I am an electrical engineer by training who is currently working as a hardware development director for a telecommunications company. Over the years, I have become more and more impressed with the ability of relatively small amounts of mathematics to help shed light on significant technical problems.

There are many types of mathematical analyses. They range from very detailed modeling exercises that are impressive, but are really for specialists, to “Fermi problems” that are exercises in gross approximation. This blog will steer a middle course and will look at the simple mathematics that crops up in the daily life of a working engineer.

1. newton says:

cool stufff! keep posting!

2. Alias says:

Where was your photo taken? It reminds me of the Muskokas in Northern Ontario. You keep writing and I’ll keep reading.

• mathscinotes says:

You are pretty close! The photo is actually from my cabin in far northern Minnesota, which is not far from the border with Ontario. This is what I see in mornings when when I look out from my door. Of course, it is all frozen right now. But this photo reminds me that spring will come and I will soon be there again.

3. XXXXXX says:

Hello -
Congratulations on this great blog – I especially love your tagline “I stumbled upon some math today”. As part of my work in XXXXX, I am also helping to manage the XXXXX blog and was wondering, if you would be available for an interview? I would like to introduce your blog to our readers and I am sure they’d love to learn more about you. If interested, please email me at XXXXX.
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• mathscinotes says:

I will send you my contact information by email.

4. Barry says:

“You are also handed two boxes: one box contains an uncharged 1 F capacitor and the other contains 1 million 1 µF capacitors. You can connect the capacitors from one box one at a time across the charged capacitor. Your job is to determine which box will allow you to discharge the voltage on the charged capacitor the most?”

What charged capacitor? Did I miss something?
rgds
Barryfish

• mathscinotes says:

I was responding to a comment about my first blog post. I get quite a few questions on the electrical engineering puzzles that I post. People always want solutions to variants of the original puzzle.

5. Hello, Great blog about a great subject; mathematical modeling. I was attracted to your blog because of the rafters problem and the article on math in baking. I have also looked at baking, architecture, construction, knots, and baking mathematically.
The thing I struggled with the most was what to call the concept of math in everyday life; Math Encounters is really good.

I wish I had time to develop all my ideas, but I have chosen to focus on baking. You can check out my website if you want to see more.

• mathscinotes says:

I like your blog. Your focus on how to clearly present technical material is near and dear to my heart. I have really struggled with the poor quality of technical presentations in general. As far as baking, I am a neophyte baker and I have a lot to learn. When I was a boy, I loved to watch my mother’s dough turn into bread in the oven. Baking is still magic to me.

The only problem with blogging about stuff is time. I really do have a large amount of material to write about, but there just isn’t time to develop it all.

6. Hello,
I discovered your blog a few weeks ago, as I was searching for some material on a paper that I am doing in school. The information on your ballistics, ogives and bullet shapes really helped me out and I will definitely urge my colleagues to refer to it. Firstly, thank you for that! I would like to ask you how to arrive at equation 3 mentioned on that page. I suppose that it must be rather obvious to the trained eye, but I fail to see it. I understand that the subtraction of the (rho.sin(alpha)) was done to effectively ‘pull down’ the ogive shape to give the volume of revolution (around x axis) formula. However, how do you arrive at the first part of the equation?

Well, questions aside, I must say that these past few weeks, I have really taken a liking to your blog. I love the way you quantify everyday problems, or as you call them, ‘Fermi Problems’. I am a big fan of ‘Gedanken experiments’, especially in Physics and this is thoroughly exciting!

Keep going!

Thank you,

• mathscinotes says:

Hi Abhranil,

Thanks you for the nice comments. I am sorry that I was not very clear on the derivation of Equation 3 (now Equation 5 after fixing an equation numbering error). I am frequently hurrying to get these blog posts out because I have more math to get done!

The equation is a bit unusual because of how I setup my coordinate system. I made the x value of point A the Origin in Figure 7. This means that point A has an x value of 0 and x increases to the right. This makes my integration simpler. The equation for a circle is given normally given by the following equation.

$y(x)=\sqrt{{{\rho }^{2}}-{{x}^{2}}}$

With the origin at the x value of point A, you can think of the circle as having been translated to the right of the new origin by $\rho \cdot \cos \left( \alpha \right)$. This means that the equation of the circle in my new coordinate system $\left( {x}',{y}' \right)$ is ${y}'(x)=\sqrt{{{\rho }^{2}}-{{\left( x-\rho \cdot \cos \left( \alpha \right) \right)}^{2}}}$. In figure 7, I actually define y as the height of the ogive, so I need to subtract off $\rho \cdot \sin \left( \alpha \right)$. This gives me my final result $y(x)=\sqrt{{{\rho }^{2}}-{{\left( x-\rho \cdot \cos \left( \alpha \right) \right)}^{2}}}-\rho \cdot \sin \left( \alpha \right)$.

I hope this helps. If you have any further questions, ask again.

mathscinotes

• Hi,
Thank you for the explanation! Yes, this definitely helps. So, as I understand it, you formulated an equation for the ogive, so in other words, how the radius, x, changes with a change in ogive height, y. Right?

Abhranil

• mathscinotes says:

The radius does not change, but x and y do. Since the ogive is a segment of a circle, I use the standard equation for a circle ${{x}^{2}}+{{y}^{2}}={{\rho }^{2}}$ and I limit the range of x to that required for the ogive. I know it seems confusing, but focus on how the equation for a circle works. Once you understand that, look at the range of the x that we are interested in and how you would generate that range of x values. Given the equation of a circle and the range of x values, you can compute the range of y values. These are the values I use in my integral.

mathscinotes

7. Yes, I understand now. Thank you again.

Keep it coming!
Abhranil

8. Don Pridgen says:

There were several comments on the rafter math post recently but the reply link on my end seems to be broken. Anyway, see if this helps clear things up;
(wS^2/2)/(S)(Rise/Run)
becomes
(wS/2)/(R/R)
becomes
.5wS/(R/R)

• mathscinotes says:

Hi Don,

Thanks for the note. I pulled the post from the web while I am working with a couple of folks on cleaning it up. I hope to put it back up in a fews days.

mathscinotes

9. Don Pridgen says:

Great, I appreciate your digging deeper. Shoot me your email if you want scans of FBD’s and calcs from a couple of other folks… being a carpenter, it takes at least 2 engineers to pull me out of the ditch. Also click on my website and go down to the rafter thrust and raised tie thrust calcs. The link to my calc on your original post is broken but feel free to link to this one, my site got hacked.

• mathscinotes says:

Hi Don,

I had a number of comments that centered on my FBD, which was incorrect. I have fixed it. Turns out my final result remained unchanged, but I wanted to review everything very carefully.

mathscinotes

10. Robert says:

Hi mathscinotes,
i was realy interrestet about your article “Learning How Electronic Parts Work” and want use it for a paper for the university. So can you give me your real name for the reference list?

regards

• mathscinotes says:

Sure. I will send a private email.

mathscinotes

11. Michael Dunn says:

Enjoying your blog! I run a blog/community site – scopejunction.com. If you think you might like to write the occasional blog there, please get in touch.

12. hammerdallas says:

Love you blog…. I do have a question for you regarding gravitational fields…by the way…I hate math…until I started reading this blog…

13. hammerdallas says:

Love your blog !!! I have a question for you regarding gravitational fields.
Thanks, D

• mathscinotes says:

Thank you for the nice comment. As far as gravitational fields, I am afraid I am not a physicist. However, if you want to ask — go ahead!

mathscinotes

14. Michael Dunn says:

Hi Mark. I’d still love to discuss blogging a bit at Scope Junction. Hope to hear from you.

• mathscinotes says:

Sorry for taking so long. I am just getting around to answering all my blog email this morning. I am interested in blogging at Scope Junction. I will send you a private note to discuss it.

Mathscinotes

15. Travis says:

I love your blog post, “An Analog Circuit Design Review”. I love your insights, and want more of them. Thanks so much for your time!

• mathscinotes says:

Glad you liked the post. I enjoy sharing my love of electrical circuits with others.

Mathscinotes

16. Victor Verma says:

I can i get in touch with you i have questions.

17. Just stumbled upon your blog. Fantastic! I also am an EE and have a great interest in mathematics. I used to derive MacLaurin series for different functions for grins. I minored in math when I got my MEE and was fascinated by numerical analysis. Anyway…keep it up, I’m glad to see I’m not the only one!

• mathscinotes says:

Numerical analysis has become an important part of my working career. In fact, my very first job was working on modifying Spice for NMOS circuit simulations. It was there that I learned many of the tricks that I still use today.

Mathscinotes

18. Richard Harris says:

Assume you are in the deep backwoods, your electronic gear goes down, but you must solve a simple equation such as X = 111.25^0.514, which would normally be solved as 0.514 * log 111.25; is there a way to approximate a log if you have no electronic gear or log book?

• mathscinotes says:

Hmmm … I guess I would do something simple like the following.

19. Richard Harris says:

Thank you very much; well done. Great blog

20. Richard Harris says:

Using ogive or logistic curves in future annual volume estimates of production from a limited, depleting resource: Cumulative production of units from the resource beginning in 2005 through 2012 by years is 15, 30, 150, 700, 1200, 2000, 3000, and 4000 units. At lunch, your boss ruins the meal by asking for an estimate or forecast of what the resource will produce each year in the future until it is depleted. He wants it by his 3:00 PM coffee break. Plotting the known annual historical data on log-log suggests it is in the form of an ogive curve. Is there a quick Fermi way using ogive/logistic equations to estimate the future unit volumes year-by-year until the curve becomes asymptotic to the production axis, which would constitute depletion and then equal the resources original recoverable volume of units?

THANKS!

• mathscinotes says:

Before I look at this question, I have to ask where your two questions have come from?

Mathscinotes

21. I am a retired geological consultant living outside Calgary in western Canada. The two questions are just things I wonder about. The questions and any answers you might provide are for my own personal use and interest. Thanks!

• mathscinotes says:

Greetings from one of your southern neighbors! I don’t get to say that to very many people.

I had to ask about the question source because I get so many homework problems sent my way. It has become so bad that I actually had one twelve-year old boy ask that I write a little bit more like a kid so my work could be copied more easily.

I will try to take a look at the problem this weekend. I have department budgeting today.

mathscinotes

22. Thanks and there is no hurry from my end. Being retired has given me time to think about stuff but seemed always too busy to pursue.
I know what you mean by ‘homework’ because that does occur on other sites like, for example, Dr. Math!

I spent about 50 years working on jobs in more than 80 countries – in oil, gas, minerals, and gemstones – so I am enjoying kicking back, enjoying a pretty mild winter, and looking at the Rockies out the west windows.

Have a nice weekend!

23. coasttal says:

Just came across your blog and have enjoyed reading almost every post. I am a mechanical engineer, BSMS/ME PE, and got BS in 77. Unfortunately, I have never had the need to use all the math that you use since college. Now that I am retired, I really want to start relearning so much of the math. Again, thank you so much for all these great posts. John

• mathscinotes says:

I started writing down my math work when I started to provide help to students. They kept telling me that they had never heard of anyone who uses math as part of their job. That was how this blog was born.

Mathscinotes