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Simple Math in Action

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Home and Church Note: Please click on the images to see them. Today is the feast of St. Sebastian's Church. It is one of the most celebrated feasts in our neighbourhood. Apart from colourful fireworks, sky lanterns were also sent. I was at home then. After the lanterns got to some level, almost all of them turned off. I wanted to calculate that height. As the above figure shows church and our house are 746.02m apart (Google Earth helped me there). I found the angle of inclination of that height. That was about \(45^o\). Assuming the lanterns travel straight up and the church and our house are at the same level, the height the lantern goes up would be about 750 meters. That height! Our village is close to sea. So maybe a ship far away might see those lanterns. What would be the maximum distance of a ship which might have seen those? Google tells me that the diameter of earth is 12742 km. We have to remember that this value is an average and Eart...
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Sinhala LaTex

LaTeX කියන්නේ ගුණාත්මකභාවයෙන් ඉහළ ලේඛන හදන්න පාවිච්චි කරන්න පුළුවන් programming language 1ක්. අපේ ලේඛනයේ ගොඩක් ගණිත සමිකරණ, වගු, ප්‍රස්තාර රුපසටහන් එහෙම තියනවනම්  LaTex පාවිච්චි කරන එක අන්තර්ජාතිකව පිළිගත් ප්‍රමිතියක්. ඔය පර්යේෂණ පත්‍රිකා එහෙම ලියන්නත් ගොඩක් LaTex යොදා ගන්නවා. LaTex වලම දිගුවක් විදිහට හඳුන්වන්න පුළුවන් XeLaTex unicode support කරන නිසා සිංහලෙනුත් LaTex ලිපි ලේඛන compile කරන්න පුළුවන් වෙලා තියනවා. පහල තියන්නේ සරල නිදසුනක්: LaTex කේතය PDF ගොනුව

A Graph Theory Problem

Suppose there are N people. They are trying to make a way to have a communication system such that all N gets the information one gets, spending least time and cost. Assume that the only way of communication is via telephone. Assume 1 person can make only n (<N) phone calls a day. Each phone call takes exactly t minutes (N  t < 1 day). What is the optimal time taken for all N to know the information?
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A Song

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Himin Sare Piya wida is a song I love, totally because its unique music composed by one of Sri Lanka's most brilliant music minds, Khemadasa. Half an year ago I tried translating the song into English. This song is filled with metaphors and similes...! So I had to avoid direct translations. This was the moment I felt how hard translating something is. I tried my best to give the idea... Bear with me with this. Hope you'll enjoy. Gently you unfold your wings Escape the thoughts as birds From the silky blankets Of the feathery divan If it's a flower, let it be so Along it's tenderness and beauty If it's a pond, let it be so Along its silky blue freshness Carried away by your soothing aroma The horizons of my dreams widen My heart is intoxicated by your tender whispers Which releases the windows of my chamber