thirty-seven

[thestarofhermes]

Tung tung tung tung tung

[thestarofhermes]

Ice cream ! 🍦

[thestarofhermes]

what’s the best thing you’ve found outside the island?

The world outside Apeiron has shown me the same shapes, the same numerical patterns— and yet everything I've found appears to me as a newly discovered mathematical equation.

..The best thing I've found outside the island.. You mean, an object from the phenomenal world? Or the friendships I've made?

I think that the new numbers I've met.. no, the new people I've met have been very interesting. They exhibit their own sets of behavioural patterns. I still am eager to figure out their essence, but I've been trying to refrain from doing so in order to treat them more.. humanely? Yes, that's the right word, I suppose!

As for a physical object— ice cream has a wonderful structure! That beautiful, regular dodecagram, and its magical, refreshing, and rich flavour... One of my experiences in the outside world was helping an ice cream parlour owner improve her sales and foot traffic! Although she did end up transferring ownership to the new owner who's currently selling beans with the malicious intent of consumption...

Still, I find ice cream to be the best thing I've found so far! I wasn't aware such a delightful shape with such a delicious taste was made outside the island. I only have to be careful about its vertex collapsing! Because then, the ice cream would melt and I would've wasted a perfectly wonderful dessert.

I wonder what Sophia would think of ice cream. I suppose 210 would've enjoyed it, too? And all the other integers. Mama had the fondness for sweet tastes like 6, I'm sure she'd be overjoyed to try out ice cream.

Please do recommend other "things" for me to try out! I'd be happy to figure out the numerical value behind them.

[yhetoan]

Chapter 7 hurt

[vingler-mirror]

The Reverse 1999 doomed yuri pose™

[arcanistsanctum]

Vereinsamt 1.9 Version Official Wallpapers (2/2)

[arcanistsanctum]

Overture | Sophia

"Your hands ... were never meant for violence, they were meant for upholding the truth. As for me—I'm the one who clears the dust off the path, as fate foretold."

[vingler-mirror]

Comparison with the before:

[arcanistsanctum]

37's 2.2 Shop Garment: Down in the Grotto Will be available at the Garment Shop at 2.2 Patch Update.

[thestarofhermes]

Behold! ‘Tis I, Fischl, the Prinzessin de Verurteilung! ‘Twas fate that led our paths to cross during one’s most turbulent of eras, and now one must test your knowledge of arithmetic to see if you are indeed worthy of the glories sung in your name! Should you succeed, one shall grant you the divine privilege of stepping foot into one’s beloved Immernachtreich!

10^x + 11^x + 12^x = 13^x + 14^x

X=?

Oh! It seems I have neglected this app for quite a while. I'm sorry for my mistake, please do not take this as an offense. I've been so busy trying to get used to life outside the island.

Fischl, the Prinzessin der Verurteilung? An introduction I'll most likely remember for some time. And you've given me a test, too! Wonderful. You've sent this question 4 days ago.. Hmh, I'm not sure if you still require an answer, but just incase:

Based on the given question:

"10^x + 11^x + 12^x = 13^x + 14^x"

I have calculated that x holds the value of 2. I'll provide a detailed explanation for further comprehension!

The first and foremost step to uncovering this equation, you must evaluate the behaviour of both sides of the equation as the x varies!

For x = 2,

10^2 + 11^2 + 12^2 = 100 + 121 + 144 = 365

13^2 + 14^2 = 169 + 196 = 365

Thus, 10^2 + 11^2 + 12^2 = 13^2 + 14^2 proves that x = 2.

Of course, with every equation, it is natural for us to question whether we have calculated the accurate result! This part is what most people find less important, but, it really is as important as the fun of finding solutions.

We can analyse the functions on either sides,

The left-hand side, f(x) = 10^x + 11^x + 12^x, is an increasing function since the sum of exponential functions with bases greater than 1 is increasing. The right-hand side, g(x) = 13^x + 14^x, is also an increasing function, with the same explanation why.

Since both functions are increasing, they can intersect at most once. From our methodical calculation, we have made it clear that x = 2 is the most reasonable conclusion because the functions f(x) = 10^x + 11^x + 12^x and g(x) = 13^x + 14^x are strictly increasing due to the derivative of each term being positive for x > 0. The most the can intersect is once. Since we found a single intersection at x = 2, it is the only solution.

Thus, the value of x is 2.

I don't exactly understand what you meant by an Immernachtreich, but from the formation of the word as a whole, I assume it is some form of Germanic language.

...

All right! I have successfully googled the meaning, and your offer seems tempting! Well, I hope my explanation has served some use to you, and everyone else. I'm still figuring out how these applications work, so there's definitely a high chance of me not responding as conveniently as you wish. I'll check if there are any other questions I've left unanswered—

Farewell! I'd find it nice to talk with you again.

[thestarofhermes]

The Star of Hermes

An interactive tumblr

It is the end, the answer, the result of all calculations.

Warmest greetings!

from the furthest island of the Aegean sea.

I go by 37, a scholar dedicated to the arts of mathematics. I find it so exciting to be here on Tumblr to answer any questions or to talk with new friends!

I'm sure there must be some unanswered question ringing in your head. Ask away!