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Author Archives: mathscinotes
Negative times a Negative is a Positive
On my team, I work hard to ensure that we have a non-threatening environment for questions – any questions. In fact, I often ask very basic questions in meetings so that I can make sure that I understand all the nuances of a situation. You would be amazed how often I learn things from asking questions so basic that you would think asking them would not be necessary. Continue reading
Posted in General Mathematics
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CML Termination Design
An engineer stopped by today and had forgotten how to use Mathcad to solve a pair of circuit equations to determine termination resistor values. I stepped in and helped. As I looked at the problem, I thought it might be useful to cover on this blog as a tool demonstration. Continue reading
Posted in Electronics
1 Comment
Rate of Technological Progress
I saw the following LED history graphic in Machine Design magazine today. I like the graphic because it shows how technological changes often occurs – I only wish there had been some additional space for the quantum mechanical developments of the 1920s. Continue reading
Posted in History of Science and Technology
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Prime Number Magnitudes
I am responsible for some of the authentication features in our products and these features use prime numbers. People often have basic questions on prime numbers, such as:
What happens if I choose the same prime number as someone else?
Are there enough prime numbers? Continue reading
Posted in General Mathematics, software
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Temperature Sensing and a Current Ratio of 17
One of the most common diagnostic functions requested for an electronic system is to measure its own temperature. We want to know the hardware temperature when a problem occurs because many system characteristics are affected by temperature and temperature may give us a clue to the problem's root cause. Continue reading
Posted in Electronics
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Reasonable Budget Plan for a Young Person
In my role as annoying father, I regularly talk to my sons about financial matters and this post summaries a recent discussion on budgeting. One reasonable goal for a young person's budget is called the "60% solution". Continue reading
Posted in Financial
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Computing Percent Differences
I have recently been computing a lot of percentage differences – mainly in variance calculations. I have been using the formula that I was taught in 7th grade and recently discovered that this formula fails miserably when dealing with negative quantities – I had never considered what happens when the O variable is negative. Continue reading
Posted in Financial
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Lighthouse Visual Ranges
Yesterday, I received a question from a reader who was puzzled by a web page written by a flat earther that presented a seemingly rational argument in favor of the flat earth position. In a nutshell, the flat earther's argument says that to see a lighthouse at long distance on spherical Earth would mean that you would have to be able to see around the horizon. Therefore, the Earth must be flat. I may be mischaracterizing their argument, so you may want to visit web sites that go into the details of the flat earth rationale. Of course, I argue that refraction can literally allow you to see "around" the horizon. Continue reading
Posted in optics
17 Comments
Earth With All the Ice Melted
Last night, one of my sons and I discussed using R to process geographic data. Related to this topic, we also discussed was how to visualize the impact of global sea level rise on certain countries. The video below does a good job showing what would happen if all the ice on Earth melted, which would raise sea level by ~70 meters. Continue reading
Posted in General Science
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Return Loss of a Glass-Air Interface
I received an email today about a deployment issue that involved the reflection of light from unterminated connectors. When light travels down a fiber and encounters a change in the index of refraction, part of the energy will reflect back toward the transmitter because of a phenomenon called Fresnel reflection, which I define below (source). Continue reading
Posted in Fiber Optics
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