word that spiders are, indeed, part of the animal kingdom.

[Spider image from https://en.wikipedia.org/wiki/Phidippus_audax. Also, I added the red arrow and ellipse to the Google-screenshot, using MS-Paint.]

An Icosahedron Augmented With Twenty Great Icosahedra, Together With the Dual of This Cluster-Polyhedron

Posted on 2 September 2018 by RobertLovesPi

The cluster-polyhedron above was formed by augmenting a central isocahedron with twenty great icosahedra. The dual of this cluster is shown below.

Both these images were created using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.

A Flashing Mandala

Posted on 2 September 2018 by RobertLovesPi

flashing mandala

Mandalas are used for meditation and contemplation. They are also supposed to represent the universe, which we now know is in a constant state of change. Generally, this means mandalas are non-moving images, and (traditionally) they certainly don’t flash. This is, therefore, an attempt to update the concept of the mandala for the modern age, reflecting our current understanding of the universe.

The Compound of the Truncated Isocahedron and the Pentakis Dodecahedron, with Related Polyhedra

Posted on 26 August 2018 by RobertLovesPi

The yellow-and-red polyhedron in the compound below is the truncated icosahedron, one of the Archimedean solids. The blue figure is its dual, the pentakis dodecahedron, which is one of the Catalan solids.

The next image shows the convex hull of this base/dual compound. Its faces are kites and rhombi.

Shown next is the dual of this convex hull, which features regular hexagons, regular pentagons, and isosceles triangles.

Next, here is the compound of the last two polyhedra shown.

Continuing this process, here is the convex hull of the compound shown immediately above.

This latest convex hull has an interesting dual, which is shown below. It blends characteristics of several Archimedean solids, including the rhombicosidodecahedron, the truncated icosahedron, and the great rhombicosidodecahedron.

This process could be continued indefinitely — making a compound of the last two polyhedra shown, then forming its convex hull, then creating that convex hull’s dual, and so on.

All these polyhedra were made using Stella 4d: Polyhedron Navigator, which you can purchase (or try for free) at http://www.software3d.com/Stella.php.

A Tessellation Featuring Regular Pentadecagons and Hexagons, As Well As Isosceles Trapezoids and Triangles

Image

Tessellation featuring regular pentadecagons and hexagons, as well as isosceles trapezoids and triangles

Tessellation Featuring Regular Enneagons and Hexaconcave Dodecagons

Posted on 18 August 2018 by RobertLovesPi

Tessellation featuring regular enneagons and hexaconcave dodecagons

Some people call nine-sided polygons “nonagons,” rather than “enneagons,” but I prefer Greek prefixes to those based on Latin.

Because I’m a Teacher

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Because I'm a teacher

Hexagon the Kitten Is Recording My Computer Activity

Posted on 12 August 2018 by RobertLovesPi

So I’m looking at Facebook, and all of a sudden Hexagon the Kitten is on the keyboard. Zap! Screenshot captured at feline speed — before I could grab the little rogue.

This is the first of four pages of information which Hexagon attempted to print this morning — a screenshot of the top of my Facebook timeline. She tricked me into losing the other three pages, which were simply more records of recent activity on Facebook.

She was also, as the image above shows, trying to print in black and white, which seemed interesting. I looked it up, and cats have far more rods than cones, compared to humans, so I guess Hexagon doesn’t see color as that important.

She also typed the following into the keyboard:

What is Hexagon’s goal with all of this computer activity? If I ever figure it out, I’ll post my findings here.

My Mother’s Epic Battle with an Armadillo

Posted on 11 August 2018 by RobertLovesPi

I just found a hilarious tale about my mother (in L. Lee Cowan’s Except for All the Snakes, I just Love It Out Here: The News from Stone County, Arkansas, Where One Life is Put Down Straight Up, p. 120). According to this published account, I was four years old when her battle to kill an armadillo entered family legend. As you can see below, Mom credits both my sister and myself with keeping the story alive over the years. A good family friend, Bruce, played a key role in bridging the gap between my mother and L. Lee Cowan, the author of the book in which this was published. It’s an amazing thing to have found.

If you like this excerpt (shown below), please buy the book, as I have done.

LLeeCohan

An Enneagonal Mandala

Posted on 10 August 2018 by RobertLovesPi

enneagonal mandala

I made this years ago — in 2010 — and just found it today, on Facebook. That was two years before this blog started. I like finding such “lost works,” but it doesn’t happen often these days.