🎓 Doc Freemo 🇳🇱 @freemo@qoto.org

Equations that changed the world..

#math #mathematics #maths

I wanted to kick off the #QotoJournal hashtag by sharing a free open-source book I started writing some time ago...

I started writing a book in an attempt to help explain how to do circuit analysis by hand. Originally it was going to include both time-domain analysis as well as frequency-domain analysis. The book is incomplete and I never got to cover the time-domain but has several complete examples showing frequency-domain analysis on many common circuits. I’ve gotten some compliments over the years, particularly from HAM radio operators, on how useful the book has been to them. I’d like to share here what I have so far in case anyone might find it useful.

As a side note if anyone would like to revive the project and work with me on expanding and completing the book it would be most welcome. Please feel free to contact me. In the meantime here is the compiled book in its current form. I don’t currently have the latex source code published anywhere but if there is any interest I will happily publish it and open-source it on github.

Here is a direct link to the book: https://discourse.qoto.org/uploads/short-url/tFY6qFBUnmFFVdnBErQ8mJdZuBF.pdf

You can also view the book as a feed in my blog here: http://jeffreyfreeman.me/frequency-domain-circuit-analysis-tutorial/

If you wish to comment or discuss it there is a discourse post for it here: https://discourse.qoto.org/t/frequency-domain-circuit-analysis-tutorial/41

#ElectricalEngineering #Electronics #Science #HamRadio #Radio #RF #math #mathematics

As it turns out, cats arent very good at math.

#math #science #joke #meme #funny #humor #cat #cats

If I did a write up explaining the difference between complex number representation of vectors vs Matrix/Linear algebra representations would anyone be interested in reading that?

I feel it would be useful to explain why and how multiplication is different between the two and why division on matrix vectors is forbidden but allowed in complex form and the repercussions of that.

Might also be useful to go into some explanation as to how to intuitively know when to use one or the other (something even i struggle with from time to time).

#science #math #maths #mathematics

Never forget your coordinate fields and unit circle. Probably one of the most important things to know as an engineer.

#science #math #maths #mathematics #euler #vectors #LinearAlgebra

I feel like I should add this to my book on Frequency-domain analysis. I've been wanting to work with Quaternions for a while now: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8378813

#math #mathematics #maths

A little diagram ive been tinkering with to show the relationship between the different types of Real Numbers.

#math #maths #mathematics #numbers

One of my favorite math problems that is easy to solve with just algebra:

Prove that 8 is the only perfect cube to follow a prime number.

If you don't know what a perfect cube is, that is simple, it is any integer raised to the power of 3. Since \(8 = 2^3\) it is a perfect cube, and it follows the number 7, which is prime. 8 is the only number that fits those conditions... prove it.

NOTE: I will give the answer as a reply. If anyone else wants to provide an answer please make sure you use a content warning.

#maths #math #mathematics #riddle #puzzle #riddles #puzzles

Oh no!

#meme #joke #humor #humour #jokes #funnt #math #mathematics

A really cool programmatic ( #Python ) solution to the 100 pots problem by @Absinthe was posted here, worth checking out:

https://discourse.qoto.org/t/the-100-pots-logic-puzzle/63

#puzzle #riddle #riddles #puzzles #math #mathematics #maths

I posted the 100 pots problem I had shared here earlier to our discourse. Even though I already gave the answer I thought I'd share it here in case anyone has anything they would like to share or discuss about the topic:

https://discourse.qoto.org/t/the-100-pots-logic-puzzle/63

#puzzle #riddle #riddles #puzzles #math #mathematics #maths

In case anyone is interested here is a link to a very difficult logic puzzle that anyone without math skills can solve (it is easy to understand though). I also include the answer with a CW for those who want to skip right to the answer.

Question: https://qoto.org/@freemo/102671555468240192

Answer: https://qoto.org/@freemo/102766450134868659

#riddle #math #maths #mathematics #puzzle #logic #logicpuzzle #science #programming #computerscience

A little tutorial I wrote explaining the Verhurst Equation (restricted logarithmic growth) as well as my own addition on this idea, modeling an artificial injection.

The equation is traditionally used to model the growth of a population (such as animals or bacteria) over time. In this write I actually use it to model advertisement and idea proliferation in a society.

https://discourse.qoto.org/t/restricted-logarithmic-growth-with-injection/54

#Mathematics #Math #Biology #DataScience #Modeling #DataModeling #Science

A little walkthrough/tutorial I wrote explaining Bayes Theorem, Conditional Probabilities, and Unconditional Probabilities.

https://discourse.qoto.org/t/conditional-probabilities-and-bayes-theorem/46

#Math #Mathematics #Maths #Science #Discourse #MachineLearning #AI #ArtificialIntelligence

Now that the #QOTO Discourse server is fully working, including the math rendering, I can start adding some content to it.

For my first post I wanted to share a tutorial I wrote on how to do frequency-domain nodal analysis on electronic circuits.

Here is the link:

https://discourse.qoto.org/t/nodal-analysis-tutorial/36

#RF #EE #Electronics #Engineering #Science #ElectricalEngineering #RFEngineering #HAM #hamradio #Mathemathics #Math #Maths

Another math joke to show off #QOTO 's math rendering. Feel free to share your own jokes!

Remember Sex is fun, its the law!

Let \(f(a) = \sqrt[n]{e^x}\)

\[
\lim_{t\rightarrow\infty} f(a) - \frac{i}{f(t)} = \frac{d}{dx} f(u) \\
\lim_{t\rightarrow\infty} f(a) - \frac{i}{\infty} = \frac{d}{dx} f(u) \\
\lim_{t\rightarrow\infty} f(a) - 0 = \frac{d}{dx} f(u)
\]

Then

\[
\sqrt[n]{e^x} = \frac{d}{dx} f(u) \\
(\sqrt[n]{e^x})^n = \frac{d}{dx} f(u)^n \\
e^x = \frac{d}{dx} f(u)^n \\
\int e^x = f(u)^n
\]

#Math #Mathematics #Maths #Joke #Jokes #Humor Humour #meme #MathJax

Some people asked me to share a lvery difficult yet simple logic puzzle that has stumped my friends. It is also my favorite interview question.

First off some background. The problem is not a trick question, as much as it may seem like one. There is no play on words, no hidden exception. Everything in this problem is exactly how it is presented and the answer doesn't rely on any slight of hand. Take this puzzle at face value.

Also **ALL ANSWERS NEED CONTENT WARNINGS** I do not want you spoiling it for others. This goes for questions and hints too.

Now on to the puzzle:

There is a room with 100 jars with lids on them all in a row. There is also a stack of papers, 100 papers each labeled 1 to 100. The papers are shuffled and one paper placed into each pot randomly.

You and your assistant are in an a joining room. Your assistant is allowed to enter the room, look in all 100 pots, and if they wish they can pick any 2 pots and switch the paper in them. They can only do this one time, they do not have to do this they can choose to also do nothing. At this point they leave the room, without talking to you.

Next, someone tells you a random number from 1 to 100. Your goal is to enter the room and open a pot tht has that number in it. You are allowed to open, at most, 50 of the pots.

Whatever process you use to open those pots must **guarantee** that by the time you open the 50th pot that the number you were given will be found. Obviously your assistant didn't know what the number is at any point.

What rules do you give your assistant, and what rules do you follow, to ensure you are successful?

@MutoShack@functional.cafe @inditoot #puzzle #riddle #riddles #puzzles #math #mathematics #maths

Russell's Paradox:

In a group of people who are shaved there is a single barber. The barber shaves all the people who do not shave themselves. Who shaves the barber?

It can't be the barber himself, because he only shaves people who do not shave themself, thus he can not shave himself. It also can't be anyone else as the barber shaves ALL people who do not shave themselves, so no one else could possibly shave another person.

Therefore it is impossible for all three properties to define a set at the same time:
* everyone is shaved
* The barber shaves people who don't shave themself
* The barber is the only person who can shave other people

This creates two sets one of the people who shave themselves and one shaved by the barber. Since the barber is not allowed to shave himself the sets must be disjoint, but since the barber must be shaved they must also intersect. Since both are not possible there is a contradiction and thus the paradox.

What this means is we can not say any arbitrary set of properties can be used to define a set, as some may give rise to a contradiction.

A more generalized example of the paradox is the idea of a set that contains "all possible sets that do not contain themselves as a set". This is called the universal set. So for example if we had set A defined as the numbers 1, 2 and 3 or A = {1,2,3}, however if set A was A = {A, 1, 2, 3} then it would be excluded. The problem arises when you consider if the universal set includes itself as an element by this definition. If it doesnt contain itself as an element then it qualifies for the rules of inclusion, and thus is included, but by including it it now DOES contain itself as an element thus can not be included. Reaching a paradox once again where the definition of the set as we defined it can not be satisfied. Another example that a set can not simply be defined by an arbitrary collection of properties. Some combinations of properties are invalid while others are not.

#math #maths #mathematics #sets #settheory

Why do sunflowers use the Golden Ratio to define their seed arrangement? Good explanation:

https://youtu.be/sj8Sg8qnjOg

#math #mathematics @science #STEM

#math #humor #joke #jokes #mathematics