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Category Archives: General Mathematics
This post will cover how to measure a countersink angle using gage balls. Figure 1 shows how a countersink is normally specified on an engineering drawing. I frequently use countersinks in my wood and metal working hobbies. In addition, using gage balls to measure the countersink angle provides a good example of how to apply basic geometry concepts to a practical problem. I use this example in my role as a volunteer adult math tutor at our local library. Continue reading
I am doing some testing at an Electromagnetic Compatibility (EMC) facility this week. Part of the test specification requires that we inject audio frequency interference on the power supply lines at discrete frequencies that range from 10Hz to 100+KHz, with 30 frequencies selected from each decade of frequencies (e.g. 10 Hz to 100 Hz, 100 Hz to 1 kHz, etc.). Figure 1 shows a specification similar to the one I am performing. My test facility that has chosen the discrete frequencies to be evenly spaced on a logarithmic axis. I started to wonder how the frequencies were selected – let's work through it. Continue reading
I was reading an article about HVAC (Heating, Ventilation, and Air Conditioning) calculations in the Journal of Light Construction that had a quote I found interesting. It said that
… 17 extra occupants added more than a half ton of cooling load. Continue reading
Back in 2011, I wrote a blog post that goes into the details on how the Blood Alcohol Content (BAC) versus drinks/time/gender are computed (Figure 1). These charts tell people how much they can drink and still stay under the BAC limits for driving under the influence. These charts are for a typical drinker and the actual BAC value will vary by person. Continue reading
I recently was asked to provide a recommendation on how to schedule the operating time for three different machines that were producing three different products. This is not a made up problem, but reflects a real production situation. My solution uses Excel's Solver and its linear programming-based optimization routine to find an optimal machine scheduling plan. The solution I provided has proven to be useful to the folks who asked for it, and I thought it was worth sharing my solution here. Continue reading
I was reading an article on National Geographic when I spotted an interesting factoid about the impact of Toilet Paper (TP) world-wide tree consumption.
Toilet paper wipes out 27,000 trees a day.
Like many factoids, I doubt there is a way to actually measure this number – it can only be estimated. Thus, it is a prime candidate for a Fermi solution. Continue reading
Ronald Reagan (Figure 1) was our oldest president at the time of inauguration – 69 years 349 days old. The 2016 US presidential election is giving us a choice of two candidates that will be relatively old at inauguration: Donald Trump (70 years, 220 days), and Hilary Clinton (69 years, 86 days). Since US presidents often serve 2 terms, it is conceivable they we may have a 77- to 78-year old president in 2024. This fact makes me curious as to what is the likelihood that a 70 year-old's natural life will be long enough for them to serve one or two terms. Continue reading
The front-end of the baby boomers began to turn 65 in 2011 and they will continue to turn 65 until 2029. I started to wonder how many boomers are turning 65 every day? The Social Security Administration estimates that 10,000 Americans are turning 65 every day (source). As I thought about, I should be able to estimate the number of people that are turning 65 every day by examining graphs of the US population and birth rate (Figure 1). It is a nice Fermi problem and the subject of this post. Continue reading
A reader mentioned to me that the Wikipedia has an good article on stellar luminosity versus stellar mass– the article is a good one. I thought I would compare the empirical relationship shown in the Wikipedia with a couple of different data sets that I found on the web. I was motivated to perform this analysis because: (1) I have been doing some reading on exoplanets, and luminosity is important when it comes to exoplanet temperature; and (2) I am presenting a seminar on Mathcad to our engineering staff, and this application provides me a nice demonstration on how to compute nonlinear piecewise functions. Continue reading
I recently read a post on Quora about the day that the arc of the Golden Gate Bridge was flattened by the load of a large number of people – some reports stated that as many as 300K people were present at the event. The bridge was opened opened to this huge throng of people as part of its golden anniversary. This was the first time I had heard of this event. Continue reading