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 | Comments Off on Negative times a Negative is a Positive

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 | Comments Off on Rate of Technological Progress

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 | Comments Off on Prime Number Magnitudes

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 | Comments Off on Temperature Sensing and a Current Ratio of 17

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 | Comments Off on Reasonable Budget Plan for a Young Person

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 | Comments Off on Computing Percent Differences

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 | Comments Off on Earth With All the Ice Melted

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 | 2 Comments