Me, Playing Poker: Man, I Fold

Lagrange Markipliers or something idk I forgot all my multivariable calc.

thank you @dressedsalad @bsdndprplplld and @rooksacrifice for nominations. the last two were my additions (to provide more variety in the choices, not bc I dislike them)

12 XII 2022

I have a test at the end of this week so I am mostly grinding for that, kinda ignoring other things along the way, planning to catch up with them during the christmas break

the new update for my tablet's OS brought the option to insert pictures into the notes, so now I can paste the problem statements directly from the book. I am not sure if this is actually efficient but it surely looks better and the notes are more readable

(I can't vouch for the correctness of those tho lol I just started learning about the Rouché's theorem)

I have been trying to keep up with the material discussed in lectures on commutative algebra and agebraic methods. with each lecture there is a set of homework problems to solve and I predefined a standard for myself that this week it's alright if I don't do the homework because grinding for the test is more important

I made some pretty notes on valuation rings

during the break I need to study finite and integral ring maps and valuation rings for commutative algebra course; resolutions, derived functors and universal coefficients theorem for algebraic methods course. I feel pretty good about the test that's coming up. sure, you can never be too prepared but so far I've been able to solve a good part of the problems I tried, so I should be ok

Someone is bisexual if they are both monosexual and episexual

Nothing but respect for this mathematician's webpage

saving this for self-care and for anyone who might need this

also, I can add: squint your eyes hard and then looking at something far away. it's supposed to help your eyes relax and a bonus simple grounding exercise!

from my personal experience, once you start paying attention to how different it feels on your eyes to look at something far away as opposed to something close, you can relax your eyes without needing an object to look at. now when I'm going to bed I imagine a tree far away and I feel my eyes relaxing, it helps with me fall alseep faster. it might be a placebo ofc, I know nothing about eyes, but it is still a good trick for falling asleep regardless of the supposed effect of it on the eyes

We need like “unclench your jaw” posts but for eye strain. Like

Go look at something 20ft away for 20 seconds.

5 IX 2022

maybe once a month is a bit too seldom to post? I kinda want to form a habit of romanticizing my academic life, I see all those studyblr accounts with beautiful photos of their desks and notes and I'm pretty sure those images exist in their minds as well

maybe one day I will be considered studyspo lol

I'm just starting to work on some geometry problems for today, haven't yet decided what I will focus on, but there is this one problem that haunted me when I tried to sleep yestarday:

given a triangle ABC with ∠A = 60°, let P be a point in the interior of ABC such that ∠APB = ∠APC = 120°. prove that ∠APX = 90°, for X being the circumcenter of ABC

it's supposed to be solved using spiral similarity, which is a composition of a rotation and homothety. there was another problem that was listed as "spiral similarity exercise", but I proved it with angle chasing exclusively, creating some nasty drawings in the process

other than geometry I'm studying homology, at the moment the basics of homological algebra, such as the first proofs by diagram chasing and exact sequences

I made some notes for exact sequences induced in homology

my perspective on doing math is slowly changing I think, I feel inspired to search for problems that I would like to solve. I noticed that I have this mental block: before I start doing math for real, I need to learn all the theory. which is absurd, you can never learn all the theory

sure, obtaining truly groundbreaking results requires years of learning theory and mastering tools if you want to specialize in algebraic topology and geometry, but the mindset I have creates the comfort zone of "play safe, just read your textbook, no challenges for now" and I'm starting to see beyond that

right now I'm taking my first steps into understanding that reading textbooks and learning how to solve basic exercises is not enough. they are just methods that are supposed to help my creativity and curiosity do their thing. essentially what I've been doing so far is not math, merely the preparation to do math in the future. no wonder I've been feeling so bored recently, all I'm doing is just learning basic tools. the idealist in me is asking to be unleashed

I feel like I'm about to see something much bigger than me

DO YOU KNOW WHAT I JUST REALIZED

YOU KNOW THE HAIKU BOT???

OFC YOU DO

YOU KNOW THAT MESSAGE HE PUTS AT THE END OF EVERY POST????

"Beep boop! I look for accidental haiku posts. Sometimes I mess up."

YEAH???????

WELL THATS A HAIKU TOO

Beep boop! I look for

accidental haiku posts.

Sometimes I mess up.

NOW YOU LOOK ME IN THE EYE AND TELL ME THATS NOT THE CUTEST THNIG YOUVE EVER HEARD

@dimiclaudeblaigan asked for a tutorial on how to begin drawing. Good news! If you can draw a funky looking stick man, you have already started!

I think that stick people are a great starting point for artists because of the things you can learn from them that will be important later on.

If you are able to draw a circle and a couple of lines, you can easily put together a stick person.

Congratulations! You have started to draw. :)

A stick person is a very minimal artistic representation of a real life person. It is simple yet recognizable, and is widely used in art, media, and signage.

But what can a stick person teach us about drawing people that look more like… well, people? Lets have a look!

By simply adding a few more lines, we can add a pair of eyes and a mouth. Maybe even a little triangle nose! Or half circles for ears. We can now draw a face, which provides a basis for all sorts of expressions.

These simple additions can allow us to explore the wide range of human emotion and individuality.

This may seem like the basics of the basics. But that is what we want! In order to get to the point where we are able to draw complex, elaborate representations of humans and objects, we will need to start with simple shapes like lines and circles and build our understanding from there.

For instance, lets give our stick person some cool new features, such as hands and feet. I chose little squiggly circles to represent hands, and triangles to represent feet.

We can go a step further and modify the body of the stick person to include shoulders, hips, elbows and knees. These parts of the human body are quite complex in real life But here, all we need to do is add a few simple lines and dots to our stick person.

The lines provide some additional structural elements to our stick person's body, which are the shoulders and the hips. The dots indicate the points of articulation - elbows and knees, the places where the arms and legs bend!

Now we can use our stick person to show us an even wider range of human movement, action, and expression.

Our little drawing of a human being is evolving! All it took was adding a few more lines and shapes here and there.

By elongating some of the existing lines and making the head an oval instead of a circle, we can give our stick person proportions that resemble that of a real life human.

By this point, we have managed to add more complexity to our stick person simply by using our ability to draw lines, circles, and other basic shapes!

These basic ideas are the building blocks that will enable us to create more complex shapes.

The next part may be a considerable step up if you are absolutely new to drawing, but I have decided to include it in order to show you how complex objects like the human body can be built from shapes that are a bit more complex than circles and lines.

For example. Two ovals and a rectangle can be combined to create a cylinder.

Six squares can be combined to create a cube, or a box. Here, each square is distorted slightly depending on which way the cube is facing.

Note that the back faces of the cube and the bottom of the cylinder are hidden. These shapes allow us to visualize that which should not normally visible.

A sphere from all perspectives can be represented by a circle. But we can make it more like a sphere by adding lighting and shadow if we so desire.

Cubes, cylinders, and spheres are examples of 'solid shapes' because they consist of 3 dimensions.

Lets see how these solid shapes can be used to compose the human body.

By stacking three cylindrical objects, we can create a torso. Two spheres have been added to form shoulders, while a smaller cylinder forms the neck.

An arm is an alternating sequence of spheres and cylinders connected together. Note that the hand has been simplified for this example.

We can apply these solid shapes to the rest of the body to give us a more recognizable representation of the human form. It doesn't even have to be perfect. And just like that, our stick figure now has a silhouette that is unmistakably a person!

In the above examples, notice that we kept the stick person at the beginning while building up the shapes and solids around it. This is because the stick person serves as a guide for positioning the body and its various parts -> also known as posing.

You can do the same thing to everyday objects! Here, I drew a wine glass by stacking these three dimensional solid shapes.

The cup and its contents are two ovoid shapes that were cut in half. The stem is a very thin cylinder shape. The base is a cylinder with a slightly wider bottom.

Solid shapes help inform us how objects and parts of the human body may appear from different perspectives.

For example, a sphere can be used to demonstrate how the human head appears when looking up or down, turned to the side, or tilted at an angle.

With these examples, I hope I have managed to convinced you that if you can draw a circle and a couple of lines, you can draw a person! You just have to train your eye to recognize the simple shapes within complex objects. Try it with everyday objects as well! Or even your favourite media! A drawing subject can be as simple or as complex as you envision it to be.

Once you have mastered that, there are many aspects of drawing you can explore from here that may require you to seek additional resources or a fellow artist's advice.

Last of all, remember that drawing is an iterative process. Even if you draw something correct the first time, you will need to draw it again and again to get it right all times! And by making small changes like the ones we explored in this tutorial, your drawings will gradually transform!

I hope what I've demonstrated here are enough to provide the basics of how to get started with drawing objects and people, and also to help refresh more experienced artists. :) Hopefully I didn't go too off topic with what was requested, and let me know if there are any more questions I can answer.

Cheers :3