-Unknown physicist.


@nodiribnmuzaffar

The Feynman Lectures on Physics

1-chapterdan parcha:

You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. (So, not satisfied to learn physics in four years, you want to learn it in four minutes?) We cannot do it in this way for two reasons. First, we do not yet know all the basic laws: there is an expanding frontier of ignorance. Second, the correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean. No, it is not possible to do it that way. We can only do it piece by piece.

Juda qiziq va tushunarli tilda yozilgan, leksiya videolari ham bor.


Link:
https://www.feynmanlectures.caltech.edu/


@nodiribnmuzaffar

ICTP Simons Associates


PhD diplomiga ega bo'lgan va rivojlanayotgan mamlakatlarda ishlaydigan olimlar uchun 3 yillik dastur.

Yo'nalishlar yuqoridagi rasmda bor.

Tartibi, agar qabul qilinsangiz har yili 1 yoki 2 oyga ICTPga mehmon ilmiy izlanuvchi sifatida tashrif buyurasiz va u yerdagi olimlar bilan hamkorlikda ilmiy ish qilib kelasiz. Har tashrif buyurganda bitta magistr yoki PhD talaba bilan birga borsangiz ham bo'ladi.


Grant siz va siz bilan boradigan bitta o'quvchi uchun, o'sha yerda sarflagan vaqtingizda yashash harajatlari, sayohat harajatlari va tibbiy sug'urta harajatlarini o'z ichiga oladi.


Deadline:
1-iyul, 2025.

Link:
https://www.ictp.it/opportunity/ictp-simons-associates


@nodiribnmuzaffar

It is raining cats and dogs!

Kutubxonadan departmentgacha yomg'ir ostida 1 daqiqa sayohat☔️.


@nodiribnmuzaffar

Uchburchak va Uning Bissektrisalari.


Uchburchak va uning 3 ta bissektrisasi haqida ikkita mashhur masala bor.
Ko'pincha shu ikkalasini chalkashtirish holatlari bo'ladi, o'zimda ham bo'lgan.
Bu postda shunga aniqlik kiritamiz.
Matematik bo'lmaganlar uchun oxirida Bonus ham bor.


Birinchisi masala:
Uchburchakning 3 ta bissektrisasi(uzunliklari) berilgan bo'lsa, shu uchburchakni yasash mumkinmi?
(Yasash deganda, chizg'ich va sirkul yordamida yasash nazarda tutilmoqda).

Javob: Umumiy holatda mumkin emas.
1903-yilda Richard Philip Bakerning Chikago universitetida yozgan "The Problem of the Angle-Bisectors" nomli tezisida bu isbotlangan.

Link:
https://quod.lib.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=AAN3028.0001.001;didno=AAN3028.0001.001;view=pdf;seq=00000004


Ikkinchi masala:
3 ta ixtiyoriy musbat m, n, p haqiqiy sonlar berilgan bo'lsin, bissektrisalarining usuzliklari m, n, p bo'lgan uchburchak mavjudmi?

Javob: HA MAVJUD, va bunday uchburchak yagona(up to isometry).

Natija: Agar ikkita uchburchakning mos bissektrisalari teng bo'lsa bu uchburchaklar ham teng(up to isometry).

Isbotni qisqacha g'oyasi:
Hamma biladigan bissektrisa uzunligini tomonlar uzunliklari orqali topish formulasidan foydalanib, 3 o'lchamli fazoni 3 o'lchamli fazoga o'tkazadigan funksiya hosil qilingan.
Keyin bu funksiya qaysidir qavariq kompakt to'plamni o'zini o'ziga o'tkazishi va uzluksizligi ko'rsatilgan.
Va sezganingizdek bunday funksiyalar Brouwer fixed-point teoremasiga ko'ra fiksirlangan nuqtaga ega(F(x)=x).
Va bu funksiyani fiksirlangan nuqtasi yagona ekanligi isbotni yakunlab bergan.

The Existence of a Triangle with Prescribed Angle Bisector Lengths
Petru Mironescu and Laurentiu Panaitopol

The American Mathematical Monthly
Vol. 101, No. 1 (Jan., 1994), pp. 58-60 (3 pages)
Published By: Taylor & Francis, Ltd.

Qiziqqanlar uchun maqola linki
Link:
https://www.jstor.org/stable/2325126


Bonus.
Fiksirlangan nuqtalar haqidagi bir nechta teoremalar bor.
Shulardan birining chiroyli natijasini ko'ramiz.

Bir mamlakatning oddiy xaritasini olaylik va bu xarita o‘sha mamlakat ichida tekis stol ustiga qo‘yilgan deb tasavvur qilaylik. Har doim xaritada mamlakatdagi aynan o‘sha nuqtaga to‘g‘ri keladigan bir "Siz shu yerda turibsiz" nuqtasi mavjud bo‘ladi.

Yanayam aniqrog'i, xaritada shunday yagona nuqta borki bu nuqta o'zi aniqlab kelayotgan(mamlakatdagi) nuqtaning aynan ustida turgan bo'ladi.
Chunki mamlakatni kichkina qo'gozga akslantirayotgan funksiya qandaydir masshtabga ega bo'ladi va bu xossa Banach fixed-point teoremasini qo'llashga yetarli.


@nodiribnmuzaffar

Proof without words.


Manba:
Mathematics Magazine, Vol. 65, No. 2 (Apr., 1992), p. 103.

Ptolomey teoremasi. Agar to'rtburchakka tashqi aylana chizish mumkin bo'lsa bu to'rtburchakning qarama-qarshi tomonlari ko'paytmalari yig'indisi diagonallari ko'paytmasiga teng.

@nodiribnmuzaffar