Author Archives: mathscinotes

Letter Folding for Envelopes

Posted on 18-November-2015 by mathscinotes

I still occasionally write paper letters. In fact, I had some letters to write the other day, and I realized that was doing a bit of math when I folded the letters for placement into standard business envelopes that was worth discussing here. Figure 1 shows the business envelope that I normally use. Continue reading →

Posted in General Mathematics, Origami | 3 Comments

How I Orient My Electrical Outlets

Posted on 16-November-2015 by mathscinotes

For years, I have mounted most my electrical outlets upside down (see Figure 1). Recently, I have started to see more folks orienting their outlets this way. I see that Finehomebuilding Magazine and the Journal of Light Construction (JLC Field Guide) recommend this approach as well. However, it is not required by the National Electrical Code. Continue reading →

Posted in Construction | 2 Comments

My Cub Scout Training Solves Test Equipment Corrosion Problem

Posted on 14-November-2015 by mathscinotes

We have recently experienced some laboratory failures during humidity testing that were due to corroded connectors (Figure 1). The connectors had corroded after they become wet from condensation that accumulated on the cables and rolled down to the lowest point on the cable – where the connectors were. Continue reading →

Posted in Electronics | 1 Comment

Venus-Like Exoplanet In the Neighborhood

Posted on 13-November-2015 by mathscinotes

I have been reading a number of articles that are reporting on a Venus-like planet (GJ 1132b) recently discovered in a nearby star system (Gliese 1132, 12.0 parsecs away). I like to work a bit with the numbers reported in these articles to determine if I actually understand what is being reported. I have to admit that I also like to imagine the day when astronomers are studying Earth-like planets around other stars. I definitely see that day coming. Discoveries like GJ1132b are particularly interesting because astronomers for a long time did not think red dwarf stars were promising for Earth-like planets. Continue reading →

Posted in Astronomy | 1 Comment

Screwed Wood Joint That is Totally Concealed

Posted on 12-November-2015 by mathscinotes

This is the first woodworking tool that I have seen that uses a two-part electric motor. I have encountered this type of two-part electric motor before in situations where some mechanical object needed to be rotated while contained in a completely sealed environment. In this case, the electric motor's armature has a screw thread that pulls the joint tight. See this web page for more details. I certainly can see several applications for this type of connection. Continue reading →

Posted in Construction | 2 Comments

WW2 Reticles

Posted on 5-November-2015 by mathscinotes

I have watched a lot of old WW2 combat footage, and I have noticed that many of the machine guns and fighter planes had similar reticles. A reticle is a fine-grid of lines used in conjunction with an eyepiece to assist in taking measurements or with accurately pointing an instrument. Figure 1 shows a reticle similar to what I have seen in numerous combat scenes. Continue reading →

Posted in Ballistics, Military History | Comments Off on WW2 Reticles

Gift Wrapping Math

Posted on 3-November-2015 by mathscinotes

My sister works as an event planner/wedding planner. She wrote me an email today with the following gift wrapping question.

I need to wrap 375 boxes. 16x14x6. The wrapping paper is 30 inches wide. I say I need about 1700 feet. People are telling me I only need half that. Continue reading →

Posted in Geometry, Paper Machines | 21 Comments

Index/Instrument Error Correction in Sextant Measurements

Posted on 31-October-2015 by mathscinotes

Sextants make measurements that are subject to systematic errors – all instruments are subject to systematic errors. Alas, much of my career has been spent on calibrating out systematic instrument errors. Even with all my efforts, residual systematic errors remain. Continue reading →

Posted in Naval History, Navigation | 2 Comments

Refraction Error Correction in Sextant Measurements

Posted on 27-October-2015 by mathscinotes

Refraction is probably the most difficult to understand of all the altitude observation corrections. It is also the most difficult to estimate accurately because it depends so strongly on atmospheric conditions, particularly the rate of temperature variation with altitude (see lapse rate). I will derive in this post a commonly used expression for the refraction correction required for a celestial object with an altitude greater than or equal to 15°. The accuracy of this expression degrades significantly for objects below 15°. Continue reading →

Posted in Astronomy, Naval History, Navigation | 3 Comments

Correcting for Sextant Parallax Error

Posted on 24-October-2015 by mathscinotes

Navigators use the altitudes of solar system objects to assist them with determining their positions. The most commonly used solar system objects are the Sun, Moon, Venus, and Mars. There is a small error caused by the fact that navigators are making their sextant measurements from the surface of the ocean and not from the center of the Earth, which is the reference point used by nautical almanacs. Parallax has no practical significance when measuring the positions of stars because they are so far away relative to the radius of the Earth. Continue reading →

Posted in Astronomy, Naval History, Navigation | 1 Comment