Thos aakritiyon ko samajhna: profile, drishya aur isometric chitra
Short mein jawab
Thos aakritiyon ko samajhna yaani unhe man mein dekhna aur kaagaz par dikhaana. Thos ka profile, ek drishti-bindu se uski rekha, jagah badalne par badalta hai. Prakshep har bindu ko seedha tal par girata hai; saamne, upar aur bagal ke drishya milkar thos batate hain. Isometric prakshep mein cube ke saare kinaare barabar dikhte hain.
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Man mein banaana
Kuch bhi banaane se pehle use man mein dekho. Aksharon ko man mein dekhkar apna naam ulta padho. Ek kaalpanik varg ke chaaron kone kaato, har kaat do padosi bhujaaon ke madhya-binduon ko jode: ek chhota, tircha varg bachta hai, aur chaaron kone ke tribhuj milkar usi size ka doosra varg banaate hain. Samabahu tribhuj ke kone tihaai nishaanon par kaato to niyamit shatbhuj bachta hai; varg ke saath yahi karo to ashtabhuj bachta hai.
Profile drishti-bindu ke saath badalta hai
Thos ko dekhne par hum uska profile dekhte hain, yaani us jagah se uski baahari rekha. Haathi saamne, bagal aur upar se teen bilkul alag rekhaayein deta hai, aur saade thos bhi aisa karte hain. Cylinder bagal se aayat aur upar se vritt dikhta hai; cone tribhuj aur vritt; tribhujiya prism aayat aur tribhuj; baalti jaisa aakaar samlamb chaturbhuj aur vritt. Ek hi jodi profile par ek se zyada thos fit ho sakte hain.
Falak, kinaare aur sheersh
Samtal falak wale thos gine ja sakte hain. Cube ke 8 sheersh, 12 kinaare aur 6 falak hain. Prism ke do aamne-saamne falak sarvaangsam bahubhuj hote hain jo samaantar chaturbhujon se jude hain; n-bhuja siron ke saath iske n + 2 falak, 3n kinaare aur 2n sheersh hain. Pyramid ka n-bhuja aadhaar ek apex se juda hota hai; iske n + 1 falak, 2n kinaare aur n + 1 sheersh hain. Tribhujiya pyramid ko tetrahedron bhi kehte hain.
Prakshep
Kisi bindu P ka tal par prakshep wo bindu O hai jahan P se nikli rekha tal se samkon par milti hai. Vastu ke har bindu ka prakshep milkar uska prakshep banta hai. Rekha ka prakshep rekha se kabhi lamba nahi hota, kyunki rekha ek samkon tribhuj ka karn hai jiski ek bhuja prakshep hai; ye barabar tabhi hote hain jab rekha tal ke samaantar ho. Samaantar rekhaayein hamesha samaantar rekhaaon mein prakshipt hoti hain, isliye samaantar chaturbhuj ka prakshep hamesha samaantar chaturbhuj (ya kinaare se, rekhakhand) hota hai. Deewar par seedhi padti dhoop ki parchhaaiyaan lagbhag prakshep hi hain.
Saamne, upar aur bagal ke drishya
Kyunki kai vastuon ka ek hi prakshep hota hai, engineer samkon par teen tal lete hain: khade tal par saamne ka drishya, letay tal par upar ka drishya aur bagal ke tal par bagal ka drishya. Drishyon se thos banaane ke liye upar ke drishya se dekho ki dher kahan khade hain, phir saamne ke drishya se har column ka, aur bagal ke drishya se har pankti ka sabse ooncha dher padho.
Isometric chitra
Cube ko ek kone par santulit karke seedha neeche prakshipt karo to saare 12 kinaare ek hi lambaai ke aate hain: ye isometric prakshep hai, ek niyamit shatbhuj. Aise shatbhujon se samtal bharne par isometric kaagaz banta hai, jiski teen dishaon ki rekhaayein lambaai, gehraai aur oonchaai ke liye hain. In dishaon mein ikaiyaan ginte hue kinaara dar kinaara thos banao; ye sahi dikhte hain kyunki samaantar kinaare samaantar rehte hain aur barabar kadam barabar rehte hain.
Aur: fractal kya hai, thos aakritiyon ke net, chapter ke notes aur NCERT solutions.
Practice karo
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Kis thos ka ek profile aayat aur doosra vritt hota hai?
Jawab dekho
Jawab: (b) cylinder
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Panchbhujiya pyramid ke kitne kinaare hote hain?
Jawab dekho
Jawab: (c) 10
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Samaantar chaturbhuj ka prakshep ho sakta hai:
Jawab dekho
Jawab: (b) samaantar chaturbhuj ya rekhakhand
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10-bhuja prism ke kitne falak, kinaare aur sheersh hain?
Jawab dekho
Jawab: 12 falak (2 sire + 10 bagal ke), 30 kinaare (har sire par 10 + unhe jodne wale 10) aur 20 sheersh (har sire par 10).
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Kone par santulit cube upar se niyamit shatbhuj kyon dikhta hai?
Jawab dekho
Jawab: Lamba vikarn khada hone par cube ek-tihaai chakkar ghumaane par waisa hi dikhta hai, isliye har kinaara utna hi jhuka hai aur utni hi lambaai mein prakshipt hota hai. Rekha chhe barabar kinaaron aur barabar konon ki banti hai: niyamit shatbhuj.
Students ke sawal
Thos ke saamne, upar aur bagal ke drishya kya hain?
Ye ek-doosre se samkon par teen talon par uske prakshep hain: saamne ke khade tal par front view, neeche ke letay tal par top view, aur bagal ke tal par side view. Milkar ye thos batate hain, jabki koi ek drishya kai thoson par fit ho sakta hai.
Isometric prakshep kya hai?
Ye aisa drishya hai jismein cube ke saare kinaare ek hi lambaai mein prakshipt hote hain; Greek mein ‘isometric’ ka matlab ‘barabar maap’ hai. Ek kone par santulit cube upar se dekhne par yahi deta hai: niyamit shatbhuj. Shatbhujon ki tiling se isometric grid kaagaz banta hai, jis par lambaai, gehraai aur oonchaai ke saath thos banaate hain.
Cube ka prakshep kaun se aakaar bana sakta hai?
Use kaise ghumaaya gaya hai uspar nirbhar: varg (falak saamne), aayat (ek kinaare ke charon or jhuka), ya shatbhuj (aur tarah se jhuka), jo kone par santulit hone par niyamit hota hai.
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