[From the website of Dr. Donald Simanek—see further down.] Browsing Martin Gardner’s books I stumbled on this diabolical puzzle. Gardner calls it “an incredible problem”. He traces it back too Samuel I. Jones’ Mathematical Nuts, 1932, p. 86. It is seen on the web in various forms, often ambiguous in wording, along with endless discussions often leading nowhere. I have tried to restate it to remove ambiguity (which isn’t easy). A hole is drilled completely through a sphere, directly through, and centered on, the sphere’s center. The hole in the sphere is a cylinder of length 6 inches. What is the volume of the remainder of the sphere (not including the material drilled out). You’d think there’s not enough information given. But there is. The solution does not require calculus. Gardner gives an insightful solution that requires only two sentences, including just one equation. Visit From mathworld.wolfram.com for more info. The answer is provided by Doctor Donald Simanek, Professor of Physics Emeritus at Lockhaven University. Visit Donald Simanek’s page at Lockhaven.edu for more brain-bending physics puzzles! Now that’s an interesting answer! Keep scrolling down… Wanna see a video answer to the brainteaser? This video was created by Tom McNaney Jr., Generalist Applications Engineer, Fellow at PTC (the company that I currently work for). Here is his detailed approach to the brainteaser using PTC’s flagship CAD program Creo Parametric! For the Holey Sphere challenge, Creo Parametric says the volume is 113.097 in^3. Interestingly, the volume remains constant regardless of the sphere Radius. Cool. I have no idea what the mathematical formula is, but probably 4/3*Pi*(something)^3. Who needs advanced math when they have Creo or Mathcad?
In the battle of the Virtual Assistants (VA), it seems like everything else, there are too many choices. Alexa, SIRI, Google Assistant, and Cortana are practically household names at this point. While each has their particular set of benefits, no one AI (i.e. Artificial Intelligence, because that’s what we’re really talking about here) can fulfill every request made of it. With next year’s pending launch of my company’s (PTC) flagship PLM platform, Windchill (integrated with Microsoft Azure’s cloud solution)—facilitating manufacturers’ efforts to rollout NPIs (i.e. new product introductions)—I thought it would be interesting to explore some aspects of where VAs/AIs are these days in a practical sense from home to business. I’d venture to guess that most homes feature more than one VA. The Digtal Batman household runs both SIRI on our iPhones/iPod and AppleTV 4K, and we run an Echo Dot featuring Alexa. It’s interesting to note the significant differences for our needs. For example: Alexa comes in handy when playing music from Amazon Music Unlimited and radio broadcasts over IHeartRadio. Whereas, SIRI dials our phone numbers, reads our texts, provides us with navigation, and helps us search/navigate our Apple TV 4K streaming device. Conversely, like most PTC employees running Windows 10 on their laptops, Cortana can easily be enabled. But I think it would be a little weird if everyone in the open seating at Seaport HQ started talking into their computers all at once! Though I haven’t used “Okay Google” in a while, it does come in handy for general searches and navigating the plethora of online/cloud‐based productivity, calendar, and meeting tools available—especially if you’re using Google Chrome. And what’s really interesting is now each of these separate VA platforms are starting to work together: organizing calendars across different devices (like cell phones), providing email from multiple...