Docendo Discimus
Pre-Reflection First off what even is a treatise? A treatise is a systematic, written argument using methodical discussion(s) of the facts, the principles involved, and the conclusions reached. Just wanted
Over the course of my lifetime I have garnered quite a collection of literature spanning the tedious to the abstract. From discussions on what is existence to specific supreme court
A little over a month ago I was pressed to prove or justify why I believed life has intrinsic value (valuable in itself, for its own sake). With this article
I'm writing this article actually rather late in comparison to the story, but oh well! So WHAT IS THE STORY ... Dave Rubin and his show the Rubin Report are
\begin{align*} & \int \cos \left( \ln (x) \right) \: dx = \dfrac{x}{2} \left( \cos \left( \ln (x) \right) + \sin \left( \ln (x) \right) \right) + C \\& \\& {\rm{Proof}}:
\begin{align*} & f(x)=\sum_{n=0}^{\infty} \phi(n) \dfrac{(-x)^n}{n!} \LongrightarrowM \left[ f(s) \right] = \int_0^{\infty} x^{s-1}f(x) dx = \Gamma(s) \phi(-s) \\& \\& \therefore \int_0^ {\infty} e^{{-x}^n} \sin (x^n) dx = \dfrac{\left( \dfrac{1}{n} \right)! \sin
Prelude I am taking this test on 10/19/19. Result: QnA If economic globalisation is inevitable, it should primarily serve humanity rather than the interests of trans-national corporations.Agree***; would rather it
\begin{align*} & \int_0^1 \ln^b{(x)} dx = (-1)^b (b)! \\& \\& {\rm{Proof}}: \\& \\& \therefore x=e^u \Longrightarrow \int_{-\infty}^0 u^b e^u du \\& \\& \therefore u=-g \Longrightarrow (-1)^b \int_0^{\infty} g^b e^{-g} dg
BPRP achieved this result using power series. Today I will solve it using the Bose Integral. \begin{align*}& \int_0^1 \ln{(x)}\ln{(1-x)} dx = 2 - \dfrac{\pi^2}{6} \\& \\& {\rm{Proof}}: \\& \\& \therefore
\begin{align*}& I(a, b) = \int_0^\infty \dfrac{x^a}{x^b+1} dx =\dfrac{\beta(\dfrac{a+1}{b}, 1-\dfrac{a+1}{b})}{b} \\& \\& {\rm{Proof}}: \\& \\& \therefore u=x^b \Longrightarrow \int_0^\infty \dfrac{u^{\frac{a-b+1}{b}}}{b(u+1)} du \\& \\& \therefore \int_0^\infty \dfrac{u^{\frac{a-b+1}{b}}}{b(u+1)} du = \dfrac{\beta(\dfrac{a+1}{b}, 1-\dfrac{a+1}{b})}{b} \\&
\begin{align*}& I(b) = \int_0^\infty \dfrac{e^{-x}-e^{-bx}}{x} dx = \ln{(b)}\\& \\& {\rm{Proof}}: \\& \\& I'(b) = \int_0^\infty e^{-bx} dx = \dfrac{1}{b} \\& \\& \therefore I(b) = \ln{(b)} + C \\& \\& \therefore
BPRP solved this integral using power series back in 2017. Today I will solve it using the Bose Integral. \begin{align*}& \int_0^1 \dfrac{\ln{(x)}}{x-1} dx = \dfrac{\pi^2}{6} \\& \\& Proof: \\& \\&
After seeing the numerous ads for Robinhood and Acorns I thought I'd give it some thought ... so yes good marketing on their part! That's something quite rare IMO. In
I want to note that I believe my argument does need some more work, and the finalized version of my argument will be available in both the Hermeneutic Pragmatism PDF
Hey y'all! Sorry I've been less than usual in my site's upkeep. Military and college got in the way. Anyways, this post is simply to give the prelude to a
Many people wish to approximate their strength level through certain exercises. These exercises include the OG bench press, squat, and so on and so forth. Fitness experts over the years
In the U.S. Army we run the 2mi and I've been interested in estimating times for this off others, just like how I try to estimate 100m, 200m, and 400m
Start with the equation: \begin{align*} &f(x) = \dfrac{1}{1+x^2}\end{align*} Integrating with respect to x from 0 to 1 yields 0.25π. What makes this a guided approach is that this integration range
\begin{align*}& {\rm{Given}}:\int_0^\infty f(x) dx \\& \\& (1) \: \rm{Queen \: Property} \\& \\&\therefore u=(x)^{-1} \Longrightarrow\int_0^\infty f[(x)^{-1}] (x)^{-2} dx \\& \\& (2) \: \rm{Jacksonian \: Property} \\& \\&\therefore u=(x)^{-n} \Longrightarrown \int_0^\infty
From the last update I did in regards to my physical fitness I do not believe I have made any progress, if not slightly regressed, and there are reasons for
I recently discovered the Fat Free Mass Index a couple of days ago. I actually have to thank the YouTube Algorithm for suggesting another video series by Vitruvian Physique on
I've long wondered this question so I thought I'd do some research based on past experiences and information given from various fitness outlets. I stumbled upon a good video by
\begin{align*}& \int_0^\infty \dfrac{1}{(1+x^g)^n} dx =\int_0^\infty \dfrac{(x)^{gn-2}}{(1+x^g)^n} dx \\& \\& \therefore x^g = t \: , \: x = t^{\frac{1}{g}} \Longrightarrowdx = \dfrac{t^{\frac{1}{g}-1}}{g} dt \\& \\& \therefore \int_0^\infty \dfrac{(x)^{gn-2}}{(1+x^g)^n} dx \Longrightarrow\int_0^\infty
\begin{align*} & \int_0^{\infty} \dfrac{1}{(1+x^2)^n} dx \\& \\& \\& {\rm{Lemma \: (1)}}: \int_0^{\infty} \left[ f(x) \right] dx = \int_0^{\infty} \left[ \dfrac{f(\frac{1}{x})}{(x^2)} \right] dx \\& \\& {\rm{Lemma \: (2)}}: \int_0^{\frac{\pi}{2}} \left[\sin(x)\right]^{2g-1} \left[\cos(x)\right]^{2h-1}
16 April 2019 Formula (19/718 sampled) \begin{align*} \rm{200m} &\approx \rm{100m} \left[ 1.997383 + \left( \dfrac{7.633557}{\rm{60m}} \right) \right] - 11.1841 \pm 0.3 \\& \approx\rm{100m} \left[ 2 + \left( \dfrac{7.65}{\rm{60m}} \right) \right]
Context I was reading through one of the various eBooks by James Gray (How to Become a Philosopher) and I wanted to see if he had written anything on Philosophy
Let me start off by saying I actually have to thank someone I formerly worked with, Kelly Hernandez. We got into a discussion about UBI, the poor, etc. and from
\begin{align*}\displaystyle I & = \int_{\alpha}^{\beta} (e)^{x^n} \: dx =\sum \limits_{\gamma=0}^\infty \left[ \dfrac{(\beta)^{n \gamma +1}-(\alpha)^{n \gamma +1}}{(n \gamma +1) (\gamma ) !} \right]\\& \\& \therefore IBP \\&\oplus \Longrightarrow (e)^{x^n} \: ;
Sid ... INTJ's (referred to as "Architects" and "The Master Mind") are a very rare personality type. They constitute ~ 2.1% of the populace (in regards to males ~3.3%). I
\begin{align*}I = \displaystyle \int_\alpha^\beta\dfrac{a(x)^n+b}{cx+d} \: dx &= \displaystyle \dfrac{a}{c} \int_\alpha^\beta\dfrac{(x)^n+ \frac{b}{a}}{x+\frac{d}{c}} \: dx \\&= \displaystyle \dfrac{a}{c} \int_\alpha^\beta\dfrac{(x)^n+ \Delta_1}{x+\Delta_2} \: dx \\& \therefore \: u=x+\Delta_2 \: \Longrightarrow \: u\mid_{\alpha+\Delta_2=\Delta_3}^{\beta+\Delta_2=\Delta_4} \\& \therefore
Walking / Running Calories Burned Based on MET by C. D. Chester Using previous data from my article on MET Values to accurately calculate caloric burn (based on weight and
\begin{aligned} I = \int_0^\infty \dfrac{1}{(x)^n+1} dx = \dfrac{\pi}{n\sin{( \frac{\pi}{n}} )} \end{aligned} \begin{aligned} \therefore \rho=\left[ (x)^n+1 \right]^{-1} \:;\: \rho \mid_0^1 \: \Longrightarrow d\rho=\dfrac{-n(x)^{n-1}}{\left[ (x)^n+1 \right]^2} \: dx\end{aligned} \begin{aligned} \therefore (n)^{-1} \int_0^1 \left[
So most people know \begin{aligned} 2 \times 2 = 4 \end{aligned} and the basic methods taught to us in school using carries (base 10 system), but what if we introduced
The Riemann Zeta Function Using The Pythagorean Theorem by C. D. Chester begin{aligned} int_0^infty dfrac{mathrm{e}^{-bx}sinleft(axright)}{a} : dx= dfrac{1}{b^2+a^2} :; a ne 0, b>0 end{aligned} This result can be easily found using
Zachary Lee "Obsessed with Integrals" https://philosophicalmath.wordpress.com/ Zachary's site is very straightforward, unlike the majority of my early work. My earliest work concerned primarily finding quality sites or online PDFs to
I=∫∞01x3+1dx=2π31.5≈1.209199576156145 Partial Fraction Decomposition Method \begin{aligned} \int_0^{\infty} \dfrac{1}{(x+1)(x^2-x+1)} \,dx \end{aligned}.\begin{aligned} \int_0^{\infty} \dfrac{1}{3(x+1)} \,dx+ \int_0^{\infty} \dfrac{x-2}{3(x^2-x+1)} \,dx \end{aligned}.\begin{aligned} \dfrac{1}{3} \int_0^{\infty} \dfrac{1}{x+1} \,dx-\dfrac{1}{3} \int_0^{\infty} \dfrac{x-2}{x^2-x+1} \,dx \end{aligned}.\begin{aligned} \left[\dfrac{1}{3} \ln{(x+1)}\right]\mid_0^{\infty}-\dfrac{1}{6}\int_0^{\infty} \dfrac{2x-1}{x^2-x+1} \,dx+\dfrac{1}{2}\int_0^{\infty} \dfrac{1}{x^2-x+1}
Context In 2018 I saw a post: Predicting 800m Timesby Sam Harding In it he used Multiple Linear Regression to perform more and more accurate 800m estimations. I had done
Context Earlier today I did a small workout using a hexagon bar (deadlift alternative). During it I managed to do 5 x 255 lb. I wondered as I got to
After perusing PubMed for awhile I have found various articles/studies on predicting body fat. You can find some here. Anyways, this one comes from one published May 11th, 2017. It
Daily Nutrient Recommendations Macronutrient g / kg / day Protein 1.2 - 2 Carbohydrate(general training) 5 - 7 Carbohydrate(athlete training) 7 - 10 Fat The rest of the calories. Minimum
Protein "The primary function of protein is to build and repair body tissues and structures. It is also involved in the synthesis of hormones, enzymes, and other regulatory peptides. Additionally,
Fat Loss Plan "So there are 3 ways to create an energy deficit: increase total physical activity, eat less or do a bit of both at the same time. The
Below comprises 11 fitness programs/plans I offer. Once you've purchased a plan expect an intial fitness goal and evaluation via email. - C. D. Chester All Products General Nutrition /
What is a MET? MET stands for Metabolic Equivalents. It is an index of energy expenditure through "the ratio of the rate of energy expended during an activity to the
In May 2018 I published an article built off a long time personal trainer and competition athlete: Martin Berkhan. I put off making the calculator for my article on it
These are all of the exercises and pre-made workouts on the Freeletics app. This will not include the drills or intervals as they vary based on the coach's evaluation of
Context For many years I've always had the same selfish goal. To look like something out of a superhero movie (but more natural looking). This year I think it will
Kyle Osborne is a writer on Medium. I am responding to his article titled What I Learned From Watching Ben Shapiro for a Week. I promised him I would more formally
So I peruse the internet for discussions (both critiques and solutions) on various topics. Medium usually is where I find the more written-out formal arguments and YouTube (YT) is more
So I also publish on Medium. You can see my articles as stories over there. Here's the link: C. D. Chester's Latest Medium Posts Everything I post on this website starting
Introduction Recently I was in a discussion on poverty, helping the poor, subsidizing education, etc. (socialist and liberal ideas/theories) with a co-worker. I, being a very libertarian capitalist, was confronted
Introduction Earlier today I had a conversation with a religious friend of mine (at least I strongly assume his views as being religious). I should note that I am a
Adam Smith The Wealth of Nations - An Inquiry Into the Nature and Causes of the Wealth of Nations Anarchism Anarchy, State, and Utopia by Robert Nozick Aristotle Poetics The
References: VO2 max by Brian Mackenzie Estimation of VO2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method by Uth et al VO2 max from a one mile
Use these estimations to figure out how many steps it takes you to walk a kilometer if you don't already know your stride length. You then estimate how far you
This test is designed to measure anaerobic capacity. All you have to do is run a 100m, wait 5min, and run a 400m. Enter the times in the appropriate spots
I should note that the KG -KM Ratio Estimate was first made aware to me by Radu Antoniu in his video Cardio for Fat Loss. In it he states,
An adapted version of the Male Fitness Multi-Calculator with the obvious equations fitting the female standards.
I spent a good 4 hours making this calculator and transposing it onto this page. I must thank uCalc.pro for allowing this to happen.
What is Number Theory? by the Mathematics Department in Brown University MATH 341 is an upper division mathematics class taught at CSULB. In it's course description it defines the class
Note that all are links to PDFs to other websites. Some are from .edu sources and others not so much. Also, some of these PDFs take a long time to