The Math Love Letter Written by a High School Senior (Respect)
This is a powerful "math love letter," with content that could be called "ironclad evidence." Take a look for yourself, and salute this formidable "talent." Lightly edited, purely for fun.
Shuzi,
Are you still mad at me?
I always like to call you Shuzi, do you know why? Because your name sounds the same as one of the characters in my favorite subject, math, and back in elementary school, math was called "arithmetic" (suanshu). more
Maybe you really are mad at me, but do you know why the time I've spent with you has become a decreasing function over the domain? There's a reason. We're both seniors now, facing all sorts of new permutations and combinations to come, and how I wish we could keep going to infinity together in the same combination, how I wish our love were a ray — with a starting point but no endpoint — rather than a line segment only as long as three years of high school.
If from now on we both study hard, then the ideal above can be realized. This is a true proposition. Everything I've done has been to draw auxiliary lines for our future. ∴ You shouldn't be angry with me, → I say to you: "Don't be angry anymore."
But you still haven't forgiven me, and you said to me: "⑴ The distance between us keeps growing. ⑵ You've gotten close with other girls." It seems I really need to prove that these two corollaries of yours are wrong.
**Proof:
⑴ You said the distance between us keeps growing.**
I took note — our classroom has seven rows across and nine rows down, plus two aisles, making it 11 rows. Let the classmate seated in row 5, column 4 be the coordinate origin, with row 4 as the x-axis and row 5 as the y-axis. Then your coordinates are: You(-4, 1); my coordinates are: Me(3, -2).
∴ The distance between us: You-Me = $\sqrt{(3+4)^2+(-2-1)^2} = 7.6$
∵ Only when the distance L ≥ 10 can it be considered "far." 0 < 7.6 < 10
∴ The distance between us is not far at all.
∴ The original proposition is false, incorrect.
⑵ You said I've gotten close with other girls.
Before working this out, let me clarify: for convenience, I'll use "her" to stand in for "other girls."
Let there be a right triangle ABC, with ∠C = 90°, hypotenuse AB = Me, and the two legs corresponding to you and her respectively. The angle between me and you is ∠ABC = α. (Note: as for why I'm only defining the angle between us, and not worrying about the angle between me and her — that's because you and I have had actual intersection, whereas you yourself said you believe my relationship with any other girl hasn't gotten to the point of even having a common perpendicular. This gives me some comfort.)
Then, for you and me together: ∵ you are above me on the triangle ∴ it's $\cos α$
For me and her: ∵ I am above her ∴ it's $\csc α$
For you and her: ∵ you are above her ∴ it's $\cot α$
∵ The angle α between you and me (which I'm certain has existed) is extremely small (small enough to be cured with just two pills)
∴ α tends to 0 (α > 0)
When α = 0: ① $\cos α = 1$, ∴ there is only one you in my heart
② $\csc α = 0$, ∴ I have no relationship with her
③ $\cot α = +\infty$, ∴ you matter infinitely more than she does
∴ I love you, not her.
By the same reasoning: I love you, not her', her', her'...
Generalizing this concept,
we can prove: I love you, not any "other girl,"
that is: I love you, and I don't love any "her" you're referring to.
**∴ I love you, and only you, uniquely.
∴ The original proposition is false, incorrect.**
Okay, so, are you still angry? Me and "her" are like an upward-opening parabola and the x-axis, and my heart toward "her" has discriminant Δ < 0,
∴ there will be no intersection point.
Me and "her" are like two skew lines — no matter how far they extend, they never meet.
Me and "her" are like the two branches of a hyperbola. Though somewhat symmetric, there is no intersection point.
Actually, Shuzi, even now, I still haven't been able to solve for the exact value of this "her" you mentioned. Let's not bring up "her" anymore — let "her" disappear forever!
Shuzi, let's get back together, forget all the unpleasant things, apply a sum-to-product transformation, and start reorganizing our train of thought anew.
Shuzi, please really forgive me. I would never secretly produce any extraneous roots behind your back — if you don't believe me, I'll submit to your verification anytime.
Shuzi, do you know? In these days that you haven't been talking to me, my life has felt like a geometric sequence ${a_n}$, with first term $a_1$ = pain, common ratio q = longing (q > 1), n = number of days, and the sum of the first n terms $S_n$ = "I really cannot bear this torment formed by the intersection of pain and longing anymore." Shuzi, give me the correct answer! Please?
Yesterday I wrote a poem — here it is for you.
Shuzi,
you are my axis of symmetry,
without you,
I can't find my other half;
Shuzi,
you are my range,
without you,
I don't know where to go;
Shuzi,
you are my axiom,
without you,
I have no clue where to start;
Shuzi,
you are my necessary condition,
maybe you can do without me,
but,
I absolutely cannot do without you!
Okay, Shuzi, that's it for now. My heart truly, forever, holds only you.
I've written so much — doesn't it seem too complicated? One last thing to say.
Answer: I love you.
From maths, begging for your forgiveness
Translated automatically with claude-sonnet-5; all equations are reproduced verbatim from the source. Copyright remains with the original author.