Triangular Gaps

There is an unfortunate gap in the triangle congruency theorems. It would be nice to be able to say that we can declare that two triangles are congruent based on a pair of sides and exactly two other bits of information, but we cannot.

If we can match up all three pairs of sides as congruent, the triangles are congruent.

If we can match up two pairs of angles and one pair of sides, the triangles are congruent.

If we can match up two pairs of sides and the angle between them, the triangles are congruent.

If we can match up two pairs of sides and a non-acute angle, the triangles are congruent.

But if we can match up two pairs of sides and an acute angle not between them, then we could be describing either of two triangles.

This gap is painful to the mathematician who prefers clear order.


I was in seventh grade, or maybe eighth, when the girl in the fuzzy sweater told me I was cute.

I still don’t know why she decided that I was going to be her boyfriend. I was awkward and out of place. I don’t remember ever fitting in, and certainly not with the girl in the fuzzy sweater.

Every time she spoke to me, I froze up and blushed. I would sink down as far as I could in my chair. At first she looked like she thought it was cute, but it wasn’t long before she was annoyed by it.

One day, as I sat in English class, I got a hot flash. My body was shaking. I was sweating. I couldn’t move.

The girl in the fuzzy sweater asked me what was wrong, and I told her, in quiet, embarrassed tones. She told me to tell the teacher. I said I couldn’t. She got mad and said that she was sick of me.

The girl in the fuzzy sweater never spoke to me again, and I never had another hot flash.

This was one of the places I learned I couldn’t.

Trump and Family (filk)

(To the tune of “The Addams’s Family”)

He’s selfish and he’s creepy
He’s grabby and he’s peepy
Let’s hope he’s getting sleepy
It’s Trump and family

His wife is kinda dour
Gaslighted and so sour
Was it worth it for the power?
It’s Trump and family

Slick! Sick! Small dick!

And don’t forget the daughter
She’s ready for a slaughter
Her brothers are marauders
It’s Trump and family


“It might just seem like a pointless detail to you, but it’s a symbol, is what it is.” He leaned in close to me, so I could smell the garlic and cigarettes on his breath. “A symbol of who I am. A cog in the machine. But not just any cog, oh no. A rusty cog, with a chipped tooth. It was once destined for greatness, but now it just grinds away. Dreaming of its lost aspirations. Waiting until it’s replaced by a newer part. Titanium, not steel. Steel was part of the past. Steel has lost its relevance.” He sat back, sighed, and found himself staring at where the two walls met the ceiling. I watched him in silence, thinking he was done. And then, in a long, defeated exhalation, he spoke: “It’s never a small detail to a small cog.”

My story began before I did

My story began before I did,
Written on leather and linen,
Papyrus and stone.

I was born in the taint of the oppressor
Stained white with a fabricated purity
Invented by men
Then forced into the mouth of God

My story was hammered into drying clay
Like pigeons’ feet
Across the centuries.

My myths were chanted
Around snow-ringed fire pits
And quilled onto leaves of hemp.

I cannot deny what has been braided
Into the sinews of my skeleton.

My story began years before I did:

This skin I wear was stitched
From killers of witches
And slayers of Indians
And enslavers of Africans.

This sin was born of the false piety
Of misguided faith.

O, that I could peel this skin like a snake!
But the venom that poisons this blood
Is not drained so easily as that.

My story began years before I did
But it does not end until my final breath.

— ptkh 051517


Today, I am a hero to a gull. And probably a sparrow.

Coming out of the Target on John R, I saw a gull attacking a heavily greased brown paper bag. He wasn’t getting very far, and was clearly frustrated.

As I walked over to look in the bag, the gull flew off to a safe distance, eyeing me warily. Was I going to steal his lunch? Was I going to make HIM lunch?

Instead, I made him lunch, but not the way he feared. It was a bag of sweet potato fries, so I dumped them on the ground and walked off.

He flew back and eagerly munched his lunch. I also saw a sparrow hopping around at a distance, presumably waiting for the gull to fly off.


On one of my routes home, there’s a signpost to which has been affixed a stuffed animal and a plastic figurine of an angel with the head of a little black girl. It’s bleached now from the sun, and the stuffed animal has gotten raggedy from the weather, and the desolation of it gives me a momentary pause that my life could be worse, that somewhere someone lost a child to tragedy near that corner. Today, it was even more poignant because a block later I saw a homeless man asleep on the sidewalk, tucked into the shadow of a building. Meanwhile, several miles south on Woodward, the Qline opens up this weekend, not far from where Mike Ilitch failed to live long enough to see the opening of the joint Red Wings/Pistons sports arena in the increasingly regentrified Heart of Detroit. How many of those gentrifying hipsters drive past the homeless black men hiding in the shadows of buildings without even noticing their existence? Meanwhile, a sunbleached angel remains in testimony that the lives of the invisible and displaced matter, too.

And tomorrow, I’ll wake up white again.

Another page

i did not dream so deeply as i did that night,
when beneath the cloudless sky,
the moon perched within the chill of air,
an ocean dotted with infinities of stars

sleep came ragged, but
the dreams washed over me
and pulled me deep into their undercurrent

dreams of my childhood,
drenched in clarity,
picked like fresh berries from the mulberry bush:
purple, succulent, sweet

dreams of adulthood,
willow trees weighed heavy
with tears of fallen angels:
green, insolent, bitter

dreams of visions yet to come,
dark chasms of loneliness
embraced by fetid vines and belladonna

behind the mire,
the glimmer and glitter of nevermind
slithered from my fingers
to remind me
that tomorrow would be

another page

ptkh 040117


am yet over rocky cliffs,
briefly divining strengths —
reluctance devouring
temporal madness
amidst hours with the id:

— ptkh 011217

The Rusted Locket

the smell of salt in the air
the creaking of the rope as it’s stretched taut
the burn of it cutting into the hands
the rocking of the ship
the sound of seagulls in the distance
the heat of the sun on the skin
the slapping of the water on the side
there in the distance…
is there something there?

Meanwhile, in the real world, he screams and covers his head as it all comes crashing down on him, like a barrage of hailstones, like a photograph found in the clutches of a dead man in a trench during World War I.

And then:

— ptkh 101516