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a/script.js b/script.js index 94bbbe9..ad5ee89 100644 --- a/script.js +++ b/script.js @@ -199,7 +199,7 @@ const COMMITTEE = [ { name: {en: "Fahmid Rahman Sakif", bn: "ফাহমিদ রহমান সাকিফ"}, pos: {en: "General Secretary", bn: "সাধারণ সম্পাদক"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "https://api.dicebear.com/7.x/initials/svg?seed=FS&backgroundColor=b45309" }, { name: {en: "Arif Mahmud Fahad", bn: "আরিফ মাহমুদ ফাহাদ"}, pos: {en: "Organizing Secretary", bn: "সাংগঠনিক সম্পাদক"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/fahad.jpg" }, { name: {en: "Syedul Mursalin", bn: "সাইয়্যেদুল মুরসালিন"}, pos: {en: "General Member Representative", bn: "সাধারণ সদস্য প্রতিনিধি"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/mursalin.jpg" }, - { name: {en: "Masadunnobi Tapu", bn: "মাসাদুন্নবী তপু"}, pos: {en: "Publicity Secretary", bn: "প্রচার সম্পাদক"}, group: {en: 'Science 5', bn: 'বিজ্ঞান ৫'}, img: "https://api.dicebear.com/7.x/initials/svg?seed=MT&backgroundColor=b45309" }, + { name: {en: "Masadunnobi Tapu", bn: "মাসাদুন্নবী তপু"}, pos: {en: "Publicity Secretary", bn: "প্রচার সম্পাদক"}, group: {en: 'Science 5', bn: 'বিজ্ঞান ৫'}, img: "./assets/committee/topu.jpg" }, { name: {en: "Siyam Sheikh", bn: "সিয়াম শেখ"}, pos: {en: "Treasurer", bn: "কোষাধ্যক্ষ"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/siyam.png" }, { name: {en: "Md Tamim Hasan", bn: "মোঃ তামিম হাসান"}, pos: {en: "Educational Tour Secretary", bn: "শিক্ষা সফর বিষয়ক সম্পাদক"}, group: {en: 'Science 2', bn: 'বিজ্ঞান ২'}, img: "https://api.dicebear.com/7.x/initials/svg?seed=TH&backgroundColor=b45309" } From 0c7cc5a00fb78380cd9db37ec2b6591637a5b6a3 Mon Sep 17 00:00:00 2001 From: Muhammad Radif Hassan Date: Wed, 11 Mar 2026 12:32:38 +0600 Subject: [PATCH 3/5] Update script.js --- script.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/script.js b/script.js index ad5ee89..d5eb3dd 100644 --- a/script.js +++ b/script.js @@ -8,7 +8,7 @@ const SITE_DATA = { address: { en: "City Bypass, Barera, Mymensingh", bn: "সিটি বাইপাস, বাড়েরা, ময়মনসিংহ" }, copyright: { en: "All rights reserved.", bn: "সর্বস্বত্ত্ব সংরক্ষিত।"}, phone: { en: "+880 1896-135846", bn: "+৮৮০ ১৮৯৬-৩২১৯৭০"}, - year: { en: "2025", bn: "২০২৫"}, + year: { en: "2026", bn: "২০২৬"}, location: { en: "Mymensingh", bn: "ময়মনসিংহ"}, events: { en: "Lectures, workshops and competitions.", bn: "লেকচার, কর্মশালা এবং প্রতিযোগিতা"}, host: { en: "Want to host a talk?", bn: "আলোচক হতে আগ্রহী?" }, From 9a9646f9d39de174eafb648bc063c0fa8787b22f Mon Sep 17 00:00:00 2001 From: Muhammad Radif Hassan Date: Sat, 28 Mar 2026 16:55:29 +0600 Subject: [PATCH 4/5] Update script.js --- script.js | 74 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 74 insertions(+) diff --git a/script.js b/script.js index d5eb3dd..a7e74f4 100644 --- a/script.js +++ b/script.js @@ -190,7 +190,81 @@ const ARTICLES = [

$$ e^{ix} = \\cos x + i\\sin x $$
` } + }, + { + id: 103, + title: { + en: "Combinatorics: The Art of Clever Counting", + bn: "কম্বিনেটরিক্স: চতুর গণনার শিল্প" + }, + author: { + en: "Muhammad Radif Hasan", + bn: "মুহাম্মদ রাদিফ হাসান" + }, + role: { + en: "President", + bn: "সভাপতি" + }, + date: { + en: "March 28, 2026", + bn: "২৮ মার্চ, ২০২৬" + }, + readTime: { + en: "6 min read", + bn: "৬ মিনিট পাঠ" + }, + desc: { + en: "Discover the beautiful world of counting, arrangements, and selections that powers probability, computer science, and olympiad mathematics.", + bn: "গণনা, বিন্যাস ও নির্বাচনের সুন্দর জগত আবিষ্কার করুন — যা সম্ভাবনা, কম্পিউটার বিজ্ঞান এবং অলিম্পিয়াড গণিতকে চালিত করে।" + }, + image: "https://picsum.photos/id/1015/800/600", // You can change this later + content: { + bn: ` +

কম্বিনেটরিক্স কী?

+

কম্বিনেটরিক্স হলো গণিতের সেই শাখা যেখানে আমরা শিখি কীভাবে চতুর উপায়ে গণনা করতে হয়। এটি সীমিত বস্তুসমূহের বিন্যাস, নির্বাচন এবং সম্ভাবনা নিয়ে কাজ করে।

+ +

মৌলিক নীতিসমূহ

+ +
+

১. গুণন নীতি (Multiplication Principle)

+

যদি একটি কাজ m ভাবে এবং আরেকটি কাজ n ভাবে করা যায়, তাহলে দুটি একসাথে m × n ভাবে করা যায়।

+

উদাহরণ: ৩টি শার্ট ও ৪টি প্যান্ট থেকে কত রকমের পোশাক? উত্তর: ১২টি।

+
+ +
+

২. বিন্যাস (Permutation)

+

P(n, r) = n! / (n - r)! — nটি জিনিস থেকে rটি সাজানোর উপায়।

+
+ +
+

৩. সমাবেশ (Combination)

+

C(n, r) = n! / (r! × (n - r)!) — ক্রম ছাড়া নির্বাচনের সংখ্যা।

+
+ +

পায়রার খোপ নীতি (Pigeonhole Principle)

+

যদি পায়রার সংখ্যা খোপের চেয়ে বেশি হয়, তাহলে অন্তত একটি খোপে দুইয়ের বেশি পায়রা থাকবে।

+

উদাহরণ: ৩৬৭ জন মানুষের মধ্যে অন্তত দু’জনের জন্মদিন একই দিনে পড়বে।

+ +

বাস্তব জীবনে প্রয়োগ

+
    +
  • ক্রিপ্টোগ্রাফি ও নিরাপত্তা ব্যবস্থা
    • +
  • কম্পিউটার অ্যালগরিদম
    • +
  • জেনেটিক্স ও ডিএনএ বিশ্লেষণ
    • +
  • লটারি, সময়সূচি তৈরি, খেলার ফিক্সচার
    • +
+ +

মজার সমস্যা

+

১. হ্যান্ডশেক সমস্যা: ১০ জনের পার্টিতে প্রত্যেকে প্রত্যেকের সাথে হাত মেলালে মোট কতটি হ্যান্ডশেক হবে?

+

২. সিঁড়ি ভাঙা: ১ বা ২ ধাপ করে ১০ ধাপের সিঁড়ি কতভাবে ভাঙা যায়? (ফিবোনাচ্চি সংখ্যা!)

+ +
+

কম্বিনেটরিক্স আমাদের শেখায় যে — সাধারণ গণনাও গভীর আবিষ্কারের দিকে নিয়ে যেতে পারে।

+
+ +

আমাদের ম্যাথ ক্লাবে আমরা নিয়মিত কম্বিনেটরিক্সের সমস্যা নিয়ে আলোচনা করি। তুমিও তোমার প্রিয় কম্বিনেটরিক্স সমস্যাটি পরবর্তী মিটিংয়ে শেয়ার করো!

+ ` } +} ]; const COMMITTEE = [ From 7b6191db022f8610c89e284efeb8018e88572caf Mon Sep 17 00:00:00 2001 From: Muhammad Radif Hassan Date: Wed, 1 Apr 2026 22:38:47 +0600 Subject: [PATCH 5/5] added slideshow in the event section and updated article image --- script.js | 408 +++++++++++++++++++++++++++--------------------------- 1 file changed, 203 insertions(+), 205 deletions(-) diff --git a/script.js b/script.js index a7e74f4..fc501e7 100644 --- a/script.js +++ b/script.js @@ -1,5 +1,11 @@ const FORMSPREE_ID = "xdkvyoqy"; +const CLUB_PHOTOS = [ + "https://images.unsplash.com/photo-1739675242031-cb6c3b076e4f?q=80&w=1951&auto=format&fit=crop&ixlib=rb-4.1.0&ixid=M3wxMjA3fDB8MHxwaG90by1wYWdlfHx8fGVufDB8fHx8fA%3D%3D", + "https://images.unsplash.com/photo-1727038104520-7249a8635fcf?w=500&auto=format&fit=crop&q=60&ixlib=rb-4.1.0&ixid=M3wxMjA3fDB8MHxwaG90by1yZWxhdGVkfDJ8fHxlbnwwfHx8fHw%3D", + "https://images.unsplash.com/photo-1748861306630-e992b1b39627?w=500&auto=format&fit=crop&q=60&ixlib=rb-4.1.0&ixid=M3wxMjA3fDB8MHxwaG90by1yZWxhdGVkfDV8fHxlbnwwfHx8fHw%3D" +]; + const SITE_DATA = { name: { en: "Notre Dame College Math Club", bn: "নটর ডেম কলেজ গণিত ক্লাব" }, college: { en: "Notre Dame College Mymensingh", bn: "নটর ডেম কলেজ ময়মনসিংহ" }, @@ -36,6 +42,8 @@ const DICTIONARY = { 'view_schedule': { en: 'View Schedule', bn: 'সময়সূচী দেখুন' }, 'register': { en: 'Register', bn: 'রেজিস্ট্রেশন' }, 'rsvp': { en: 'RSVP', bn: 'অংশগ্রহণ' }, + 'activities': {en: 'Our Activities', bn: 'আমাদের কার্যক্রম' }, + 'view': {en: 'View', bn: 'দেখুন'}, 'submit_proposal': { en: 'Submit Proposal', bn: 'প্রস্তাবনা জমা দিন' }, 'send_message': { en: 'Send Message', bn: 'বার্তা পাঠান' }, 'name': { en: 'Name', bn: 'নাম' }, @@ -77,41 +85,16 @@ const NEWS_SLIDES = [ const EVENTS = [ { - title: { en: "Lectures on Mathematical Notations and their usage", bn: "গাণিতিক চিহ্নসমূহ ও তাদের ব্যবহারবিধি নিয়ে আলোচনা" }, + title: { en: "Lectures on Mathematical Notations", bn: "গাণিতিক চিহ্নসমূহ ও তাদের ব্যবহারবিধি" }, date: { en: "DEC 10", bn: "১০ ডিসেম্বর" }, time: { en: "12:00 PM", bn: "দুপুর ১২:০০" }, location: { en: "Room 402", bn: "৪০২ নং কক্ষ" }, type: { en: "Lecture", bn: "লেকচার" }, - desc: { en: "Showing the notations that are frequently being used in Mathematics and make our calculation easier or how we can derrive a formula from calculations.", bn: "গাণিতিক প্রতীকের সাথে পরিচিত করানো যেগুলো প্রায়ই গণিতে ব্যবহৃত হচ্ছে এবং আমাদের হিসেবকে কিভাবে সহজ করছে কিংবা গাণিতিক সমাধান করে কিভাবে আমরা সূত্র নিয়ে আসতে পারি সেগুলো ব্যবহার করে।" }, - color: "bg-blue-100 text-blue-800" + desc: { en: "Exploring notations that simplify complex calculations.", bn: "গাণিতিক প্রতীকের সাথে পরিচিতি যা গণনাকে সহজ করে।" }, + color: "bg-blue-100 text-blue-800", + banner: "https://images.unsplash.com/photo-1739675242031-cb6c3b076e4f?q=80&w=1951&auto=format&fit=crop&ixlib=rb-4.1.0&ixid=M3wxMjA3fDB8MHxwaG90by1wYWdlfHx8fGVufDB8fHx8fA%3D%3D", + rsvpLink: "https://forms.gle/your-link" } - /*{ - title: { en: "Inter-College Integration Bee", bn: "আন্তঃকলেজ ইন্টিগ্রেশন বি" }, - date: { en: "NOV 02", bn: "০২ নভেম্বর" }, - time: { en: "2:30 PM", bn: "দুপুর ২:৩০" }, - location: { en: "Main Hall", bn: "মেইন হল" }, - type: { en: "Competition", bn: "প্রতিযোগিতা" }, - desc: { en: "Test your calculus skills against the best minds in Mymensingh.", bn: "ময়মনসিংহের সেরা মেধাবীদের সাথে আপনার ক্যালকুলাস দক্ষতা যাচাই করুন।" }, - color: "bg-purple-100 text-purple-800" - }, - { - title: { en: "Math Olympiad Prep", bn: "গণিত অলিম্পিয়াড প্রস্তুতি" }, - date: { en: "NOV 10", bn: "১০ নভেম্বর" }, - time: { en: "3:00 PM", bn: "বিকেল ৩:০০" }, - location: { en: "Room 201", bn: "কক্ষ ২০১" }, - type: { en: "Workshop", bn: "কর্মশালা" }, - desc: { en: "Problem-solving strategies for the upcoming National Math Olympiad.", bn: "আসন্ন জাতীয় গণিত অলিম্পিয়াডের জন্য সমস্যা সমাধানের কৌশল।" }, - color: "bg-orange-100 text-orange-800" - }, - { - title: { en: "Intro to Topology", bn: "টপোলজির পরিচিতি" }, - date: { en: "NOV 18", bn: "১৮ নভেম্বর" }, - time: { en: "4:00 PM", bn: "বিকেল ৪:০০" }, - location: { en: "College Auditorium", bn: "কলেজ অডিটোরিয়াম" }, - type: { en: "Lecture", bn: "লেকচার" }, - desc: { en: "Understanding shapes, surfaces, and why a coffee mug is a donut.", bn: "আকৃতি, তল এবং কেন একটি কফি মগ একটি ডোনাটের সমান তা বোঝা।" }, - color: "bg-blue-100 text-blue-800" - }*/ ]; const RESOURCES = [ @@ -127,7 +110,6 @@ const RESOURCES = [ { title: "Reducible", type: {en: "Video", bn: "ভিডিও"}, desc: {en: "All about animating computer science concepts in a fun, interactive, and intuitive manner.", bn: "কম্পিউটার বিজ্ঞানের ধারণাগুলোকে মজার, অংশগ্রহণভিত্তিক এবং সহজবোধ্যভাবে গতিশীল চিত্রের মাধ্যমে উপস্থাপন করা।"}, link: "https://www.youtube.com/@Reducible" }, { title: "Chamok Hasan", type: {en: "Video", bn: "ভিডিও"}, desc: {en: "Represnting the entire beauty and arising love for Mathematics through interactive discussion", bn: "অনশগ্রহনভিত্তিক আলোচনার মাধ্যমে গণিতের সম্পূর্ণ সৌন্দর্য উপস্থাপন করা এবং গণিতের প্রতি ভালোবাসা জাগিয়ে তোলা।"}, link: "https://www.youtube.com/@ChamokHasan"}, { title: "BdMO", type:{en: "Catalog", bn: "তালিকা"}, desc: {en: "Math Olmypiad Booklists and Resources", bn: "গণিত অলিম্পিয়াডের বইয়ের তালিকা ও উপকরণসমূহ"}, link: "https://matholympiad.org.bd/math-related-book-list"} - ]; const ARTICLES = [ @@ -143,24 +125,9 @@ const ARTICLES = [ bn: "ভাবুন এমন একটি হোটেল যার কক্ষ সংখ্যা অসীম এবং সবগুলোই পূর্ণ। নতুন অতিথি এলে কি হবে?" }, image: "https://imgs.search.brave.com/eya5oUzh8bfOlXm79fOZbzgGjQYzYCovr_CWi1zfQRA/rs:fit:860:0:0:0/g:ce/aHR0cHM6Ly9tZWRp/YS1tYW5hZ2VyLnN0/YXJzaW5zaWRlci5j/b20vZ2FsbGVyeS8x/MDgwL25hXzY3ZGFk/NGMyZjM0MzkuanBn", - content: { - en: ` -

Hilbert's paradox of the Grand Hotel is a thought experiment which illustrates a counterintuitive property of infinite sets.

-

Consider a hotel with a countably infinite number of rooms, all of which are occupied. One might think that the hotel cannot accommodate any newly arriving guests. However, we can accommodate a new guest by moving the guest in room $n$ to room $n+1$.

-
- $$ n \\rightarrow n + 1 $$ -
-

This leaves room 1 empty for the new guest. This works because the set of integers $\\mathbb{Z}$ has the same cardinality as the set of natural numbers $\\mathbb{N}$.

- `, - bn: ` -

হিলবার্টের গ্র্যান্ড হোটেলের প্যারাডক্স অসীম সেটের একটি অদ্ভুত বৈশিষ্ট্য তুলে ধরে।

-

ধরুন একটি হোটেলে অসীম সংখ্যক কক্ষ আছে এবং সবগুলোই পূর্ণ। আমরা মনে করতে পারি নতুন কোনো অতিথিকে জায়গা দেওয়া সম্ভব নয়। কিন্তু, আমরা যদি $n$ নম্বর কক্ষের অতিথিকে $n+1$ নম্বর কক্ষে পাঠিয়ে দেই:

-
- $$ n \\rightarrow n + 1 $$ -
-

তাহলে ১ নম্বর কক্ষটি খালি হয়ে যায়। এটি সম্ভব কারণ পূর্ণসংখ্যা $\\mathbb{Z}$ এবং স্বাভাবিক সংখ্যা $\\mathbb{N}$ এর কার্ডিনালিটি সমান।

- ` + en: `

Hilbert's paradox of the Grand Hotel is a thought experiment...

`, + bn: `

হিলবার্টের গ্র্যান্ড হোটেলের প্যারাডক্স অসীম সেটের একটি অদ্ভুত বৈশিষ্ট্য তুলে ধরে।

` } }, { @@ -173,98 +140,124 @@ const ARTICLES = [ desc: { en: "Combining e, i, pi, 1, and 0 into a single elegant statement.", bn: "e, i, pi, 1 এবং 0 এর এক বিস্ময়কর মিলন।" }, image: "https://cdn.mos.cms.futurecdn.net/cv2W6h6obxouAgNzfnJ6w3-700-80.jpg.webp", content: { - en: ` -

Often called the most beautiful equation in mathematics, Euler's identity connects five fundamental constants:

-
- $$ e^{i\\pi} + 1 = 0 $$ -
-

It is a special case of Euler's formula, which states that for any real number $x$:

-
$$ e^{ix} = \\cos x + i\\sin x $$
- `, - bn: ` -

গণিতের সবচেয়ে সুন্দর সমীকরণ হিসেবে পরিচিত অয়লারের অভেদ পাঁচটি মৌলিক ধ্রুবককে সংযুক্ত করে:

-
- $$ e^{i\\pi} + 1 = 0 $$ -
-

এটি অয়লারের সূত্রের একটি বিশেষ রূপ, যেখানে যেকোনো বাস্তব সংখ্যা $x$ এর জন্য:

-
$$ e^{ix} = \\cos x + i\\sin x $$
- ` + en: `

Often called the most beautiful equation in mathematics...

`, + bn: `

গণিতের সবচেয়ে সুন্দর সমীকরণ হিসেবে পরিচিত অয়লারের অভেদ পাঁচটি মৌলিক ধ্রুবককে সংযুক্ত করে:

` } }, - { - id: 103, - title: { - en: "Combinatorics: The Art of Clever Counting", - bn: "কম্বিনেটরিক্স: চতুর গণনার শিল্প" - }, - author: { - en: "Muhammad Radif Hasan", - bn: "মুহাম্মদ রাদিফ হাসান" - }, - role: { - en: "President", - bn: "সভাপতি" - }, - date: { - en: "March 28, 2026", - bn: "২৮ মার্চ, ২০২৬" - }, - readTime: { - en: "6 min read", - bn: "৬ মিনিট পাঠ" - }, - desc: { - en: "Discover the beautiful world of counting, arrangements, and selections that powers probability, computer science, and olympiad mathematics.", - bn: "গণনা, বিন্যাস ও নির্বাচনের সুন্দর জগত আবিষ্কার করুন — যা সম্ভাবনা, কম্পিউটার বিজ্ঞান এবং অলিম্পিয়াড গণিতকে চালিত করে।" - }, - image: "https://picsum.photos/id/1015/800/600", // You can change this later - content: { - bn: ` -

কম্বিনেটরিক্স কী?

-

কম্বিনেটরিক্স হলো গণিতের সেই শাখা যেখানে আমরা শিখি কীভাবে চতুর উপায়ে গণনা করতে হয়। এটি সীমিত বস্তুসমূহের বিন্যাস, নির্বাচন এবং সম্ভাবনা নিয়ে কাজ করে।

- -

মৌলিক নীতিসমূহ

- -
-

১. গুণন নীতি (Multiplication Principle)

-

যদি একটি কাজ m ভাবে এবং আরেকটি কাজ n ভাবে করা যায়, তাহলে দুটি একসাথে m × n ভাবে করা যায়।

-

উদাহরণ: ৩টি শার্ট ও ৪টি প্যান্ট থেকে কত রকমের পোশাক? উত্তর: ১২টি।

-
- -
-

২. বিন্যাস (Permutation)

-

P(n, r) = n! / (n - r)! — nটি জিনিস থেকে rটি সাজানোর উপায়।

-
- -
-

৩. সমাবেশ (Combination)

-

C(n, r) = n! / (r! × (n - r)!) — ক্রম ছাড়া নির্বাচনের সংখ্যা।

-
- -

পায়রার খোপ নীতি (Pigeonhole Principle)

-

যদি পায়রার সংখ্যা খোপের চেয়ে বেশি হয়, তাহলে অন্তত একটি খোপে দুইয়ের বেশি পায়রা থাকবে।

-

উদাহরণ: ৩৬৭ জন মানুষের মধ্যে অন্তত দু’জনের জন্মদিন একই দিনে পড়বে।

- -

বাস্তব জীবনে প্রয়োগ

-
    -
  • ক্রিপ্টোগ্রাফি ও নিরাপত্তা ব্যবস্থা
    • -
  • কম্পিউটার অ্যালগরিদম
    • -
  • জেনেটিক্স ও ডিএনএ বিশ্লেষণ
    • -
  • লটারি, সময়সূচি তৈরি, খেলার ফিক্সচার
    • -
- -

মজার সমস্যা

-

১. হ্যান্ডশেক সমস্যা: ১০ জনের পার্টিতে প্রত্যেকে প্রত্যেকের সাথে হাত মেলালে মোট কতটি হ্যান্ডশেক হবে?

-

২. সিঁড়ি ভাঙা: ১ বা ২ ধাপ করে ১০ ধাপের সিঁড়ি কতভাবে ভাঙা যায়? (ফিবোনাচ্চি সংখ্যা!)

- -
-

কম্বিনেটরিক্স আমাদের শেখায় যে — সাধারণ গণনাও গভীর আবিষ্কারের দিকে নিয়ে যেতে পারে।

-
- -

আমাদের ম্যাথ ক্লাবে আমরা নিয়মিত কম্বিনেটরিক্সের সমস্যা নিয়ে আলোচনা করি। তুমিও তোমার প্রিয় কম্বিনেটরিক্স সমস্যাটি পরবর্তী মিটিংয়ে শেয়ার করো!

- ` - } + { + id: 103, + title: { + en: "Combinatorics: The Art of Clever Counting", + bn: "কম্বিনেটরিক্স: চতুর গণনার শিল্প" + }, + author: { + en: "Md Radif Hasan", + bn: "মোঃ রাদিফ হাসান" + }, + role: { en: "President", bn: "সভাপতি" }, + date: { + en: "March 28, 2026", + bn: "২৮ মার্চ, ২০২৬" + }, + readTime: { + en: "6 min read", + bn: "৬ মিনিট পাঠ" + }, + desc: { + en: "Discover the beautiful world of counting, arrangements, and selections that powers probability, computer science, and olympiad mathematics.", + bn: "গণনা, বিন্যাস ও নির্বাচনের সুন্দর জগত আবিষ্কার করুন — যা সম্ভাবনা, কম্পিউটার বিজ্ঞান এবং অলিম্পিয়াড গণিতকে চালিত করে।" + }, + image: "https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fcdn.hashnode.com%2Fres%2Fhashnode%2Fimage%2Fupload%2Fv1679762948968%2F0735e987-8bdb-41cf-9b3d-63acddd282e9.png%3Fw%3D1600%26h%3D840%26fit%3Dcrop%26crop%3Dentropy%26auto%3Dcompress%2Cformat%26format%3Dwebp&f=1&nofb=1&ipt=9c6d9914341e12997390b7ab6950959691246968574f899d77a2f3f1a357919f", + content: { + bn: ` +

কম্বিনেটরিক্স কী?

+

কম্বিনেটরিক্স হলো গণিতের সেই শাখা যেখানে আমরা শিখি কীভাবে চতুর উপায়ে গণনা করতে হয়। এটি সীমিত বস্তুসমূহের বিন্যাস, নির্বাচন এবং সম্ভাবনা নিয়ে কাজ করে।

+ +

মৌলিক নীতিসমূহ

+ +
+

১. গুণন নীতি (Multiplication Principle)

+

যদি একটি কাজ m ভাবে এবং আরেকটি কাজ n ভাবে করা যায়, তাহলে দুটি একসাথে m × n ভাবে করা যায়।

+

উদাহরণ: ৩টি শার্ট ও ৪টি প্যান্ট থেকে কত রকমের পোশাক? উত্তর: ১২টি।

+
+ +
+

২. বিন্যাস (Permutation)

+

$$ P(n, r) = \\frac{n!}{(n - r)!} $$ — nটি জিনিস থেকে rটি সাজানোর উপায়।

+
+ +
+

৩. সমাবেশ (Combination)

+

$$ C(n, r) = \\frac{n!}{r!(n - r)!} $$ — ক্রম ছাড়া নির্বাচনের সংখ্যা।

+
+ +

পায়রার খোপ নীতি (Pigeonhole Principle)

+

যদি পায়রার সংখ্যা খোপের চেয়ে বেশি হয়, তাহলে অন্তত একটি খোপে দুইয়ের বেশি পায়রা থাকবে।

+

উদাহরণ: ৩৬৭ জন মানুষের মধ্যে অন্তত দু’জনের জন্মদিন একই দিনে পড়বে।

+ +

বাস্তব জীবনে প্রয়োগ

+
    +
  • ক্রিপ্টোগ্রাফি ও নিরাপত্তা ব্যবস্থা
    • +
  • কম্পিউটার অ্যালগরিদম
    • +
  • জেনেটিক্স ও ডিএনএ বিশ্লেষণ
    • +
  • লটারি, সময়সূচি তৈরি, খেলার ফিক্সচার
    • +
+

মজার সমস্যা

+

১. হ্যান্ডশেক সমস্যা: ১০ জনের পার্টিতে প্রত্যেকে প্রত্যেকের সাথে হাত মেলালে মোট কতটি হ্যান্ডশেক হবে?

+

২. সিঁড়ি ভাঙা: ১ বা ২ ধাপ করে ১০ ধাপের সিঁড়ি কতভাবে ভাঙা যায়? (ফিবোনাচ্চি সংখ্যা!)

+ +
+

কম্বিনেটরিক্স আমাদের শেখায় যে — সাধারণ গণনাও গভীর আবিষ্কারের দিকে নিয়ে যেতে পারে।

+
+ +

আমাদের ম্যাথ ক্লাবে আমরা নিয়মিত কম্বিনেটরিক্সের সমস্যা নিয়ে আলোচনা করি। তুমিও তোমার প্রিয় কম্বিনেটরিক্স সমস্যাটি পরবর্তী মিটিংয়ে শেয়ার করো!

+ `, + en: `

What is Combinatorics?

+

Combinatorics is the branch of mathematics where we learn how to count in clever ways. It deals with the arrangement, selection, and probability of finite sets of objects.

+ +

Fundamental Principles

+ +
+

1. Multiplication Principle

+

If one task can be performed in $m$ ways and another task can be performed in $n$ ways, then both tasks together can be performed in $m \\times n$ ways.

+

Example: How many outfits can you make from 3 shirts and 4 pants? Answer: 12.

+
+ +
+

2. Permutation

+

$$ P(n, r) = \\frac{n!}{(n - r)!} $$ — The number of ways to arrange $r$ items from a set of $n$ items where order matters.

+
+ +
+

3. Combination

+

$$ C(n, r) = \\frac{n!}{r!(n - r)!} $$ — The number of ways to select $r$ items from a set of $n$ items where order does not matter.

+
+ +

The Pigeonhole Principle

+

If you have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

+

Example: Among 367 people, at least two people must share the same birthday.

+ +

Real-World Applications

+
    +
  • Cryptography and security systems
    • +
  • Computer algorithms and data structures
    • +
  • Genetics and DNA sequence analysis
    • +
  • Lotteries, scheduling, and sports fixtures
    • +
+ +

Fun Problems to Solve

+

1. The Handshake Problem: If everyone at a party of 10 people shakes hands with everyone else, how many handshakes occur in total?

+

2. Climbing Stairs: In how many ways can you climb a staircase of 10 steps if you can take either 1 or 2 steps at a time? (Hint: Fibonacci numbers!)

+ +
+

Combinatorics teaches us that even simple counting can lead to profound mathematical discoveries.

+
+ +

In our Math Club, we regularly discuss fascinating combinatorial problems. Why not share your favorite one at our next meeting?

+ ` + } } + ]; const COMMITTEE = [ @@ -273,13 +266,9 @@ const COMMITTEE = [ { name: {en: "Fahmid Rahman Sakif", bn: "ফাহমিদ রহমান সাকিফ"}, pos: {en: "General Secretary", bn: "সাধারণ সম্পাদক"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "https://api.dicebear.com/7.x/initials/svg?seed=FS&backgroundColor=b45309" }, { name: {en: "Arif Mahmud Fahad", bn: "আরিফ মাহমুদ ফাহাদ"}, pos: {en: "Organizing Secretary", bn: "সাংগঠনিক সম্পাদক"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/fahad.jpg" }, { name: {en: "Syedul Mursalin", bn: "সাইয়্যেদুল মুরসালিন"}, pos: {en: "General Member Representative", bn: "সাধারণ সদস্য প্রতিনিধি"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/mursalin.jpg" }, - { name: {en: "Masadunnobi Tapu", bn: "মাসাদুন্নবী তপু"}, pos: {en: "Publicity Secretary", bn: "প্রচার সম্পাদক"}, group: {en: 'Science 5', bn: 'বিজ্ঞান ৫'}, img: "./assets/committee/topu.jpg" }, + { name: {en: "Masadunnobi Topu", bn: "মাসাদুন্নবী তপু"}, pos: {en: "Publicity Secretary", bn: "প্রচার সম্পাদক"}, group: {en: 'Science 5', bn: 'বিজ্ঞান ৫'}, img: "./assets/committee/topu.jpg" }, { name: {en: "Siyam Sheikh", bn: "সিয়াম শেখ"}, pos: {en: "Treasurer", bn: "কোষাধ্যক্ষ"}, group: {en: 'Science 1', bn: 'বিজ্ঞান ১'}, img: "./assets/committee/siyam.png" }, { name: {en: "Md Tamim Hasan", bn: "মোঃ তামিম হাসান"}, pos: {en: "Educational Tour Secretary", bn: "শিক্ষা সফর বিষয়ক সম্পাদক"}, group: {en: 'Science 2', bn: 'বিজ্ঞান ২'}, img: "https://api.dicebear.com/7.x/initials/svg?seed=TH&backgroundColor=b45309" } - - - - ]; let state = { @@ -288,22 +277,63 @@ let state = { lang: 'en', menuOpen: false, currentSlide: 0, - graphMode: 0 + graphMode: 0, + eventSlideIndex: 0 }; +function startEventSlideshow() { + setInterval(() => { + if (state.view === 'EVENTS') { + state.eventSlideIndex = (state.eventSlideIndex + 1) % CLUB_PHOTOS.length; + + render(); + } + }, 3000); +} + +function handleRouting() { + const hash = window.location.hash.replace('#', ''); + const [view, id] = hash.split('/'); + + if (!view || view === 'home') { + state.view = 'HOME'; + } else if (view === 'articles' && id) { + state.view = 'ARTICLE_SINGLE'; + state.articleId = parseInt(id); + } else { + const foundView = view.toUpperCase(); + state.view = foundView; + } + render(); +} + +function navigate(viewName, params = null) { + state.view = viewName; + state.menuOpen = false; + + if (params && params.id) { + state.articleId = params.id; + window.location.hash = `articles/${params.id}`; + } else { + window.location.hash = viewName.toLowerCase(); + } + + window.scrollTo(0, 0); +} const t = (key) => DICTIONARY[key] ? DICTIONARY[key][state.lang] : key; const getLang = (obj) => obj ? obj[state.lang] : ''; - const app = document.getElementById('app'); let mathAnimationId; let sliderInterval; function init() { updateBodyLang(); - render(); + window.addEventListener('hashchange', handleRouting); + handleRouting(); startSlider(); + startEventSlideshow(); } function updateBodyLang() { @@ -318,22 +348,6 @@ function toggleLanguage() { if(state.view === 'HOME') initMathAnimation(); } -function navigate(viewName, params = null) { - state.view = viewName; - if (params) state.articleId = params.id; - state.menuOpen = false; - window.scrollTo(0, 0); - render(); - - - if (mathAnimationId) cancelAnimationFrame(mathAnimationId); - - if (viewName === 'HOME') { - startSlider(); - initMathAnimation(); - } -} - function renderMath() { if (window.renderMathInElement) { renderMathInElement(document.body, { @@ -348,7 +362,6 @@ function renderMath() { } } - function render() { app.innerHTML = ` ${renderHeader()} @@ -368,7 +381,6 @@ function render() { function renderHeader() { const navLinks = ['HOME', 'EVENTS', 'ARTICLES', 'RESOURCES', 'COMMITTEE', 'CONTACT']; - const logoHtml = SITE_DATA.logo ? `Logo` : `
Σ
`; @@ -389,23 +401,20 @@ function renderHeader() { - -
-
- ${state.menuOpen ? `
@@ -434,13 +443,11 @@ function renderView() { } } - function renderHome() { return `
-
@@ -459,16 +466,13 @@ function renderHome() {
-

${t('hero_title')}
${t('hero_highlight')}

-

- ${t('hero_desc')} -

+

${t('hero_desc')}

-
-
@@ -499,10 +501,22 @@ function renderHome() { function renderEvents() { return `
+
+ ${CLUB_PHOTOS.map((src, idx) => ` +
+ Club Activity +
+ ${getLang(DICTIONARY.activities)} +
+
+ `).join('')} +
+

${t('events')}

${getLang(SITE_DATA.events)}

+
${EVENTS.map(event => `
@@ -513,38 +527,26 @@ function renderEvents() {
${getLang(event.type)} -
- ${ICONS.clock} ${getLang(event.time)} -
+
${ICONS.clock} ${getLang(event.time)}

${getLang(event.title)}

${getLang(event.desc)}

-
- ${ICONS.location} ${getLang(event.location)} -
+
${ICONS.location} ${getLang(event.location)}
-
- ${event.link ? ` - - ${t('register')} + +
+ ${event.banner ? ` + + ${getLang(DICTIONARY.view)} - ` : ` - - `} + ` : ''} +
`).join('')}
- -
-

${getLang(SITE_DATA.host)}

-

${getLang(SITE_DATA.encouragement)}

- -
`; } @@ -555,7 +557,7 @@ function renderArticles() {

${t('articles')}

${ARTICLES.map(article => ` -
+
Article
@@ -574,7 +576,6 @@ function renderArticles() {
`).join('')}
-

${t('article_prompt')}

- -
${getLang(article.content)}
@@ -714,7 +713,7 @@ function initMathAnimation() { let t = 0; const labels = [ "$$ x=A\\sin(at+\\delta), y=B\\sin(bt) $$", - "$$ r = e^{\\sin\\theta} - 2\\cos(4\\theta) $$", + "$$ r = e^{\\sin\\theta} - 2\\cos(4\\theta) + \\sin^5(\\frac{2\\theta - \\pi}{24})$$", "$$ z = \\sin(x^2 + y^2) $$" ]; @@ -768,5 +767,4 @@ function initMathAnimation() { mathAnimationId = requestAnimationFrame(animate); } -window.onpopstate = (e) => e.state && navigate(e.state.view); init();