ꯊꯨꯅꯥ ꯍꯟꯊꯕ
ꯁ꯭ꯄꯤꯟꯒꯤ ꯑꯁꯦꯡꯕꯗ ꯈꯪꯖꯤꯅꯕ ꯌꯥꯕ ꯁꯔꯨꯛ ꯑꯃꯈꯛ꯫
ꯇ꯭ꯔꯦꯛꯇ ꯕꯣꯜ ꯊꯨꯅꯥ ꯍꯟꯊꯕ ꯑꯁꯤ ꯐ꯭ꯔꯤꯛꯁꯟ ꯑꯃꯁꯨꯡ ꯗ꯭ꯔꯦꯒꯅ ꯂꯦꯞꯊꯣꯀꯄ ꯃꯤꯟꯅꯕ ꯀꯔꯚ ꯑꯃꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅꯥ ꯆꯠꯂꯤ꯫ ꯀꯣꯏꯕ ꯈꯔꯒꯤ ꯃꯇꯃꯗꯒꯤ ꯇꯥꯕꯒꯤ ꯃꯇꯝ ꯑꯗꯨ ꯆꯦꯛꯀꯟꯗ ꯑꯃꯒꯤ ꯁꯔꯨꯛ ꯈꯔꯒꯤ ꯃꯅꯨꯡꯗ ꯈꯪꯖꯤꯅꯕ ꯌꯥꯏ꯫ ꯃꯇꯨꯡꯒꯤ ꯊꯥꯗꯣꯛꯄꯅ ꯆꯨꯝꯕ ꯑꯗꯨꯒꯤ ꯃꯔꯛ ꯌꯥꯝꯅ ꯃꯥꯡꯍꯜꯂꯤ꯫
ꯃꯣꯗꯦꯜ
ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯍꯣꯡꯗꯕ ꯁꯔꯨꯛ a (ꯔꯣꯂꯤꯡ ꯐ꯭ꯔꯤꯛꯁꯟ) ꯑꯃꯁꯨꯡ ꯊꯨꯅꯥꯒꯥ ꯃꯥꯟꯅꯅ ꯍꯦꯅꯒꯠꯂꯀꯄ ꯁꯔꯨꯛ b·v (ꯅꯨꯡꯁꯤꯠꯀꯤ ꯗ꯭ꯔꯦꯒ ꯑꯃꯁꯨꯡ ꯊꯨꯅꯥꯗ ꯃꯈꯥ ꯄꯣꯟꯕ ꯃꯥꯡꯕꯁꯤꯡ) ꯅ ꯊꯨꯅꯥ ꯍꯟꯊꯍꯜꯂꯤ ꯍꯥꯌꯅ ꯂꯧꯕꯤꯌꯨ: dv/dt = −(a + bv)꯫ ꯃꯁꯤꯒꯤ ꯄꯥꯎꯈꯨꯝ ꯑꯁꯤ ꯀ꯭ꯔꯤꯇꯤꯀꯦꯜ ꯇꯥꯕꯒꯤ ꯊꯨꯅꯥꯒꯤ ꯃꯥꯏꯀꯩꯗ ꯑꯦꯛꯁꯄꯣꯅꯦꯟꯁꯤꯌꯦꯜ ꯃꯑꯣꯡꯗ ꯅꯛꯂꯛꯄꯅꯤ꯫ ꯃꯔꯝ ꯑꯗꯨꯅ ꯂꯦꯞꯀꯤ ꯃꯇꯝ T = 2πr/v ꯑꯁꯤ ꯂꯦꯞ ꯈꯨꯗꯤꯡꯗ ꯍꯦꯅꯒꯠꯂꯀꯄ ꯈꯔꯅ ꯁꯥꯡꯂꯛꯏ꯫ ꯑꯍꯥꯅꯕ ꯂꯦꯞ ꯈꯔꯗꯒꯤ a ꯑꯃꯁꯨꯡ b ꯐꯤꯠ ꯇꯧꯔꯕꯗ ꯂꯦꯃꯍꯧꯔꯤꯕ ꯂꯦꯞꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯇꯥꯕꯒꯤ ꯃꯇꯝ ꯈꯪꯏ꯫ ꯃꯐꯝ ꯑꯁꯤꯗ ꯑꯉꯀꯄ ꯀꯔꯤꯁꯨ ꯂꯩꯇꯦ; ꯃꯁꯤ ꯇ꯭ꯔꯦꯛ ꯑꯃꯗ ꯂꯩꯕ ꯕꯣꯜ ꯑꯃꯗ ꯁꯤꯖꯤꯟꯅꯕ ꯑꯍꯥꯅꯕ ꯆꯍꯤꯒꯤ ꯃꯦꯀꯥꯅꯤꯛꯁꯅꯤ꯫
ꯈꯪꯖꯤꯅꯕ ꯑꯁꯤꯅ ꯀꯔꯤ ꯄꯤꯕꯒꯦ
ꯆꯦꯛꯀꯟꯗ 0.2 ꯒꯤ ꯃꯅꯨꯡꯗ ꯆꯨꯝꯕ ꯇꯥꯕꯒꯤ ꯃꯇꯝ ꯑꯃꯥ, ꯆꯦꯛꯀꯟꯗ ꯈꯨꯗꯤꯡꯗ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 15 ꯒꯤ ꯔꯣꯇꯔꯒꯤꯈꯨꯠꯂꯥꯏꯔꯣꯇꯔꯄꯣꯀꯦꯠꯁꯤꯡ ꯄꯨꯔꯛꯄ ꯆꯛꯔꯒꯤ ꯀꯣꯏꯕ ꯁꯔꯨꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯨꯅꯥꯒꯥ ꯂꯣꯌꯅꯅ, ꯇꯥꯕ ꯃꯐꯝꯒꯤ ꯃꯈꯥꯗ ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯗꯨ ꯄꯣꯀꯦꯠ ꯑꯍꯨꯝ ꯃꯇꯧꯒꯤ ꯃꯅꯨꯡꯗ ꯊꯤꯗꯣꯀꯏ꯫ ꯃꯁꯤ ꯈꯪꯖꯤꯅꯕꯒꯤ ꯈꯨꯠꯂꯥꯏ ꯑꯃꯒꯤꯗꯃꯛ ꯐꯕ ꯄꯥꯎꯅꯤ꯫ ꯐꯠꯇꯕ ꯄꯥꯎꯗꯤ ꯃꯇꯨꯡꯗ ꯕꯣꯜ ꯑꯗꯨꯅ ꯑꯦꯞꯔꯟꯈꯨꯠꯂꯥꯏꯑꯦꯞꯔꯟꯕꯣꯜ ꯇ꯭ꯔꯦꯛ ꯑꯃꯁꯨꯡ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯈꯣꯡꯕꯥꯟ ꯃꯐꯝ, ꯃꯐꯝ ꯑꯗꯨꯗ ꯗꯤꯐ꯭ꯂꯦꯛꯇꯔꯁꯤꯡ ꯂꯩ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯥꯟꯊꯣꯀꯏ, ꯗꯤꯐ꯭ꯂꯦꯛꯇꯔꯈꯨꯠꯂꯥꯏꯗꯤꯐ꯭ꯂꯦꯛꯇꯔꯇꯥꯗ꯭ꯔꯤꯕ ꯕꯣꯜ ꯑꯗꯨ ꯁꯟꯗꯣꯛꯍꯟꯕ ꯑꯦꯞꯔꯅꯗ ꯂꯩꯕ ꯃꯦꯇꯦꯂꯒꯤ ꯑꯊꯤꯡꯕꯁꯤꯡꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯀꯦꯅꯨ, ꯗꯥꯏꯃꯟꯗ, ꯄꯤꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯊꯨꯡꯂꯛꯏ ꯑꯃꯁꯨꯡ ꯐ꯭ꯔꯦꯠꯁꯤꯡꯒꯤꯈꯨꯠꯂꯥꯏꯐ꯭ꯔꯦꯠꯆꯛꯔꯗ ꯄꯣꯀꯦꯠ ꯑꯅꯤꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯃꯦꯇꯦꯂꯒꯤ ꯈꯥꯌꯗꯣꯛꯄ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯊꯛꯇ ꯆꯣꯡꯊꯔꯛꯏ, ꯑꯃꯁꯨꯡ ꯑꯔꯣꯏꯕ ꯄꯣꯀꯦꯠ ꯑꯗꯨ ꯄꯣꯀꯦꯠ 20 ꯗꯒꯤ 30 ꯐꯥꯑꯣꯕ ꯄꯥꯛꯂꯕ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯑꯃꯗ ꯁꯟꯗꯣꯀꯏ꯫ ꯇ꯭ꯔꯦꯛ ꯐꯦꯖꯀꯤ ꯆꯨꯝꯕ ꯑꯗꯨ ꯇꯥꯕ ꯐꯦꯖꯀꯤ ꯊꯥꯗꯣꯛꯄꯅ ꯌꯥꯝꯅ ꯃꯥꯡꯍꯜꯂꯤ꯫
ꯀꯔꯤ ꯂꯦꯃꯍꯧꯔꯤꯕꯒꯦ
ꯊꯥꯗꯣꯛꯄꯒꯤ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯑꯗꯨꯗ ꯃꯣꯗ ꯑꯃꯥ ꯂꯩꯔꯕꯗ, ꯍꯥꯌꯕꯗꯤ ꯕꯣꯜ ꯑꯗꯨ ꯔꯦꯟꯗꯝꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯇꯥꯕ ꯄꯣꯀꯦꯠꯀꯤ ꯃꯅꯥꯛꯇ ꯂꯥꯛꯂꯕꯗ, ꯈꯪꯖꯤꯅꯈꯤꯕ ꯄꯣꯀꯦꯠꯀꯤ ꯃꯅꯥꯛꯀꯤ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯕꯦꯠ ꯊꯝꯕꯅ ꯑꯄꯤꯛꯄ ꯑꯦꯖ ꯑꯃꯥ ꯄꯤ꯫ ꯁ꯭ꯃꯣꯜ ꯑꯃꯁꯨꯡ ꯆꯦ (Small and Tse, 2012) ꯅ ꯂꯦꯕꯇ ꯀꯦꯃꯦꯔꯥ ꯑꯃꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯁꯤ ꯊꯥꯖꯈꯤ ꯑꯃꯁꯨꯡ ꯈꯪꯖꯤꯅꯈꯤꯕ ꯁꯦꯛꯇꯔꯗ ꯂꯥꯀꯄꯒꯤ ꯔꯦꯠ ꯑꯁꯤ ꯍꯥꯎꯁ ꯑꯦꯖꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯄꯔꯁꯦꯟꯇ ꯈꯔꯒꯤ ꯑꯦꯖ ꯑꯣꯏꯍꯟꯕ ꯉꯝꯅꯕ ꯋꯥꯡꯏ ꯍꯥꯌꯅ ꯐꯪꯈꯤ꯫ ꯃꯈꯣꯌꯒꯤ ꯐꯤꯚꯃꯁꯤꯡ, ꯃꯊꯛꯇꯒꯤ ꯃꯄꯨꯡ ꯐꯥꯅ ꯎꯕ, ꯈꯉꯂꯕ ꯆꯛꯔ ꯑꯃꯥ, ꯕꯣꯜ ꯊꯥꯗꯣꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯕ, ꯂꯥꯏꯕ ꯇꯦꯕꯜ ꯑꯃꯗ ꯂꯩꯇꯦ꯫
ꯄꯨꯡ ꯑꯃꯗꯒꯤ ꯄꯨꯡ ꯑꯃꯗ ꯀꯔꯤ ꯍꯣꯡꯂꯛꯂꯤꯕꯒꯦ
ꯀꯟꯁ꯭ꯇꯦꯟꯠ ꯑꯅꯤ ꯑꯁꯤ ꯆꯛꯔ ꯑꯃꯒꯤꯗꯃꯛ ꯍꯣꯡꯗꯕ ꯅꯠꯇꯦ꯫ 1970 ꯁꯨꯕꯗ ꯆꯍꯤ ꯀꯌꯥ ꯀꯦꯁꯤꯅꯣ ꯆꯛꯔ ꯑꯃꯒꯤ ꯃꯇꯝ ꯂꯧꯈꯤꯕ ꯌꯨꯗꯦꯃꯟꯁꯤꯡ (Eudaemons) ꯅ ꯊꯨꯅꯥ ꯍꯟꯊꯍꯟꯕꯒꯤ ꯌꯥꯝꯕꯥ ꯁꯔꯨꯛ ꯑꯗꯨ ꯇ꯭ꯔꯦꯛꯅ ꯅꯠꯇꯅ ꯅꯨꯡꯁꯤꯠꯅ ꯇꯧꯏ ꯑꯃꯁꯨꯡ ꯕꯣꯜ ꯑꯗꯨꯁꯨ ꯃꯔꯨꯑꯣꯏ ꯍꯥꯌꯅ ꯐꯪꯈꯤ: ꯇꯦꯐ꯭ꯂꯟ ꯕꯣꯜ ꯑꯃꯅ ꯕꯤꯂꯤꯌꯥꯔꯗ ꯕꯣꯜꯒꯤ ꯀꯝꯄꯣꯖꯤꯠꯇꯒꯤ ꯁꯦꯝꯕ ꯕꯣꯜ ꯑꯃꯗꯒꯤ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯨꯅꯅ ꯊꯨꯅꯥ ꯃꯥꯡꯈꯤ꯫ ꯃꯈꯣꯌꯅ ꯊꯣꯉ ꯑꯃꯥ ꯍꯥꯡꯗꯣꯀꯄꯗ ꯅꯠꯔꯒ ꯅꯨꯡꯁꯤꯠ ꯍꯣꯡꯂꯛꯄꯗ ꯃꯈꯣꯌꯒꯤ ꯈꯪꯖꯤꯅꯕꯁꯤꯡ ꯄꯨꯡ ꯈꯨꯗꯤꯡꯗ 5 ꯗꯒꯤ 10% ꯆꯨꯃꯗ꯭ꯔꯕꯥ ꯎꯈꯤ, ꯃꯔꯃꯗꯤ ꯏꯁꯤꯡ ꯌꯥꯎꯕ ꯅꯠꯔꯒ ꯌꯥꯡꯕ ꯅꯨꯡꯁꯤꯠꯅ ꯕꯣꯜ ꯑꯗꯨꯒꯤ ꯊꯨꯅꯥ ꯊꯨꯅꯅ ꯍꯟꯊꯍꯜꯂꯤ꯫ ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌꯒꯤ ꯄ꯭ꯔꯣꯒ꯭ꯔꯥꯃꯅ ꯕꯣꯜ ꯑꯗꯨꯒꯤ ꯊꯨꯅꯥ ꯍꯟꯊꯕꯒꯤ ꯔꯦꯠ ꯑꯃꯁꯨꯡ ꯇ꯭ꯔꯦꯛ ꯊꯥꯗꯣꯀꯄꯒꯤ ꯊꯨꯅꯥꯒꯤꯗꯃꯛ ꯇꯣꯉꯥꯟꯅ ꯁꯦꯇꯤꯡ ꯊꯝꯃꯤ, ꯑꯃꯁꯨꯡ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯗꯨꯅ ꯇꯦꯕꯜ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯈꯪꯖꯤꯅꯕꯁꯤꯡ ꯆꯨꯃꯗ꯭ꯔꯕꯥ ꯍꯧꯔꯀꯄ ꯃꯇꯝ ꯈꯨꯗꯤꯡꯗ ꯑꯅꯤꯃꯛ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯁꯦꯠ ꯇꯧꯈꯤ꯫
ꯂꯦꯕꯅ ꯃꯁꯤ ꯀꯔꯤꯒꯤ ꯇꯥꯀꯄꯤꯔꯤꯕꯅꯣ
ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯅ ꯇꯧꯅꯕ ꯅꯠꯇꯦ꯫ ꯁꯥꯟꯅꯕ ꯑꯁꯤꯒꯤ ꯔꯦꯟꯗꯝ ꯑꯣꯏꯕ ꯑꯗꯨ ꯑꯁꯦꯡꯕꯗ ꯀꯔꯤꯅ ꯁꯦꯃꯒꯠꯂꯤꯕꯒꯦ ꯍꯥꯌꯕ ꯎꯠꯅꯕꯅꯤ: ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯃꯃꯥꯡꯗ ꯕꯦꯠ ꯊꯤꯡꯖꯤꯟꯕ ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯀꯣꯏꯕꯒꯤ ꯃꯁꯤꯡꯅ ꯉꯥꯀꯊꯣꯀꯄ ꯈꯪꯖꯤꯅꯕ ꯌꯥꯕ ꯐꯦꯖ ꯑꯃꯥ, ꯑꯃꯁꯨꯡ ꯗꯤꯐ꯭ꯂꯦꯛꯇꯔꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯅꯦꯝꯕ ꯐ꯭ꯔꯦꯠꯁꯤꯡꯅ ꯉꯥꯀꯊꯣꯀꯄ ꯀꯦꯑꯣꯇꯤꯛ ꯐꯦꯖ ꯑꯃꯥ꯫ ꯃꯁꯤ ꯈꯉꯕ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ 2.70% ꯑꯁꯤ ꯀꯔꯤꯒꯤ ꯉꯥꯀꯊꯣꯛꯂꯤꯕꯅꯣ ꯍꯥꯌꯕꯗꯨ ꯈꯉꯏ꯫
ꯍꯤꯁꯥꯕ ꯑꯗꯨ ꯅꯁꯥꯃꯛꯅ ꯇꯧꯕ
ꯀꯔꯤꯒꯨꯝꯕ ꯁ꯭ꯇ꯭ꯔꯤꯝ ꯑꯃꯗ ꯕꯣꯜ ꯑꯗꯨꯅ ꯗꯤꯐ꯭ꯂꯦꯛꯇꯔ ꯑꯃꯥ ꯂꯥꯟꯊꯣꯀꯄꯒꯤ ꯃꯇꯝ ꯂꯦꯞ ꯑꯍꯨꯝ ꯂꯧꯕꯤꯌꯨ ꯑꯃꯁꯨꯡ ꯃꯈꯥ ꯆꯠꯊꯕꯤꯌꯨ; ꯃꯇꯝ ꯌꯥꯝꯅ ꯅꯍꯥꯛ ꯇꯥꯕ ꯑꯗꯨꯗꯒꯤ ꯂꯦꯞ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯂꯩꯒꯅꯤ, ꯃꯁꯤꯅꯤ ꯈꯪꯖꯤꯅꯕ ꯌꯥꯕ ꯐꯦꯖ ꯑꯗꯨ ꯐꯣꯡꯗꯣꯀꯈꯤꯕ ꯃꯇꯨꯡ ꯏꯟꯅꯥ ꯊꯕꯛ ꯇꯧꯕꯗꯨ꯫ ꯃꯇꯨꯡꯗ ꯇꯥꯕ ꯃꯐꯝꯒꯤ ꯃꯈꯥꯗ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯀꯥ ꯃꯔꯤ ꯂꯩꯅꯅ ꯕꯣꯜ ꯑꯗꯨ ꯑꯁꯦꯡꯕꯗ ꯀꯗꯥꯏꯗ ꯂꯥꯛꯂꯤꯕꯒꯦ ꯌꯦꯡꯕꯤꯌꯨ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ ꯌꯥꯡꯈꯩ ꯑꯃꯗ ꯃꯤꯠꯌꯦꯡ ꯊꯝꯕꯤꯌꯨ꯫ ꯃꯤꯠꯌꯦꯡ ꯑꯗꯨ ꯊꯥꯗꯣꯛꯄꯒꯤ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯑꯃꯅꯤ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯒꯤ ꯄꯥꯛ ꯑꯗꯨ “ꯀꯔꯤꯒꯤ ꯃꯁꯤ ꯃꯥꯏꯊꯤꯕ ꯄꯤꯕ ꯌꯥꯗꯕꯅꯣ?” ꯍꯥꯌꯕꯒꯤ ꯄꯥꯎꯈꯨꯃꯅꯤ꯫
ꯐꯣꯔꯃꯨꯂꯥ
ꯋꯥꯍꯪꯁꯤꯡ
ꯅꯠꯇꯦ꯫ ꯐ꯭ꯔꯤꯛꯁꯟ ꯑꯁꯤ ꯃꯩꯐꯨ, ꯏꯁꯤꯡ ꯅꯨꯡꯁꯤꯠ ꯑꯃꯁꯨꯡ ꯁꯣꯛꯄꯒꯥ ꯂꯣꯌꯅꯅ ꯍꯣꯡꯏ꯫ ꯈꯪꯖꯤꯅꯕꯒꯤ ꯈꯨꯠꯂꯥꯏꯁꯤꯡꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯐꯤꯠ ꯇꯧꯏ꯫
ꯑꯍꯨꯃꯅ ꯃꯈꯜ ꯊꯨꯅꯥ ꯈꯪꯖꯤꯅꯕ ꯑꯃꯥ ꯄꯤ; ꯃꯉꯥ ꯅꯠꯔꯒ ꯇꯔꯨꯛꯅ ꯐꯕ ꯑꯃꯥ ꯄꯤ꯫ ꯁ꯭ꯇꯨꯗꯤꯑꯣꯁꯤꯡꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯃꯔꯤꯅ ꯕꯦꯠ ꯊꯝꯅꯕ ꯃꯇꯝ ꯌꯥꯝꯅ ꯂꯦꯃꯍꯧꯗꯦ, ꯑꯃꯁꯨꯡ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯣꯏꯔꯕꯁꯨ ꯕꯦꯠꯁꯤꯡ ꯊꯤꯡꯖꯤꯜꯂꯦ꯫
ꯈꯔꯅꯥ, ꯃꯇꯝ ꯈꯔꯒꯤ ꯑꯣꯏꯅ, ꯈꯨꯠꯂꯥꯏꯁꯤꯡꯒꯥ ꯂꯣꯌꯅꯅ, ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯃꯈꯣꯌ ꯃꯁꯥ ꯍꯣꯡꯗꯣꯀꯄ ꯑꯃꯁꯨꯡ ꯑꯥꯏꯅꯁꯤꯡ ꯂꯥꯛꯠꯔꯤꯉꯩꯗ꯫ ꯑꯦꯗꯚꯥꯟꯇꯦꯖ ꯄ꯭ꯂꯦ ꯌꯦꯡꯕꯤꯌꯨ꯫
ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ
ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫
ꯂꯦꯡꯕ ꯍꯟꯊꯔꯛꯂꯤꯕ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤ ꯊꯣꯔꯞꯀꯤ ꯈꯨꯗꯝ ꯃꯣꯗꯦꯂꯗ, ꯇ꯭ꯔꯦꯛꯇ ꯆꯨꯛ ꯑꯃꯥ ꯀꯣꯏꯕꯗ ꯆꯦꯛꯀꯟꯗ T ꯆꯪꯂꯕꯗꯤ, ꯕꯣꯜ ꯑꯗꯨꯅ ꯇ꯭ꯔꯦꯛ ꯊꯥꯗꯣꯛꯠꯔꯤꯉꯩ ꯃꯃꯥꯡꯗ ꯆꯨꯛ 1/(e^(3T/20) − 1) − 10/3 ꯂꯦꯃꯒꯅꯤ꯫ ꯆꯦꯛꯀꯟꯗ ꯌꯥꯝꯈꯥꯏꯒꯤ ꯆꯨꯛ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯑꯃꯁꯨꯡ ꯆꯦꯛꯀꯟꯗ ꯑꯃꯒꯤ ꯆꯨꯛ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯀꯌꯥ ꯂꯦꯃꯒꯅꯤ? T = 0.8 ꯗ ꯆꯦꯛꯀꯟꯗ 0.012 ꯒꯤ ꯃꯇꯝ ꯂꯥꯟꯅꯕꯅ ꯄ꯭ꯔꯤꯗꯤꯛꯁꯟ ꯑꯗꯨ ꯀꯌꯥ ꯂꯥꯞꯅ ꯍꯣꯡꯍꯜꯂꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯆꯦꯛꯀꯟꯗ ꯌꯥꯝꯈꯥꯏꯒꯤ ꯆꯨꯛ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯆꯨꯛ 9.5 ꯈꯔ ꯑꯃꯁꯨꯡ ꯆꯦꯛꯀꯟꯗ ꯑꯃꯒꯤ ꯆꯨꯛ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ 2.85꯫ ꯃꯇꯝ ꯂꯥꯟꯅꯕ ꯑꯗꯨꯅ ꯄ꯭ꯔꯤꯗꯤꯛꯁꯟ ꯑꯗꯨ ꯆꯨꯛ 0.12 ꯈꯔ, ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 4½ ꯈꯔ ꯍꯣꯡꯍꯜꯂꯤ꯫
T = 0.5: 3T/20 = 0.075 ꯑꯃꯁꯨꯡ e^0.075 ≈ 1.0779, ꯃꯔꯝ ꯑꯗꯨꯅ 1/0.0779 ≈ 12.84, ꯑꯃꯁꯨꯡ 12.84 − 3.33 ≈ 9.51 ꯆꯨꯛ꯫ T = 1: e^0.15 ≈ 1.1618, 1/0.1618 ≈ 6.18, ꯑꯃꯁꯨꯡ 6.18 − 3.33 ≈ 2.85꯫ ꯊꯨꯅ ꯀꯣꯏꯕ ꯆꯨꯛ ꯑꯃꯅ ꯆꯨꯛ ꯀꯌꯥ ꯂꯦꯃꯒꯅꯤ ꯍꯥꯌꯕ ꯇꯥꯛꯏ, ꯑꯃꯁꯨꯡ ꯑꯃꯨꯛ ꯑꯅꯤ ꯂꯦꯡꯕ ꯆꯨꯛ ꯑꯃꯅ ꯁꯔꯨꯛ ꯑꯍꯨꯃꯗ ꯑꯃꯗꯒꯤ ꯍꯟꯊꯅ ꯂꯦꯃꯍꯜꯂꯤ꯫
T = 0.8 ꯗ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯗꯨꯅ ꯆꯨꯛ 4.51 ꯄꯤ; T = 0.812 ꯗ 4.39 ꯄꯤ꯫ ꯆꯦꯛꯀꯟꯗ ꯑꯃꯒꯤ ꯂꯤꯁꯤꯡ ꯁꯔꯨꯛ 12 ꯒꯤ ꯃꯇꯝ ꯂꯥꯟꯅꯕ, ꯕꯣꯜ ꯑꯗꯨꯅ ꯃꯁꯥꯒꯤ ꯄꯥꯛ ꯆꯥꯎꯕ ꯑꯗꯨ ꯀꯣꯏꯕꯗ ꯆꯪꯕ ꯃꯇꯝ ꯈꯔ, ꯄ꯭ꯔꯤꯗꯤꯛꯁꯟ ꯑꯗꯨ ꯆꯨꯛ 0.12 ꯍꯣꯡꯍꯜꯂꯤ: ꯄꯣꯀꯦꯠ 37 ꯂꯩꯕ ꯆꯛꯔꯒꯤ ꯄꯣꯀꯦꯠ 4½ ꯈꯔ꯫ ꯃꯇꯝ ꯂꯥꯟꯅꯕ ꯑꯃꯈꯛ ꯑꯁꯤꯅ ꯕꯣꯜ ꯑꯗꯨꯒꯤ ꯃꯇꯝ ꯂꯦꯞꯄꯒꯤꯗꯃꯛ ꯊꯣꯔꯞꯀꯤ ꯑꯔꯥꯟꯕꯒꯤ ꯕꯖꯦꯠꯅ ꯌꯥꯍꯜꯂꯤꯕ ꯄꯣꯀꯦꯠ 5.5 ꯒꯤ ꯌꯥꯝꯕ ꯁꯔꯨꯛ ꯂꯧꯏ (ꯑꯦꯗꯚꯥꯟꯇꯦꯖ ꯄ꯭ꯂꯦ ꯌꯦꯡꯕꯤꯌꯨ), ꯑꯃꯁꯨꯡ ꯃꯔꯝ ꯑꯁꯤꯅ ꯄ꯭ꯔꯤꯗꯤꯛꯇ ꯇꯧꯔꯤꯕ ꯃꯤ ꯑꯃꯕꯨ ꯍꯤꯁꯥꯕꯅ ꯅꯠꯇꯅ ꯘꯔꯤꯅ ꯉꯝꯈꯩ ꯊꯝꯂꯤ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯇꯥꯕ ꯐꯥꯑꯣꯕ ꯈꯪꯖꯤꯅꯕ ꯌꯥꯏ꯫ ꯃꯇꯨꯡꯗ ꯗꯤꯐ꯭ꯂꯦꯛꯇꯔꯁꯤꯡ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Bass, T. A. The Eudaemonic Pie.
- Thorp, E. O. “Optimal gambling systems for favorable games.”