Irreducibility and Divisor Laws in the Gravesian Integer Octonions

I think Octonions are special – I am reluctant to launch into a detailed explanation of what they are and why I think that; perhaps I will find the motivation at some point. For now, I am simply going to announce that I was doing some research into a class of them with respect to […]

Globe Orrery

This orrery I built tracks each of the ancient planets: Sun, Mercury, Venus, Moon, Mars, Jupiter and Saturn. It is built around a programed Arduino on a custom printed circuit board. It caches nasa web data locally one a day and interpolates in between every couple seconds to aim the arrow at the celestial object. […]

GREAT CIRCLE ALIGNMENT OF ANCIENT SITES

I came across an intriguing claim on X that I wanted to validate. It ended up being a very quick endeavor (less than an hour) but seemed like something that might be of interest here. The claim is that many of the notable ancient sites on Earth are all found along a straight line around […]

Snake Wall

It was a bright sunny day and I was laying under a three walled beach tent in the yard of a friend. He’s known for organizing festival-like music performances on his property and really bringing together some incredible talent. Between a set we got to talking a little bit about some of the odd creations […]

Liberty BillBot

Each year more that 5000 bills are introduced in Congress and most people have no idea what’s in them. Most will be introduced so that they can be used for campaigning, sometime all the more effective if the bill goes nowhere; the fate of the vast majority. Others will be introduced and fast tracked in […]

Anunnaki Human Genome Analysis

On a recent walk I was listening to a podcast that discussed translations of ancient Sumerian tablets and the lore they contained about the Anunnaki. I won’t expound on it very much except to say that it conveys an incredible set of creation myths, many of which you can directly trace elements right up through […]

Quantum Addendum to my Hypothesis on the nature of antimatter

I write this with a degree of uncertainty as to whether it is ready to share as I cannot yet fully defend it against criticisms that I can fully anticipate. Therefore, I ask that you to consider this a novel thought experiment. It extends a past hypothesis upon which I have written concerning a reimagining […]

Programatic Circular Mosaic Filtering

Inspired by some artwork consisting of overlapping circles shaded different colors I decided to write a program to generate my own interpretation. My objective was to create an aesthetic abstract picture from a source image as a mosaic where the pattern was constructed from overlapping circles. The software first takes a picture and generates a […]

Mechanical Phi Ruler

This is a pretty small project compared to most I publish, but I thought it was interesting enough warrant a quick post! I think many people are familiar, at least in passing, with the Golden Ratio, but for those that are not here is a very quick introduction. Mathematically the Golden Ratio, is represented by […]

Parachute-Free Rockets

I’ve been doing a little bit of model rocketry with the kids and started to think about 3d printing my own custom rockets. They seemed cheap and easy to make so I figured we could even fire them out of over the woods and not even bother worrying about parachuting them down because they would […]

Angel Tray

The ottoman in our living room made for a poor surface for drinks, games and such so I decided to make a tray that could sit on top of it. I went a bit overboard and ended up with an heirloom piece I am rather proud of. The warm wood tones, subtly reflective copper, mult-layered, […]

Kinnor / Lyre

My niece’s 3rd birthday was coming up and hearing about her recent interest in music I thought perhaps a small harp would make for a nice gift; I remember my children enjoying one when they were young. After a little shopping I decided that perhaps I would build one instead of buying something but before […]

Photo biomodulation Brain Stimulator

Photobiomodulation (PBM) is a therapeutic technique wherein light, delivered by laser or LED, is used for treating wounds and pain. The mechanism of action varies depending on the nature of the therapy which can call for different protocols regarding wavelength, intensity and application. Many studies have explored the opportunity to leverage PBM for treating traumatic […]

Etch-A-NFT robot

Have you ever wanted to doodle on an etch-a-sketch but didn’t feel like getting up from your computer? Worry not my nostalgic lazy friend, for this dilemma has now been solved using robots, the cloud and blockchain! Let me introduce you to the Etch-A-NFT, now live at www.etchanft.live! What the hell am I looking at? […]

Ouroboros

Over the course of the past couple of weeks I’ve written and published my first book, well short story really; although I prefer the much classier sounding description of ‘novella’! Like many of my endeavors, this was in fact an experiment. What may come as little surprise to those that follow my blog, before writing […]

Building Mazes in Photos

I was leaning back in my chair gazing out the window last week looking for inspiration for a photo project. A small house across the street has so many surfaces and facets but it’s stark whiteness caught my attention as supplying a unique blank canvas. So I waited until sunset and snuck over there with […]

Paint Dipping Robot Crane

Like most homeowners, I have a sizeable stash of half used and expired paint cans that I know that I am never really going to use for touch ups around the house. That got me to thinking about what I might be able to use them for. I remembered reading about “motor agates” and “fordites” […]

Study of a Modulo Sequence

As I’ve discussed before, many great findings in mathematics have arisen from the study of silly arbitrary functions. These functions often look quite simple but produce surprising results when carried out at length. Occasionally I attempt to come up with my own novel routine and almost always find that they collapse to something well known […]

CryptoQuakes NFT

Further exploring unique possibilities for NFTs I decided to develop a system to create videos generated from seismographic readings! Substantial research and development was required to obtain the appropriate data direct from seismographic stations around the world, process it, generate the necessary data, imaging, audio and video. Even more work was required to implement a […]

4 Dimensional Morse Shadow Puzzle NFT

I have a very long history of studying, constructing and playing with higher dimensional objects and since they are naturally of an intangible nature it seemed to me that NFTs are perhaps a perfect medium to actually possess one. Not sure what a Non Fungible Token (NFT) is? Look into it and come back! To […]

Studies in Chlandi Figures

Ernst Chlandi was a scientist in the late 18th century that is often referred to as the father of acoustics. One of his contributions was the development of Chlandi Plates, a means of studying wave patterns. In these experiments a metal plate of a particular geometry is suspended, sand is placed on it and a […]

Pandora’s Box

For many years I’ve thought about designing and building a puzzle box built around a poem. My vision was for each stanza of the poem to be written on each of its six sides and that when read in the correct order a secret compartment would open! In fact I created a prototype core that […]

Moon Orrery

orrery [ awr–uh-ree, or– ] noun,plural or·rer·ies. an apparatus for representing the positions, motions, and phases of the planets, satellites, etc., in the solar system. This endeavor has been the longest continuous build I have ever committed to so it is with great personal excitement to finally post about my Moon Orrery. The […]

3d Printer Laser Etching

This year for my birthday I stepped up my 3d printing game from my 3yr old Monoprice Select V2 to a new Ender-5 Plus; huge upgrade after many years of headache. I was left with what to do with my old printer, certainly too much potential to just throw it away. I thought it too […]

Cathedral Radio

I’ve always wanted a cathedral radio, the antique sort that is at the corner of classy and gothic. Last summer I came across one at a flea market, it was in incredibly sorry shape which commanded the meager price I was actually willing to pay to own one. Initially I sought to restore the original […]

Framed Skull Relief

I was sitting in the study with my daughter and we were discussing art. After a while we decided we were in the mood to make something ourselves so we sat for a time looking for inspiration. My eyes kept being drawn to the fluffy quilt of talc-like ash in the fireplace and I started […]

How to Take the Fun out of a Word Game

Some time back I created a word game to play with the kids on long car rides. The objective of the game is to agree on two words and then see who can first come up with a series of changes starting from the first word that get you to the second. The changes allowed […]

IBM Ponder This 04-19 Solved

Credited with solving this (unusually easy) puzzle: Ponder This Challenge: This month’s challenge is from Reda Kebbaj. (Thanks!) Find nine different prime numbers that can be placed in a 3×3 square in such a way that the average of every row, column, and diagonal is also a prime number. I don’t know what happened here, […]

IBM Ponder This 03-19 Solved

Credited with solving this puzzle: Ponder This Challenge: Every real number can be approximated as a ratio of two integers. For example, pi is close to 22/7 but even closer to 3138/999; and there is an even better approximation with a denominator < 1000 (what is it?). We define m=BAT(x,N) as the denominator, m, of […]

Magick Summoning Device

This endeavor combined perhaps three of my main artistic interests: difficult mathematical puzzles, quirky engineering and occult oddities with undertones of the macabre. This is a very long article so if you are a TL;DR sort of person you can scroll down to the bottom for a video of the mechanical contraption in action! A […]

Avocado Pit Raft

I was eating my breakfast this morning and decided I want to grow my avocado pit. I had one my dad grew me that lasted a long time that I had loved. I naturally went to grab some toothpicks to suspend it over a glass of water and then I remembered how I roll, so […]

IBM Ponder This 01-19 Solved

Credited with solving this puzzle: Ponder This Challenge: Alice and Bob are playing the following game: they start from a number N and each one of them in his or her turn (Alice starts) divides N by any divisor that is either a prime or a product of several distinct prime numbers. The winner is […]

Faerie Specimen

I created this oddity that purports to showcase an aged museum specimen of a faerie’s skeleton. I made the skeleton with the 3d printer using human skeletal models and bird wing skeleton drawings. I made the backdrop by combing various diagrams found online. All annotations reworked, positioned and (tediously) translated into latin. The museum placard […]

Firing Lasers at Ghosts

Back in the day I always wanted to send the Ghost Hunters TV show a device and see it used on TV. I didn’t want compensation or credit, I just wanted to see something I made on a TV show. One of these devices I thought of was to be left unattended with audio/video equipment […]

Squid Vambrace

With a plasma cutter now in my arsenal and a desire to make an edgy piece of wearable art I decided to attempt to make a piece of armor. After a number of drawings I settled on the idea of a squid wrapped around an arm where the tentacles (squid = 8 legs + 2 […]

Disco-Punk Jukebox

I found this nifty old stereo-furniture piece at a consignment shop that had a center section that folded down to reveal a hidden turntable. I have kind of been on the lookout for an old stereo to refinish and contemporize but I had wanted (and still do) a piece from an older era that might […]

Hurricane Flood Restored Dresser

I received a message from a friend who was in Texas helping his family recover from hurricane Harvey. In their coastal town there was significant flooding and when he arrived he discovered a dresser with sentimental value to the family floating in salt water now for several days. He asked if I would help to […]

Railroad Spike Knife

I am fortunate to have a friend who is an amateur blacksmith who took the time to get me started hammering hot metal. Here is the first knife I attempted to make out of a rusty old railroad spike. It’s not the prettiest knife out there, but I’m pretty proud of it for a first […]

Mushroom Specimen

I have a friend with a sizeable collection of spooky oddities that I thought might enjoy adding an evil mushroom specimen to it. I intended to make a hollow core in order to run blue LEDs in it so that the mushroom might have translucent spots that would slowly pulse a color. As I got […]

IBM Ponder This 03-18 Solved

Credited with solving this puzzle: Ponder This Challenge: Alice and Bob are given an interesting challenge. Alice will be given a random vowel (A, E, I, O, or U) in a room without Bob with six randomly set toggle (on/off) switches. She may change the state of at most one switch and then leave the […]

Scarab Bass Relief

I recently had a hall mirror fall and the glass and frame broke. After a couple days seeing it ready to go in the garbage I decided to embrace the Japanese philosophy of Wabi-sabi and in particular it’s common artistic form of Kintsugi. I repaired the cracked mirror with a gold seam to bind the […]

Melancholy Nude Charcoal

Still on a little bit of an art kick from the holiday time off in between a lot of work on an electronic device I am looking forward to finishing and posting about! Drew this on a little break today.

Painting of an Avenging Angel

I was motivated to break out some paints over the holiday break, here is one of the pieces I painted:

IBM Ponder This 10-17 Solved

Credited with solving this puzzle: Ponder This Challenge: The solutions for the polynomial equation 131839*x^5+17585*x^4-13258*x^3-18104*x^2-419356*x+52715 = 0 (mod 11100101) encode something related to IBM security, with a single bit error. What does it encode? What is the wrong bit? And how is it related to IBM Security? The solution is that if you order the […]

Geometric Nature of Integers (incomplete)

Rather than fully bake this idea before writing up a post on it (not that anyone reads this stuff but me anyhow) I thought I would experiment with writing as I think with minimal retroactive edits, so let’s see how this goes! I am playing with the point of view that all integers can be […]

IBM Ponder This 05-17 Solved

Credited with solving this puzzle: Ponder This Challenge: In the string CABACB, each letter appears exactly twice and the number of characters between the “A”s is one, between the “B”s is two, and between the “C”s is three. The same problem with the letters A-E cannot be solved, but adding a space (in the form […]

Walking on Grids

Infrequently I stay in Manhattan for work. On one occasion I ended up staying quite some distance away from the office to save the company some money but I still opted to walk in. Along the way I came to think that there is a certain potential efficiency to traveling between two points in the […]

IBM Ponder This 04-17 Solved

Credited with solving this puzzle: Ponder This Challenge: IBM recently announced a commercial Quantum computer. Such a computer can factor large numbers, using a Shor algorithm. The challenge this month is to factor at least one of the following three numbers: 27771495424394652906650011597233066116343506387184320546233728271726480989807112498372640545334956743914011373 98296593067163321549931012857525979998165090637663230976866143160359417516252340928637985390415053795128313 1412534667091752138605679066750993949837793629454397369052717798704788621599573184763086599428517731585079 Bonus ‘*’ if you factor all three. Hint: The challenge is […]

Other Conway Geometries

I am a huge fan of cellular automata. The fingerprint of God is in the nature of the universe from atomic, to biologic, to economic, to cosmic and at each scope the emergence of complex systems arise not in spite of the lack of a central control but precisely because of it. This is how […]

Magic Square Sigils

While there are variations, a Magic Squares is a grid of numbers where any row, column and the diagonals sum to a singular constant. There is no shortage of material on constructing them and interesting mathematic facts about them, but of interest to me was the ancient occult fascination with them. They are found around […]

Themed Cocktail Menus

Occasionally bartending private themed craft cocktail parties I enjoy putting together appropriate menus, here are a couple:

Multidimensional Minecraft

Imagining physical worlds in higher dimensional space is a passion of mine and I found myself thinking about what architectural features a building might have if it were designed in higher dimensions. To that end I decided I wanted to create a 4d CAD system of sorts so that I could design and explore 4d […]

Fire Pit with Cast Concrete Top

It was high time that we had a proper fire pit area and I wanted it in time for the summer so I worked double time to knock this out in just 2 weekends (plus months of drawing diagrams… like I do…). I set it with good visual symmetry to my back yard where it […]

Modular Craft Bar

I’m a collector of some of the more exotic craft spirits, an enthusiast for historically accurate cocktails and a hobby bartender. As such I needed to build a bar that would server my needs at home in various locations inside and outside as well as for travel for events. The construction is from cabinet grade […]

Hypothesis on the Nature of Matter

If you follow my blog you have probably noticed that I spend a good amount of time thinking about and simulating interactions and geometry in higher dimensional spaces. I enjoy looking for ways to describe mundane behavior we experience through higher dimensional mechanics. While this often describes the simple and obvious through convoluted means, I […]

Tiki Statue

I got a pretty good sunburn working out in the yard the day before but I really wanted to be outside to enjoy the nice weather so I was looking for something do in the shade. I took a little walk in my woods and decided with an upcoming Tiki party I would take a […]

IBM Ponder This 03-16 Solved

Credited with solving this puzzle (w/ extra credit!): Ponder This Challenge: This month’s challenge is from Yan-Wu He (thanks!) For a non-zero number (in list) (a1,a2,..,an), its square is (…, an,..,a2,a1), Let’s call the number N “squareversed” if its square ends with the reverse of N. For example, N=69714 is “squareversed”, since its square is […]

Warre Beehives

Built a pair of Warre hives! From lumber to built: Making all the top bars was a bit of a chore: Done!

IBM Ponder This 02-16 Solved

Credited with solving this puzzle (w/ extra credit!): Ponder This Challenge: This month’s challenge is about IBM’s InterConnect 2016 conference. Assign each letter a different digit such that the following mathematical equations would be correct (** denotes exponentiation): a**connect = c (mod inter) a**connect = a**toe (mod at) a**connect = a**toe (mod cm) n**i = […]

IBM Ponder This 12-15 Solved

Credited with a solving this puzzle. Tricky one, only a couple solutions in the world submitted: Ponder This Challenge: Last month, Gene Amdahl, an IBM fellow who was the chief architect of the legendary IBM 360 system, died at age 92. In memory of his work, this month’s challenge focuses on the IBM-360 character set […]

IBM Ponder This 11-15 Solved

Credited with solving this puzzle. I added an extra twist to this one to make the phrase have some meaning and I set out to submit a second one that was inappropriate to make the judge chuckle 🙂 Ponder This Challenge: To mark the announcement by IBM CEO Ginni Rometty about a new era of […]

Gendered Numbers

An observation I’ve made on mathematics is that much of it seems to be able to be traced back to some bored mathematician coming up with a seemingly arbitrarily rule system for fun and following it through to conclusion. In so doing they discover interesting and often seemingly useless principles along the way. This fine […]

Linear Motion via Higher Dimensional Rotations

Expressing a known behavior in a new way has the potential to expose new thinking and opportunities. I was thinking a bit about how to express absolute position exclusively via rotation. I started to think about the rotating light in a light house and the light it would cast on a curtain hung between you […]

IBM Ponder This 08-15 Solved

Credited with solving this puzzle. This was fun software to write! Ponder This Challenge: Find a way to fold a loop of string in three-dimensional space such that all three projections will be loop-free (i.e., you won’t be able to make a path from a point to itself without backtracking). Provide your answer as a […]

Alchemist Cocktail Analysis

How might the prototypical alchemist go about designing the perfect cocktail? It would seem to me that they might start by defining the nature of each ingredient and expect the cocktail to be the composite nature of its parts. While somewhat tongue-in-cheek, I was interested to see what I would learn by taking to completion […]

IBM Ponder This 07-15 Solved

Credited with solving this puzzle: Ponder This Challenge: Four people stand in line with hats on their heads. On the back of each hat is a unique number (i.e., no two people have the same number) between 1 and 6. Each person can see only the numbers of the people in front of him. One […]

Multidimensional Visualizer

I spend a lot of time thinking about and working on multidimensional problems. This can be particularly daunting to visualize so I created a visual tool to allow for the exploration of multidimensional problems. First, let’s better explain what I mean by a multidimensional problems; so let’s look at an example. Let’s say my mood […]

IBM Ponder This 06-15 Solved

Credited with solving this puzzle: Ponder This Challenge: IBM’s QRadar system keeps track of events by measuring something every second. It has an anomaly detection system that alerts the user when the current measurement is more than three standard deviations away from the average of all previous measurements. An imaginary attacker is trying to deceive […]

IBM Ponder This 05-15 Solved

Credited with solving this puzzle: Ponder This Challenge: Three people are playing the following betting game. Every five minutes, a turn takes place in which a random player rests and the other two bet against one another with all of their money. The player with the smaller amount of money always wins, doubling his money […]

Bacardi Bat House

My daughter is allergic to mosquitoes, so we made a bat house Other pics:

Planets Made of Fat

Walking through the kitchen I stopped and became fascinated with the bizarre texture of the fat drippings in a pan my wife had on the stove… so naturally I made them into planets! Source material:

Autocomplete Fun

Before all the Facebook fun was common with posting silly autocomplete recommendations I was a trailblazer laughing at the recommendations Google had for completing your search strings so I decided to write some software to explore this further. It took a bit of dabbling but I was able to feed text and pull back recommendations […]

IBM Ponder This 11-14 Solved

Credited with a solution for this puzzle: Ponder This Challenge: There are 24 letters in the Greek alphabet, from alpha, beta, and gamma, through chi, psi, and omega. The names of the letters are of different lengths, from short two-letter names like mu or pi through the seven letters in omicron. We want to generate […]

Wooden Sword for my Daughter

So Ana asked me to make her this sword she drew: Here is how it came out!

Zelda Sword and Shield

Pretty happy with how nice the shield came out, I took a crack at the sword too; fun build. Making of:

IBM Ponder This 09-14 Solved

Credited with solving this puzzle: Ponder This Challenge: Let b = (2^3^4^5) / (e^n), otherwise stated as “two to the power of (three to the power of (4 to the power of 5)) over e to the nth power”, where n is an integer such that 1 < b < e. Find b, with an […]

IBM Ponder This 07-14 Solved

Credited with solving this puzzle: Ponder This Challenge: 32 pebbles are placed on the six edges of a tetrahedron, as shown in the following figure. Two players are playing a game. Each player, on her turn, can take as many pebbles as she chooses, but a minimum of one pebble must be taken each turn, […]

Balancing a Triangle

I recall I was taking a shower and was thinking about the mathematics of mobiles, something for another post, but during this I got to thinking about how to generalize a formula for finding the point to balance a triangle such that it would hang like this: I sorted most of it out in my […]

IBM Ponder This 06-14 Solved

Credited with solving this puzzle (w/ extra credit!): Ponder This Challenge: Design 25 cubes so that each cube’s six faces display integer numbers in the range 0,1,…,31 such that: On each cube, all the numbers are different Any given two cubes share exactly one common number Please give your answer as 25 lines of six […]

IBM Ponder This 05-14 Solved

Credited with solving this puzzle: Ponder This Challenge: This month’s challenge is from Michael Kleber, based on a problem invented by David Wilson. Every second, a gun shoots a bullet in the same direction at a random constant speed between 0 and 1. The speeds of the bullets are independent uniform random variables. Each bullet […]

IBM Ponder This 04-14 Solved

Credited with solving this puzzle: Ponder This Challenge: Inspired by the viral 2048 game (http://en.wikipedia.org/wiki/2048_%28video_game%29) game, this month’s question is a simpler one-dimensional version of it. Assume that random independent numbers, either 2 or 4 with a 50% chance each, come in from the right side of a bar with N slots. The numbers are […]

IBM Ponder This 03-14 Solved

Credited with solving this puzzle: Ponder This Challenge: N lamps are set in a circle, and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps. Find a possible N which satisfies the following statements: The sum of its digits is less than 10. […]

IBM Ponder This 12-13 Solved

Credited with solving this puzzle: Ponder This Challenge: This month’s challenge is from Michael Brand (thanks!) and a related riddle can be found as the December challenge on his site (“Using your Head is Permitted”, http://www.brand.site.co.il/riddles). Every Christmas, the employees of MegaCorp play a gift-giving lottery game. On the first of December, each of the […]

Microwave Gun

I repurposed an old microwave with the intent to make a microwave gun. When I first had the idea I had an initial delusional vision of it being able to be effective at considerable range, but unfortunately the math just doesn’t hold up. Just the same I studied the design principals of a properly sized […]

Imbroglio Board Game

I am a bit of a board game geek with a relatively sizable collection. I most prefer collaborative games and fancy a good dungeon crawl, so I set out to make a moderator-less collaborative dungeon crawling game. After a bit of tinkering I put some creative together and had a one-off prototype produced. After a […]

IBM Ponder This 11-13 Solved

Credited with solving this puzzle: Ponder This Challenge: A three-dimensional cube has eight vertices, twelve edges, and six faces. Let’s call them 0-D, 1-D, and 2-D faces, respectively. Denote f(d,k) as the number of k-dimensional faces of an d-dimensional hyper cube, so f(3,1)=12. Find three cubes (with different dimensions d1, d2, and d3) such that […]

Optimal Target for Playing 501 in Darts

I joined a local darts league at my bar and a game we frequently played was 501. Part of the goal of 501 is to reduce the value 501 to 0 by subtracting the scores you hit on the dartboard. So if you were at 501 and you hit a 10, a 1 and a […]

Multidimensional Encryption

As more of a study in multidimensional reflections I devised and built the software for an encryption system that obfuscates a message through essentially multidimensional billiards. The process works like this: I define two boundaries, a large outer hypercube within which is a smaller hypercube. Bounded within the large hypercube and containing the smaller hypercube […]

Apothecary Box

I made this as a gift to the master bartender that indoctrinated me into period craft cocktails from ingredients and preparation to history and lore. For all his talents I noticed that he was not well organized with the plethora of interesting and experimental ingredients all around him in mason jars, droppers and such. I […]

IBM Ponder This 12-12 Solved

Credited with solving this puzzle (w/ extra credit!): Ponder This Challenge: 36 people live in a 6×6 grid, and each one of them lives in a separate square of the grid. Each resident’s neighbors are those who live in the squares that have a common edge with that resident’s square. Each resident of the grid […]

Turtle 4D

As a child of the 80s I fondly recall learning to program in Logo. This was a simple language that allowed you to instruct a turtle to draw pictures. You could give it instructions such as move forward 50 spaces, turn 60 degrees, move forward 50 spaces and repeat 4 times more and it would […]

Mandelbrot Fractal Into 4-Space

I worked out a method to extend the Mandelbrot fractal into 4-Space and then built an interactive simulation of it allowing you to fly around in the space and advance/animate the 4th dimension.

IBM Ponder This 11-12 Solved

Credited with solving this puzzle: Ponder This Challenge: Thanks to Adir Pridor for the following challenge: A gardener plants a tree on every integer lattice point, except the origin, inside a circle with a radius of 9801. The trees are cylindrical in shape and all grow together at the same rate. As the trees grow, […]

Generalized Area of a Polygon Solution

There is a fun visual proof for the formula for the area of circle and it can be used to illustrate the essence of calculus. Here is a fun animation: As you can see, you peel away the circumference of a circle and lay it down as a horizontal line. Then you peel away the […]

IBM Ponder This 05-12 Solved

Credited with solving this puzzle: Ponder This Challenge: This month’s challenge is based on a wooden puzzle presented at the tenth Gathering for Gardner conference at Atlanta. There are six sets of jobs. Each set is performed on a different server and each set contains jobs that take 1,2,3,…,10 minutes to run. Obviously, all six […]

IBM Ponder This 04-12 Solved

Credited with solving this puzzle, this was a fun one: Ponder This Challenge: This month’s challenge is based on a model suggested by Harry Buhrman, Serge Fehr, Christian Schaffner, and Florian Speelman, who described the garden-hose model in their paper “The Garden-Hose Game: A New Model of Computation, and Application to Position-Based Quantum Cryptography” ( […]

Math Music

I don’t recall what I was puzzling over at the time but it was some set of formulas that I was struggling to understand the relationship between. In my frustration I started to wonder if I were to be able to “hear” the equations would their relationship be easier to grasp, like harmony. Our brains […]

IBM Ponder This 03-12 Solved

Credited with solving this puzzle: Ponder This Challenge: Arrange the numbers 1, 2, 3,…, 63 on the nodes of a balanced binary tree of height 6 such that each distance 1, 2, 3,…, 62 is realized on an edge; i.e., it is the difference of two vertices which are connected with an edge. Please supply […]

ElectroResistivity 3D Scanner

I experimented with the notion of being able to generate 3d scans of objects based on their electrical resistance. This came out of the work I did on my water keyboard that was controlled by locating your hand in a trough of water. Aside from being able to simply create a novel 3d imaging system […]

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