Cool and Fun Formulas

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Do you have a favorite formula? I like n(n-1)/2. I don't know if it has a name but I learned this when studying for my Network+, if you have a number of nodes and want to create a mesh network, you can use this formula to determine the number of possible connections: Complete Graph - Wikipedia

I also like permutations, like how many different combinations of Red, Green and Blue can you have? You can sit there and go RGB, RBG, BRG, etc, or you can use a formula: Combinations and Permutations Calculator

I'm not very good at math or knowledgeable of math but I still like this stuff, I like the concept of just being able to plug values into a formula to figure to find answers to these kinds of questions, I often wonder if there is a formula to figure out certain things that pop in my head and will spend a lot of time trying to phrase the question correctly in Google to find what I'm looking for. I hated math in school but now that I'm not obligated to learn it to earn a passing grade suddenly I'm less intimidated and more curious about it these days, hopefully it will make me better at puzzle solving and gaming, or coding when it's relevant.

I know it's kind of dumb, but I think vacuously true mathematical statements are very interesting.

You know... things like 0 = [(1-1) - (1-1)]/[(1-1) -(1-1)]

The part I find interesting is the potential of complexity in the mathematical process without requiring value or meaningful computation.

I used to have metaphysical thoughts about it, like conceiving of cosmic totality as intrinsically without substantial being... merely an execution of expressive potential without requiring any more than particular arrangements of logical semantics. "Everything from nothing" and all that.

I like thinking everything in existence is vacuously true, and that you are "unzipping the compressed, dynamic potential expression" of reality when you perceive it with your sense organ. It's actually a rather old idea in philosophy but is more interesting with modern science being able to give us data on how cognition/learning/differentiation works and increasing insight on "what are the fundamental material substances/processes of the universe?"

I have always found Maxwell's Equations particularly intriguing...

Not exactly a "formula" (though I suppose someone could find a way to express it as an equation). This is an interesting and fun mathematical conundrum.

In the medical world 95% of the time we look at arterial blood pressures and calculate the mean, in only rare cases are systolic and diastolic values themselves of any interest. This is because the MAP shows how well the organs are perfused at a particular point in time. Every 30 second increment the patient is in a state of hypoperfusion leads to a measurable increase in all cause mortality.

In patients who don't have an arterial line or where the NIBP doesn't calculate MAP for you the formula you do in your head is:

((Diastolic x 2) + systolic) then divide by 3.

Modern medical equipment means that I don't do this calculation much anymore as most equipment also shows a MAP in brackets after the SBP and DBP.

MAPs under 60 warrant urgent attention and review of if anything is needed (pressors, inotropes or filling).
MAPs of around 50 and certainly anything under ALWAYS require immediate attention and may be seen to be sentinel of a patient who is in immediate risk of crashing.

Adequate perfusion in critically ill people saves lives.

Let me explain the n(n-1)/2 : )

When you want to sum up a sequence of numbers like {1, 2, 3, 4, 5} you can observe that 1+5 =2+4=3, and as we know the sum of all the elements is equal to the product of average value the elements and the number of elements. The sum of the sequence above is 3*5. A complete graph or clique has an edge between all nodes and so if you have 3 nodes, A, B, C, then you need the edges A-B, A-C, B-C. We will say an edge starts at the lexicographical lower node. In this case A goes to B,C and B goes to C. The graph is undirected but this is only to make the explanation simpler. We can denote this as {2, 1, 0} because A goes to 2 nodes, B goes to 1 node, C goes to 0 nodes. As you can see this is similar to the sequence above. If we have a complete graph with the nodes A->E inclusive then we would get {4, 3, 2, 1, 0}. From what we learned above we can sum this by taking the average, 2, and then multiplying this by the number of elements, 5. We observe that the first value will be the number of nodes minus one (n-1) and that the last value will be 0. Hence the average value will be (n-1)/2. Hence we get (n-1)*n.

I have no idea if that made ANY sense but i like to explain things i think i know to make sure i actually know them. Please share more formulas, i promise i wont explain them

Discriminant one love <3

Bayes Theorem: https://en.wikipedia.org/wiki/Bayes%27_theorem