Circles captivate us, and inscribed circles doubly so. In a previous post, we tackled finding the area of a shaded region. Today we pursue a similar goal with a twist. Here we have an square...

I was given an interesting math problem on a post-it note recently. The setup is pictured below: two circles (of radius ) are inscribed within a rectangle. I've chosen, without loss of generality, ....

A good mathematical puzzle often begins not with a question, but with a statement—one so elegant it feels both obvious and impossible. For me, this moment arrived during a commute, watching a...

There's a recurring theme in my life's adventures: I'll head out on a backpacking trip with friends, some intriguing question will inevitably surface as we muck about, a lively discussion ensues, and...

Is technology not innate to us as webs are to the patient spider's craft? We weave our networks, ever more complex, both born of instinct, shaped by nature's law. But here we part from spider's...

I had an interesting discussion this past weekend on the "beginning of things." Someone making their case implied early on that "all things have a beginning". One way or another, I got to thinking:...

Whosoever puts themselves to task, In pursuit of whatever consumes them-- Not after scraps, But doggedly after their true quarry, Like a greyhound set on course, Will discover in themselves, The...

Heavy is the head that wears the crown, Forged of lofty expectations, And sagged are the shoulders, Underneath a world unborn, But heavier still, Are man and his dreams taken together, Sat astride...

Author's note: This article is unstructured, so handle with care as things won’t transition or segue as nicely as they could. I didn’t bother very hard to change that, it’d have been more work than...

A man tended his garden, lost in routine When fluttered in a butterfly, unannounced, More brilliant than anything he’d ever seen, Entranced, he laid down his shears, And proclaimed: “O’ butterfly,...

Author's note: I went backpacking with a couple of friends up in Desolation wilderness (southwest of Lake Tahoe) this past weekend. The timing was fortuitous because I've recently really gotten into...

In the hollow of his grand piano, Silence sang, Ecstatic in her soundless melody, For as time passed, a maestro’s fascination with Music’s theory, Eclipsed his desire to play, He starved her of all...

TLDR: Meta's decision to open-source Llama 3.1 is a calculated bet on the future of content creation and ad campaign creation. By making AI models like Llama widely available, Meta is poised to...

Author's note: The following is inspired by an entry in my journal reflecting on recent events at the office. After three and a half years of professional experience, I finally feel entitled to some...

All belongs to the genuine, Who do not flinch from their own passion, Nor douse their own fiery spirit, Having vowed to never forge a false self, Or anything resembling an aped imitation of a living...

Author's note: This work departs from the traditional essay format. It presents a series of personal annotations and critical reflections inspired by excerpts from Henry George’s seminal text,...

Heaven determined that the cosmos be like a frozen sea, And were its mandate met, All would be commanded still in icy thrall, O’ mankind! Take inspiration from the defiant stars, Those selfless...

How lonely is the branch with no bird to give perch, Wasted is the flower’s nectar when there is no bee, And barren is the garden from disuse; The tree under which the poet lies gives no shade, So...

Author's note: This poem was inspired by a quote attributed to Napoleon from a book I'd recently finished titled "Mind of Napoleon" compiled by J. Christopher Herold. "Everybody has loved me and...

There is a certain arrogance in man, That has him believe, Despite all, that he will make it happen, But like a deluge wherefor man would fix a dam in prevention, God humbles him, For God intended...

Author's note: This poem was inspired by a quote I came across online that I now know came from Werner Herzog's memoir. I know nothing of the man, but the following quote had me thinking: "I'd rather...

How perfect you looked beneath the moonlight, So I bought the moon and named it after you, Wove the stars into our own constellation, And wrapped your tapestry in the velvety black of night, And in...

Among a row of houses sat a solitary great house atop a high hill. This great house was an old house, by and large considered one of the "better" houses. Nevertheless, like all material things, it...

Man is first pliable, Only when compelled to run through nature’s course, Through her crags and bramble, and under an angry sun and an inhospitable cold, Is he made firm, sharp, and with purpose,...

Author’s note: Inspiration taken from Aesop’s fable “The Tortoise and The Eagle”. Variations of it can be found here https://fablesofaesop.com/the-tortoise-and-the-eagle.html. A Tortoise declared to...

If it's true, as oft they claim, That one's eyes are windows to one's soul, Then come close, peer deep within, Glimpse the depths of this restless heart of mine. Hear you my heart? How fiercely it...

O Lord, Steer me through affairs of the heart, Mine vessel I surrender to thee, Take from me the wheel, Bind me steadfast to the bowsprit, So my weeping, Tears akin to mortal rain, May fall...

Author's note: Driving back from a party late at night and my slight astigmatism causing the other vehicle's lights to seem like halos, my mind went straight to stars, their beauty, and the kernel of...

Readily will I unburden Sisyphus, Without care to crest the Mountain in which Man finds banal suffering and his very Soul trapped, I shall relieve Sisyphus of that accursed boulder. So readily will I...

I’ve often said May things go the ideal way and so furiously do I urge it on that much like a boy, who in his little sail boat will blow furiously against her sails supremely confident that with his...

Much to the disappointment of romantics But of no surprise to the sensible Poems are a lousy medium for one’s feelings For already it is clear to me— The sorry amateur I am That I’d sooner run out of...

Two lovers Apart Separated by large and empty desert expanse On which the wind gently rocks tumbleweeds to and fro So tangled so as to never unravel Between— Two lovers gazing longingly at the other,...

Author's note: I'd written this for a philosophy class my last semester at MIT. The main thesis here is pretty contrived, forced, and probably wrong, but is in my opinion, interesting nonetheless....

Author's note: I've been having a hard time writing: I'll open up my notes app and upon seeing the several, unfinished drafts of essays, I immediately lose motivation and close the app. That said, I...

Author's note: I'd written this piece for a class on Justice at MIT in response to a prompt--however, as per the professor's request, I will not be sharing the prompt; that said, the article remains...

Author's note: I'd written this piece for a class on Justice at MIT in response to a prompt--however, as per the professor's request, I will not be sharing the prompt; that said, the article remains...

Author's note: This was the start of my serious research at MIT, and the technical start for some of my later work with power systems. I'd written this during the summer of 2018. (I was watching the...

Author's note: This article is the second installment of my “Musings on x” series with regards to political economy and its attendant philosophy. (COVID-19’s made me something of an arm-chair...

Author's note: This article is inspired by one of the themes explored in Martin Luther King, Jr’s “Remaining Awake through a Great Revolution” speech. As a result, riddled throughout this article are...

A recurring theme of mine is that shortly after reading a book, particularly a biography, I'll pick up a few things from the story's protagonist and try to implement them in my own life. The drawings...

Here are my thoughts on Steven Pinker's The Enlightenment Now. I'd read this sometime in 2018, probably in March, shortly after the book came out. I took some notes while reading the book, and for...

I had written this on January 7, 2017 while I was in Freetown, Sierra Leone. I believe this was written shortly after reading "The Wealth and Poverty of Nations" by David Landes for the second time....

I'd written this last summer for the Muslim Student Association here at MIT. I am by no means a financial expert, but I want to share with you all the things I've learned about saving for retirement...

What a time to be alive! 🙌🏿🙌🏿