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13.
• 1897 gÀ°è
eÉ.eÉ xÁªÀÄì£ï £Àqɹ «¸Àdð£Á £À½PÉ ¥ÀæAiÉÆÃUÀ ¢AzÀ PÁåxÉÆÃqï QgÀtUÀ¼ÀÄ, CªÀÅUÀ¼À ®PÀëtUÀ½AzÀ ¥ÀgÀªÀiÁtÄUÀ¼À°è IÄuÁ«zÀÄåzÀA±À EgÀĪÀ E¯ÉPÁÖç£ïUÀ¼À£ÀÄß PÀAqÀÄ»rzÀgÀÄ.
14.
• 15 cm
GzÀÝ ªÀÄvÀÄÛ 3 cm ªÁå¸ÀzÀ UÁf£À «¸Àdð£Á£À½PÉAiÀÄ JgÀqÀÄ vÀÄ¢UÀÄ ¯ÉÆúÀzÀ «zÀÄåzÁUÀæ C¼ÀªÀr¸ÀĪÀgÀÄ. • £À½PÉAiÀÄ M¼ÀV£À MvÀÛqÀ PÀrªÉÄ ªÀiÁr ºÉaÑ£À «¨sÀªÁAvÀgÀ ¥ÀæAiÉÆÃV¸ÀĪÀgÀÄ. • zsÀ£ÁUÀæzÀ vÀÄ¢AiÀÄÄ ºÀ¹gÀÄ ¨É¼ÀQ¤AzÀ «Ä£ÀÄUÀ¯ÁgÀA©ü¹vÀÄ. • IÄuÁUÀæ¢AzÀ ºÉÆgÀºÉÆ«ÄäzÀ QgÀtUÀ¼ÀÄ UÁf£À £À½PÉAiÀÄ ªÀįÉäöÊUÉ §rzÀÄ ºÀ¹gÀÄ §tÚPÉÌ PÁgÀtªÁ¬ÄvÀÄ. • F QgÀtUÀ¼À£ÀÄß PÁåxÉÆÃqï QgÀtUÀ¼ÀÄ J£ÀÄߪÀgÀÄ.
15.
• ¥ÀgÀªÀiÁtÄ«£À°è PÉêÀ®
E¯ÉPÁÖç£ï UÀ¼ÀµÉÖ E¢ÝzÀgÉ, ¥ÀgÀªÀiÁtĪÀÅ IÄt«zÀÄåzÀA±À DVgÀ¨ÉÃPÀ®èªÉ? • zÀæªÀåªÀÅ ¸ÀºÀ IÄt«zÀÄåzÀA±À DVgÀ¨ÉÃPÀ®èªÉ? ? • DzÀgÉ, • zÀæªÀåªÀÅ vÀl¸ÀܪÁVzÉ...... • ºÉÃUÉ????
16.
• 1886 gÀ°è
UÉÆïïعÖçÃ£ï «¸Àdð£Á £À½PÉAiÀÄ°è gÀAzsÀæAiÀÄÄvÀ IÄuÁUÀæ §¼À¹ ¥ÀæAiÉÆÃUÀ £ÀqɹzÀgÀÄ. • IÄuÁUÀæ QgÀtUÀ¼ÀÄ ZÀ°¸ÀĪÀ ¢QÌUÉ «gÀÄzÀݪÁV ZÀ°¸ÀĪÀ QgÀtUÀ¼À£ÀÄß ¥ÀqÉzÀgÀÄ. • CªÀÅUÀ¼ÀÄ zsÀ£À «zÀÄåzÀA±À ¨sÀjvÀ PÀtUÀ½AzÀ DVgÀĪÀÅzÀjAzÀ zsÀ£ÁUÀæ QgÀtUÀ¼ÀÄ JAzÀgÀÄ. • zsÀ£ÁUÀæ QgÀtUÀ¼ÀÄ ¨sÁgÀªÁzÀ PÀtUÀ¼ÁVgÀĪÀÅzÀjAzÀ «ZÀ®£ÉAiÀÄÄ IÄuÁUÀæ QgÀtUÀ½UÉ ºÉÆð¹zÀgÉ vÀÄA§ PÀrªÉÄ. • F PÀtUÀ¼À£ÀÄß ¥ÉÆæÃl£ï J£ÀÄߪÀgÀÄ. • ¥ÉÆæÃl£ï DªÉñÀ +1. • MAzÀÄ ¥ÉÆæÃl£ï gÁ²AiÀÄÄ 1840 E¯ÉPÁÖç£ïUÀ¼À gÁ²UÉ ¸ÀªÀÄ.
17.
• ¥ÀgÀªÀiÁtĪÀ£À°è ¥ÉÆæÃmÁ£ï
ªÀÄvÀÄÛ E¯ÉPÁØç£ï UÀ¼ÀÄ KPÀgÀÆ¥ÀªÁV ºÀAaPÉ DVªÉ JAzÀÄ ¨sÁ«¸À¯ÁVvÀÄÛ. • 1911gÀ°è gÀÄzÀgï ¥ÉÆÃqïð £ÀqɹzÀ ¥ÀæAiÉÆÃUÀªÀÅ ¥ÀgÀªÀiÁtĪÀ£À°è ¥ÉÆæÃmÁ£ï ªÀÄvÀÄÛ E¯ÉPÁØç£ï ºÀAaPÉAiÀÄ avÀætªÀ£Éß §zÀ¯Á¬Ä¹vÀÄ.
18.
• gÀÄzÀgï ¥ÉÆÃqïð
¥ÀæAiÉÆÃUÀ: • zsÀ£À DªÉñÀ PÀtUÀ¼ÁzÀ D¯ÁáPÀtªÀ£ÀÄß ¥À槮 ªÉÃUÀ¢AzÀ a£ÀßzÀ vɼÀÄ ºÁ¼ÉAiÀÄ ªÉÄÃ¯É C¥ÀླྀÀĪÀAvÉ ªÀiÁrzÀgÀÄ. 1. ºÉaÑ£À D¯ÁáPÀtUÀ¼ÀÄ a£ÀßzÀ ºÁ¼ÉAiÀÄ ªÀÄÆ®PÀ ºÁzÀÄ ºÉÆÃzÀªÀÅ. 2. PÉ®ªÀÅ D¯ÁáPÀtUÀ¼ÀÄ ªÀÄÆ® ¥ÀxÀ¢AzÀ «±Á®PÉÆãÀzÀ°è «ZÀ®£É ºÉÆA ¢zÀªÀÅ. 3. PÉêÀ® PÉ®ªÀÅ D¯ÁáPÀtUÀ¼ÀÄ §AzÀ zÁjAiÀÄ°è »A¢gÀÄVzÀªÀÅ.
19.
20.
• gÀÄzÀgï ¥ÉÆÃqïð
¥ÀæAiÉÆÃUÀzÀ ¤tðAiÀÄ: • zsÀ£À DªÉñÀ PÀtUÀ¼ÀÄ ¥ÀgÀªÀiÁtÄ«£À PÉÃAzÀæ ¨sÁUÀzÀ°è §A¢ü¸À®ànÖªÉ. EzÀ£ÀÄß £ÀÆåQèÃAiÀĸï(©Ãd PÉÃAzÀæ) J£ÀÄߪÀgÀÄ. F PÉÃAzÀæªÀÅ E¯ÉPÁÖç£ïUÀ½AzÀ ¸ÀÄvÀÄÛªÀjAiÀÄ®ànÖªÉ. • ¥ÀgÀªÀiÁtÄ«£À UÁvÀæPÉÌ ºÉÆð¹zÀgÉ ©ÃdPÉÃAzÀæzÀ UÁvÀæ vÀÄA§ aPÀÌzÀÄ. • ¥ÀgÀªÀiÁtÄ«£À ºÉaÑ£À zÀæªÀå gÁ²AiÀÄÄ ©Ãd PÉÃAzÀæzÀ°è PÉÃA¢æPÀÈvÀªÁVzÉ. • ©ÃdPÉÃAzÀæªÀÅ zsÀ£À«zÀÄåzÁªÉñÀ ºÉÆA¢zÀÄÝ CzÀgÀ ¥ÀgÀªÀiÁtªÀÅ ¨ÉÃgÉ ¨ÉÃgÉ zsÁvÀÄUÀ½UÉ ¨ÉÃgÉ ¨ÉÃgÉAiÀÄVgÀÄvÀÛzÉ. • «zÀÄåvï vÀl¸ÀÜ ¥ÀgÀªÀiÁtÄ«£À ©ÃdPÉÃAzÀæzÀ ºÉÆgÀV£À E¯ÉPÁÖç£ïUÀ¼À ¸ÀASÉåAiÀÄÄ ©ÃdPÉÃAzÀæzÀ M¼ÀVgÀĪÀ zsÀ£À «zÀÄåzÀA±ÀzÀ PÀtUÀ½UÉ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
21.
• ¥ÀgÀªÀiÁtÄ«£À £ÀÆåQèÃAiÀĸï
gÁ²AiÀÄÄ ¥ÉÆæÃmÁ£ïUÀ¼À MlÄÖ gÁ²VAvÀ ºÉaÑgÀĪÀÅzÀÄ. • EzÀjAzÀ ¥ÀgÀªÀiÁtÄ«£À°è ¥ÉÆæÃmÁ£ïUÀ¼À zÀæªÀågÁ²UÉ ¸ÀªÀÄ£ÁzÀ vÀl¸ÀÜ PÀt EgÀ§ºÀÄzÉAzÀÄ gÀÄzÀgï ¥ÉÆÃqïð ªÀÄÄ£ÀÆìa¹zÀÝgÀÄ. • 1932 gÀ°è eÉêÀÄì ZÁqï«Pï vÀl¸ÀÜ PÀtUÀ¼ÁzÀÀ £ÀÆåmÁæ£ï EgÀÄ«PÉAiÀÄ£ÀÄß ¥ÀæAiÉÆÃVPÀªÁV vÉÆÃj¹zÀgÀÄ. • £ÀÆåmÁæ£ïUÀ¼À zÀæªÀågÁ²AiÀÄÄ ¥ÉÆæÃmÁ£ïUÉ ¸ÀªÀĪÁVgÀÄvÀÛªÉ.
22.
• ªÀÄÄSÁåA±ÀUÀ¼ÀÄ: 1. ¥ÀgÀªÀiÁtĪÀÅ
3 ªÀÄÆ®¨sÀÆvÀ PÀtUÀ½AzÁVzÉ. 2. CªÀÅUÀ¼ÉAzÀgÉ, ¥ÉÆæÃmÁ£ï, £ÀÆåmÁæ£ï, ªÀÄvÀÄÛ E¯ÉPÁÖç£ï. 3. ¥ÉÆæÃmÁ£ï zsÀ£À DªÉñÀ ¨sÀjvÀ PÀt + ve . 4. £ÀÆåmÁæ£ï «zÀÄåvï DªÉñÀ gÀ»vÀ PÀt. 5. E¯ÉPÁÖç£ï IÄt DªÉñÀ ¨sÀjvÀ PÀt -ve. 6. «zÀÄåvï vÀl¸ÀÜ ¥ÀgÀªÀiÁtÄ«£À°è ¥ÉÆæÃmÁ£ï ¸ÀASÉåUÉ ¸ÀªÀÄ£ÁV E¯ÉPÁÖç£ïUÀ½gÀÄvÀÛªÉ. 7. £ÀÆåmÁæ£ïUÀ¼À zÀæªÀågÁ²AiÀÄÄ ¥ÉÆæÃmÁ£ïUÉ ¸ÀªÀĪÁVgÀÄvÀÛªÉ. 8. E¯ÉPÁÖç£ï zÀæªÀågÁ²AiÀÄÄ ¤®ðQë¸ÀĪÀµÀÄÖ PÀrªÉÄ EgÀÄvÀÛzÉ..
23.
• ¥ÀgÀªÀiÁtÄ ¸ÀASÉå: •
¥ÀgÀªÀiÁtÄ«£À°ègÀĪÀ MlÄÖ ¥ÉÆæÃl£ï ¸ÀASÉå (Z). • ¥ÀgÀªÀiÁtÄ gÁ² ¸ÀASÉå: • ¥ÀgÀªÀiÁtÄ«£À°ègÀĪÀ MlÄÖ ¥ÉÆæÃl£ï ªÀÄvÀÄÛ £ÀÆåmÁæ£ïUÀ¼À ¸ÀASÉå (A). • ZXA
24.
• 1913 gÀ°è
¤Ã¯ïì ¨ÉÆÃgï ¥ÀgÀªÀiÁtÄ ªÀiÁzÀjAiÀÄ£ÀÄß ¥Àæ¸ÀÄÛvÀ ¥Àr¹zÀgÀÄ. • ¥ÀgÀªÀiÁtÄ ©ÃdPÉÃAzÀæzÀ ¸ÀÄvÀÛ E¯ÉPÁÖç£ïUÀ¼ÀÄ ¤¢ðµÀÖªÁzÀ ªÀÈvÁÛPÁgÀzÀ ¥ÀxÀzÀ°è ¸ÀÄvÀÄÛvÀÛªÉÀ. • F ¥ÀxÀUÀ¼À£ÀÄß PÀPÉëUÀ¼ÀÄ J£ÀÄߪÀgÀÄ. • ©ÃdPÉÃAzÀæzÀ CvÀåAvÀ ¸À«ÄÃ¥ÀzÀ ¥ÀæxÀªÀÄ PÀPÉë K. £ÀAvÀgÀzÀªÀÅ L,M,N,O…… • ¥ÀæwAiÉÆAzÀÄ PÀPÉëAiÀÄÄ UÀjµÀÖ 2n2 E¯ÉPÁÖç£ï ºÉÆA¢gÀÄvÀÛªÉ. • K = 2n2 = 2(1)2 = 2. • L = 2n2 = 2(2)2 = 8. • M = 2n2 = 2(3)2 = 18
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