Day -1(mod19)

Szia!

Today was full of even more math, walking, and food. After yet another breakfast of nutella, baguettes, and grapefruit juice (we're becoming awfully fond of this meal) we learned all about Euler's function. His useful little theorem helps us to calculate the number of positive integers less than an integer n which are relatively prime to n. Confused? You should be, the proof for this is almost two pages long. Starved after such intense mental strain, we headed down the street for some 2 dollar gyros. Considering we had more math in store, we also swung by our favorite little cafe, The Goatherder, for some sweets. With our chocolate cravings satiated we returned to the classroom for a lecture by Csaba Szabo, a Hungarian professor from ELTE with a passion for number theory and a knack for posing questions that had you second guessing everything you knew about basic mathematics. Is the product of two odds in fact an odd??? For the next hour we tried to prove the irrationality of √2 and √3. Professor Szabo likes to draw a flower in his proof wherever we get stuck, and by the end of the class the chalkboard looked a lot like a garden in spring time.

After our double dose of number theory, we headed to the Gellérthegyi Barlang cave church. A popular spot, I know, the quad squad reported on this yesterday. However, we have some new pictures to add and can reaffirm that it is indeed a charming church, and quite warm for a cave thanks to the thermal springs running under the rock. After exiting the church, we decided to pay a second sunset visit to our friend Lady Liberty. The view isn't something you tire of easily. Hiking up there on the other hand... We've been hitting our 10,000 steps consistently in the early afternoon on this trip (thanks Fitbit, you the real mvp).

Syver trying out the new Beats by Dre

3 is just prime #skol

inside the cave church

the blue Danube

Hungry and exhausted, we decided to revisit our favorite Italian restaurant for the 2nd time this week. Passing through a shopping mall on the way took a tragic turn as Jono dropped his water bottle and wedged it in the escalator (rip Gatorade sport bottle). Dinner however quickly had us in high spirits with pasta, pizzas, and steak all cooked to perfection. It was time to return to the hotel and finish our homework over some cake we had snagged at the Great Market Hall. Now that our blogging is done, we can sauna and plan out the weekend because IT'S ANNIKA'S 20TH BIRTHDAY TOMORROW (can I get a what what)!!! A birthday in Budapest doesn't sound too bad to us, especially when the gelato place nearby makes ice cream cakes. This is our last entry and the next time you hear from room 364, we'll be back in the states, but until then we'll say szia!

Much love, Annika, Brynna, and Sydney

way to go, Jono

not pictured: Jono's tears