ᕕᐳᓈᑦᓯ ᐸᕐᓇᐅᑎ ᕉᓚᑦᒥ
ᕕᐳᓈᑦᓯ ᐸᕐᓇᐅᑎ ᕉᓚᑦᒥ, ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᑦ ᒪᓕᒃᑐᑦ 1, 1, 2, 3, 5, 8, 13… ᐊᓯᐅᔾᔨᓂᐅᑉ ᑭᖑᐊᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᐊᕐᓗᑎᑦ, ᐊᔪᒐᕐᓂᐅᑉ ᑭᖑᐊᓂ ᒪᕐᕉᓂᒃ ᐅᑎᕐᓗᑎᑦ.
ᐊᒃᓴᓗᐊᕐᒥᒃ ᐊᔪᖅᑎᑦᓯᙱᑦᑐᖅ; ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᓐᓄᑦ ᐸᕐᓇᐅᑎ ᐊᔪᖅᑎᑦᓯᔪᓐᓇᙱᑦᑐᖅ. ᒫᑎᓐᒐᐃᓪᒥᑦ ᓱᒃᑲᐃᓂᖅᓴᐅᔪᖅ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ ᐊᑯᓂᓂᖅᓴᒥᒃ ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᐊᑦᑕᓇᙱᓐᓂᖅᓴᐅᔪᑦ ᑭᒡᓕᖓ ᑎᑭᓚᐅᖅᑎᓐᓇᒍ, ᐅᑎᕐᓂᖓᓗ ᓱᒃᑲᐃᓂᖅᓴᐅᔪᖅ. ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅ ᐊᔾᔨᒌᒃᑐᖅ 2.70%-ᖑᔪᖅ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓂᑮᓇᐅᔭᖅᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑦᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐱᙳᐊᕈᑎᒋᔭᐅᔪᑦ ᑲᑎᓪᓗᒋᑦ, ᐊᔪᒐᐅᑎᑦ ᐱᙳᐊᕈᑎᒋᖃᑦᑕᖅᑕᐅᔪᑦ ᐃᓚᓗᒋᑦ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᕼᐋᓐᑐᓪ, ᐋᒃᓴᓐ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →.
ᖃᓄᖅ ᓈᓴᐅᑏᑦ ᑐᓪᓕᕆᐊᖏᑦ ᓴᓇᔭᐅᕙᑦᑐᑦ
ᓈᓴᐅᑎᑕᒫᑦ ᓯᕗᓂᐊᓃᑦᑐᑦ ᒪᕐᕉᒃ ᑲᑎᓯᒪᓂᖏᑦ.
ᑕᐃᒪᓐᓇ 8 ᐊᒻᒪ 13 ᑭᖑᓂᐊᒍᑦ 21 ᑐᓪᓕᐊᖃᖅᑐᖅ.
ᓈᓴᐅᑎᑕᒫᑦ ᓯᑕᒪᐅᔪᓕᒃ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᔾᔨᓕᐅᕐᓗᒍ, ᓯᑕᒪᐅᔪᓖᓪᓗ ᐊᑐᓂᑦ ᑲᑎᓐᓇᖅᑐᑦ: ᓄᑖᑕᒫᑦ ᑕᑭᓂᖓ ᓯᕗᓂᐊᓃᑦᑐᑦ ᒪᕐᕉᒃ ᓴᓂᓕᕇᑦᑎᓪᓗᒋᑦ ᑕᑭᓂᖏᑦᑎᑐᑦ. ᓯᑕᒪᐅᔪᓕᑕᒫᖅ ᐊᒃᓴᓗᐊᕋᔪᒃᑐᖅ ᓯᑕᒪᐅᓕᖓ ᐊᒃᓴᓗᐊᕋᔪᒃᑐᒥᒃ ᑲᑎᓐᓇᖅᑐᖅ.
ᑐᓪᓕᕆᐊᖏᑦ ᒪᓕᓪᓗᒋᑦ
ᐊᓯᐅᔾᔨᓂᖅ ᑕᓕᖅᐱᐊᓄᑦ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᐊᖅᑎᑦᓯᔪᖅ. ᐊᔪᒐᕐᓂᖅ ᒪᕐᕉᓐᓂᒃ ᐅᑎᖅᑎᑦᓯᔪᖅ.
ᐱᙳᐊᕈᑏᑦ ᑮᓇᐅᔭᖏᑦ ᐃᓱᓕᓐᓂᖏᓪᓗ ᐱᒋᐊᕈᑎ ᐱᙳᐊᕈᑎᐅᑉ ᐊᑦᔨᐅᑎᖏᓐᓂ.
ᕕᐳᓈᑦᓯ ᐸᕐᓇᐅᑎ ᕉᓚᑦᒥ ᖃᓄᖅ ᐊᐅᓚᑦᑎᕙ?
ᕕᐳᓈᑦᓯᐸᕐᓇᐅᑎᕕᐳᓈᑦᓯᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᓈᓴᐅᑏᑦ 1, 1, 2, 3, 5, 8, 13… ᑐᓪᓕᐊᓂᖏᓐᓂᒃ ᒪᓕᒃᑐᖅ: ᐊᓯᐅᔾᔨᓂᖅ ᑭᖑᓂᖓᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᑦ, ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᖓᓂ ᒪᕐᕉᓂᒃ ᑐᓄᒧᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓈᓴᐅᑏᑦ ᑎᑎᕋᖅᓯᒪᓗᒋᑦ: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. ᑕᒪᕐᒥᒃ ᓯᕗᓂᐊᓂ ᒪᕐᕉᒃ ᑲᑎᑕᐅᓯᒪᔪᑦ. ᓯᕗᓪᓕᖅᐹᒥ ᐱᒋᐊᕐᓗᑎᑦ ᑕᐃᑦᑐᓂᒃ ᐊᑦᔨᐅᑎᓂᒃᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕈᑎᓕᐅᕐᓗᑎᑦ. ᐊᓯᐅᔾᔨᒃᐸᑦ, ᐊᑕᐅᓯᕐᒥᒃ ᑕᓕᖅᐱᐊᓄᑦ ᐊᐅᓪᓚᖅᑎᑦ. ᐊᔪᒐᒃᐸᑦ, ᒪᕐᕉᓂᒃ ᓴᐅᒥᐊᓄᑦ ᐅᑎᖅᑎᑦ, ᐅᕝᕙᓘᓐᓃᑦ ᐃᓂᖃᙱᒃᐸᑦ ᐱᒋᐊᕐᕕᒻᒧᑦ. ᑕᐃᒪ ᐸᕐᓇᐅᑎ ᑕᒪᐃᓐᓂᒃ. ᓈᓴᐅᑎᓕᐊᑦ ᐱᓕᕆᐊᖅ ᑕᒪᕐᒥᒃ ᖃᓄᑎᒋ ᐊᑭᖃᕐᓂᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᔪᑦ: ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᐱᙳᐊᕐᕕᐅᑉ ᑭᒡᓕᖓᓄᑦᐱᙳᐊᕐᕕᒃᐱᙳᐊᕐᕕᐅᑉ ᑭᒡᓕᖓᐱᙳᐊᕈᑎ ᒥᑭᓛᖅ ᐊᖏᓛᕐᓗ ᐊᖏᖅᑕᐅᔪᑦ. ᐊᖏᓛᖅ ᒪᕐᕉᕆᐊᖅᑎᑦᓯᔪᑦ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᓄᖅᑲᖅᑎᑦᑕᖏᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᕈᑎᒃᓴᕐᓄᑦᑮᓇᐅᔭᖅᐱᙳᐊᕈᑎᒃᓴᐃᑦᑮᓇᐅᔭᑦ ᐃᓘᓐᓇᖏᑦ ᐱᙳᐊᕐᓂᕐᒧᑦ ᐊᕕᒃᓯᒪᔭᐅᔪᑦ. ᐱᙳᐊᕈᑎᒃᓴᓂᒃ ᐊᐅᓚᑦᓯᓂᖅ ᑐᑭᖃᖅᑐᖅ ᖃᔅᓯᑦ ᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᓗ ᐊᑐᓂ ᐊᓯᐅᔪᓐᓇᖅᑕᐅᓂᐊᕐᒪᖔᑕ ᐃᓱᒪᓕᐅᕐᓂᕐᒥᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓄᖅᑲᖅᑎᑕᐅᔪᑦ ᑕᒪᐃᓐᓂᒃ ᐱᙳᐊᕈᑎᐅᓯᒪᔪᓂᒃ ᑲᑎᓪᓗᒋᑦ ᐊᓯᐅᔾᔨᔪᑦ.
ᐱᙳᐊᖅᑕᐅᓂᖓ ᖃᓄᐃᓕᖓᕙ?
$10 ᐱᒋᐊᕐᓂᖓ ᐊᕐᕕᓂᓖᑦ ᒪᕐᕉᓪᓗ ᑲᐃᕙᕐᓃᑦ: L L W L L L W W (L = ᐊᓯᐅᔾᔨᓂᖅ, W = ᐊᔪᒐᕐᓂᖅ). ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᑦ 10, 10, 20 (ᐊᔪᒐᕐᓂᖅ, ᒪᕐᕉᓂᒃ ᐅᑎᕐᓂᖅ, ᐱᓕᕆᐊᖅ 1-ᒧᑦ), 10, 10, 20, 30 (ᐊᔪᒐᕐᓂᖅ, ᒪᕐᕉᓂᒃ ᐅᑎᕐᓂᖅ, ᐱᓕᕆᐊᖅ 2-ᒧᑦ), 10 (ᐊᔪᒐᕐᓂᖅ, ᐱᒋᐊᕐᕕᒻᒧᑦ ᐅᑎᕐᓂᖅ). ᐊᓯᐅᔾᔨᓃᑦ: 10 + 10 + 10 + 10 + 20 = 60. ᐊᔪᒐᕐᓃᑦ: 20 + 30 + 10 = 60. ᑕᓪᓕᒪᑦ ᐊᓯᐅᔾᔨᓃᑦ, ᐱᖓᓱᑦ ᐊᔪᒐᕐᓃᑦ, ᐊᔪᒐᙱᓪᓗᑎᑦ ᐊᓯᐅᔾᔨᙱᓪᓗᑎᓪᓗ. ᑕᐃᒪ ᐸᕐᓇᐅᑎᐅᑉ ᐱᔪᒪᓇᕐᓂᖓ. ᐊᑭᖓ ᐊᔾᔨᒌᒃᑐᒥ ᑎᑎᕋᐅᔭᕐᒥ ᐃᓚᐅᔪᖅ: $120 ᐱᙳᐊᕈᑎᐅᔪᑦ ᑕᐃᑲᓂ ᑎᑭᑦᑐᓐᓇᕐᓂᕐᒧᑦ, ᑖᓚ ᑕᒪᕐᒥᒃ ᐱᙳᐊᕈᑎᐅᔪᖅ ᑳᓯᓅᑉ ᐃᓚᖓᓂᒃᓈᓴᐃᓂᖅᑳᓯᓅᑉ ᐃᓚᖓᐱᙳᐊᕈᑎ ᐊᑐᓂ ᑳᓯᓅᑉ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ ᐱᓯᒪᓂᖅᓴᖅᑕᖓ: ᐃᐅᕌᐸ ᕉᓚᑦᒥ 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᑕᖃᖅᑐᖅ.
ᓱᒻᒪᑦ ᒪᕐᕉᓂᒃ ᐅᑎᕐᓂᖅ, ᐊᑕᐅᓯᐅᙱᑦᑐᖅ?
ᐊᑕᐅᓯᖅ ᐊᔪᒐᕐᓂᖅ ᒪᕐᕉᓂᒃ ᐊᓯᐅᔾᔨᓂᕐᓂᒃ ᐊᑭᓕᐅᑎᒋᓪᓚᕆᒻᒪᑦ. ᓈᓴᐅᑎ ᑕᒪᕐᒥᒃ ᓯᕗᓂᐊᓂ ᒪᕐᕉᒃ ᑲᑎᑕᐅᓯᒪᒻᒪᑕ, 5 ᐊᑦᔨᐅᑎᓂᒃ ᐊᔪᒐᕐᓂᖅ 2-ᒥᒃ 3-ᒥᒡᓗ ᓯᕗᓂᐊᓂ ᐊᓯᐅᔾᔨᓯᒪᔪᓂᒃ ᐅᑎᖅᑎᑦᓯᔪᖅ. ᑐᖕᒥᕋᐃᑦ ᐃᓱᒪᒋᓗᒋᑦ: ᐊᓯᐅᔾᔨᓂᖅ ᑕᒪᕐᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᖁᒻᒧᐊᖅᑎᑦᓯᔪᖅ, ᐊᔪᒐᕐᓂᖅ ᑕᒪᕐᒥᒃ ᒪᕐᕉᓂᒃ ᐊᑦᑎᒧᐊᖅᑎᑦᓯᔪᖅ. ᓇᖏᖅᓯᕕᓐ ᑐᖕᒥᕋᖅ ᐊᑭᓖᒃᓴᐃᑦ. ᐱᓕᕆᐊᖅ 5-ᒥ 7 ᐊᑦᔨᐅᑏᑦ ᐊᓯᐅᔾᔨᓯᒪᔪᑎᑦ, ᐱᓕᕆᐊᖅ 8-ᒥ 33 ᐊᓯᐅᔾᔨᓯᒪᔪᑎᑦ, ᓯᕗᓪᓕᖅᐹᒧᓪᓗ ᐅᑎᖅᑯᕕᑦ ᐊᔪᒐᙱᓪᓗᑎᑦ ᐊᓯᐅᔾᔨᙱᓪᓗᑎᓪᓗ. ᑮᓇᐅᔭᒃᓴᕐᓂᖅ ᓯᕗᓪᓕᖅᐹᒥ ᐱᓕᕆᐊᕐᒥ ᐊᔪᒐᕐᓂᕐᓂᑦ ᑭᓯᐊᓂ ᐱᓯᒪᔪᖅ, ᐊᑕᐅᓯᕐᒥᒃ ᐊᑦᔨᐅᑎᒥᒃ ᐊᑕᐅᑦᑎᒃᑯᑦ.
ᐊᔪᒐᕐᓃᑦ ᐊᓯᐅᔾᔨᓃᑦ ᖃᓂᒋᔭᖏᓐᓂᒃ ᐊᒥᓲᓂᖃᖅᑎᓪᓗᒋᑦ, ᐊᑕᐅᓯᕐᒧᑦ ᒪᕐᕉᒃ ᐱᐅᔪᑎᑐᑦ ᑐᓴᕐᓇᖅᑐᖅ, ᐊᒥᓱᐊᕐᓗᒍᓗ ᑐᖕᒥᕋᐃᑦ ᐊᑦᑎᒧᑦ ᐅᑎᖅᑎᑦᓯᔪᑦ. ᐱᑦᔪᑎᒋᔭᐅᔪᖅ ᐅᓇᐅᔪᖅ: ᑐᖕᒥᕋᐃᑦ ᖁᒻᒧᐊᕐᓂᕐᒥ ᐊᖏᒡᓕᕙᒃᑐᑦ. ᖁᓕᑦ ᐊᔪᒐᕐᓃᑦ ᓯᕗᓪᓕᖅᐹᒥ ᐱᓕᕆᐊᕐᒥ 10 ᐊᑦᔨᐅᑏᑦ ᐱᔪᑦ. ᐱᖓᓱᑦ ᐊᓯᐅᔾᔨᓃᑦ ᐱᓕᕆᐊᓂ 6, 7, 8-ᒥᓗ 8 + 13 + 21 = 42 ᐊᑭᖃᖅᑐᑦ.
- p10 −$500
- p25 −$500
- ᐊᑯᓐᓂᐊᓃᑦᑐᖅ −$500
- p75 +$250
- p90 +$920
ᕕᐳᓈᑦᓯ ᐸᕐᓇᐅᑎ ᐊᐅᓚᑦᑎᕙ?
ᐊᐅᓚᑦᑎᙱᑦᑐᖅ. ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒧᑦ ᐊᑐᕈᓐᓇᙱᑦᑐᖅ. ᓈᓴᐃᓂᖅ ᐸᕐᓇᐅᑏᑦ ᑕᒪᐃᓐᓄᑦ ᐊᔾᔨᒌᒃᑐᖅ: ᐱᙳᐊᕈᑎ ᑕᒪᕐᒥᒃ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ 1/37-ᖓᓂᒃ ᐊᓯᐅᔾᔨᔪᖅ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ ᑐᓪᓕᖅᑐᑦ ᑕᒪᐃᑦ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᑕ 1/37-ᖓᓂᒃ ᐊᓯᐅᔾᔨᔪᑦ. ᕕᐳᓈᑦᓯ ᑐᓪᓕᖅᑐᑦ ᕉᓚᑦᒥ ᐊᑐᕐᓂᖏᑦ ᑕᒪᑐᒥᖓ ᐊᓯᑦᑐᖅᑎᑦᓯᙱᑦᑐᑦ, ᐊᒃᓴᓗᐊᖅ ᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᔪᓐᓇᕐᓂᖏᓐᓂᒃ ᐊᑭᓕᐅᑎᖃᕐᒪᑦ ᓯᑉᑮᓇᐅᔭᖅᓯᑉᓇᓗᓇᐃᒃᑯᑎ ᐊᑭᖃᐃᓐᓇᖅᑐᖅ, ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥ ᐃᓕᔭᐅᔪᖅ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ. ᐊᓯᐊᓂ ᐊᑎᖓ: ᓯᐊᒃ (check).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᖃᓄᑎᒋ ᐊᖏᑎᒋᒐᓗᐊᖅᐸᑦ. ᕕᐳᓈᑦᓯ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᑦ ᖁᕝᕙᓯᒃᐸᓪᓕᐊᔪᑦ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ ᑲᐃᕙᕐᓂᕐᒧᑦ ᐊᒥᓱᓂᖅᓴᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᖅᑐᖅ ᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒥᑦᐸᕐᓇᐅᑎᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖅ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᑕᒪᐃᑦ ᑕᒪᑐᒧᖓ ᐊᔾᔨᒌᒃᓯᔭᐅᕙᒃᑐᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →, ᐊᒻᒪ ᐱᙳᐊᖅᑕᐅᓂᖓᓄᑦ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖓᓈᓴᐃᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᐊᕐᓕᒃᓗᒍ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓄᑦ; ᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐊᓯᐅᔾᔨᓂᖅ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᖏᓂᖅᓴᐅᔪᖅ. ᒫᑎᓐᒐᐃᓪᐸᕐᓇᐅᑎᒫᑎᓐᒐᐃᓪᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᐊᓯᐅᔾᔨᓂᖅ ᑕᒪᐃᓐᓂ ᐱᙳᐊᕈᑎ ᒪᕐᕉᕆᐊᖅᑐᖅ. ᐸᕐᓇᐅᑏᑦ ᐃᓚᖓᓂ ᑕᑯᓗᒍ ᖃᓄᐃᓕᐅᕐᓂᖓ ᖃᓄᐃᓕᐅᙱᓐᓂᖓᓗ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᒥᓱᓂᖅᓴᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᖅᑐᖅ, ᐊᓯᐅᔾᔨᓂᖅᓴᐅᓪᓗᓂᓗ.
ᒫᑎᓐᒐᐃᓪᒥᑦ ᐅᓗᕆᐊᓇᙱᓂᖅᓴᐅᕙ?
ᓱᒃᑲᐃᓂᖅᓴᐅᔪᖅ, ᐊᔾᔨᒌᙱᑦᑐᖅ. ᕕᐳᓈᑦᓯ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᑦ ᐱᓕᕆᐊᕐᒧᑦ 1.6× ᖃᓂᒋᔭᖓᓂ ᐊᖏᒡᓕᕙᒃᑐᑦ, 2×-ᐅᙱᑦᑐᖅ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ $10 ᐱᒋᐊᕐᓂᖓᓂᑦ $500 ᑭᒡᓕᖓ ᑎᑭᑕᐅᔪᖅ ᖁᓕᑦ ᖃᓂᒋᔭᖏᓐᓂ ᐊᓯᐅᔾᔨᓂᕐᓂ ᑐᓪᓕᖅᑐᓂ, ᐱᖓᓲᔪᖅᑐᓂᐅᙱᑦᑐᖅ. ᑕᐃᒪ ᐊᓪᓚᕐᓂᖅ ᖃᓄᐃᓕᖓᔾᔮᙱᓂᖅᓴᐅᔪᖅ: ᖁᓕᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ (19/37)¹⁰ ≈ 0.13%, ᐱᖓᓲᔪᖅᑐᓄᑦ (19/37)⁶ ≈ 1.8%. ᑭᓯᐊᓂ ᐊᓪᓚᕐᓂᖅ ᖁᑦᑎᓂᖅᓴᐅᔪᖅ, ᑎᑭᓚᐅᖅᑎᓐᓇᒍ ᐊᒥᓱᓂᖅᓴᐃᑦ ᐱᙳᐊᕈᑎᐅᓯᒪᒻᒪᑕ, ᐊᑕᐅᓯᕐᓗ ᐊᔪᒐᕐᓂᖅ ᐅᑎᖅᑎᑦᓯᔪᓐᓇᙱᑦᑐᖅ.
ᓈᓴᐅᑏᑦ ᓇᑭᙶᖅᐸᑦ?
ᐅᑲᓕᓐᓄᑦ ᐃᓱᒪᓕᐅᕈᑎᒥᑦ. ᓕᐅᓇᑐ ᐱᓴᒥᐅᑕᖅ (Leonardo of Pisa), ᑭᖑᓂᐊᒍᑦ ᕕᐳᓈᑦᓯᒥᒃ ᐊᑎᖅᑖᖅᑐᖅ, ᑎᑎᕋᖅᓯᒪᓚᐅᖅᑐᖅ Liber Abaci-ᒥ 1202-ᒥ: ᐊᑕᐅᓯᕐᒥᒃ ᐱᐊᕆᖃᖅᓗᑎᑦ ᐱᒋᐊᕐᓗᑎᑦ, ᐱᐊᕆᑦ ᑕᒪᕐᒥᒃ ᑕᖅᑭᒧᑦ ᓄᑖᒥᒃ ᐱᐊᕆᓕᐅᖅᐸᒃᑐᑦ ᒪᕐᕉᐊᓂ ᑕᖅᑭᐊᓂ ᐱᒋᐊᖅᓗᑎᒃ, ᐱᐊᕆᓪᓗ ᓈᓴᓗᒋᑦ. ᑭᐅᔾᔪᑎ 1, 2, 3, 5, 8, 13. ᒪᓕᒐᖅ ᓯᕗᓪᓕᖅᐹᖑᓪᓗᓂ ᓇᓂᓚᐅᙱᑦᑐᖅ. ᐃᓐᑎᐊᒥᐅᑦ ᐃᓕᓐᓂᐊᖅᑏᑦ ᐃᖏᐅᓯᐅᑉ ᐊᑦᔨᐅᑎᖏᓐᓂᒃ ᓯᕗᓂᐊᓂ ᑎᑎᕋᖅᓯᒪᓚᐅᖅᑐᑦ: ᓯᖕ (Singh) (1985) ᕕᕋᕼᐊᖕᑲ (Virahanka)-ᒧᑦ ᐅᑎᖅᑎᑦᓯᔪᖅ, 600-ᓗ 800-ᓗ ᐊᑯᖏᓐᓂ, ᑭᖑᓂᐊᒍᑦ ᑯᐸᓚ (Gopala)-ᒧᑦ ᕼᐃᒪᓴᓐᑐᕋ (Hemachandra)-ᒧᓪᓗ.
ᐃᓚᖏᑦ ᐊᒃᓴᓗᐊᕐᒥᒃ ᐃᓱᒪᒋᔭᖃᓚᐅᙱᑦᑐᑦ. ᐅᕙᓂ ᐱᕝᕕᒋᔭᐅᔪᑦ ᑭᓇ ᓯᕗᓪᓕᖅᐹᒥᒃ ᑐᓪᓕᖅᑐᓂᒃ ᒪᓕᒃᓗᓂ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓᓂᒃ ᐅᖃᙱᑦᑐᑦ. ᓇᓗᓇᐃᖅᓯᔭᖏᑦ ᐅᓇᐅᔪᖅ: ᑐᓪᓕᖅᑐᑦ ᓈᓴᐃᓂᖓ ᕉᓚᑦᓗ ᓈᓴᐃᓂᖓ ᑲᑎᙱᑦᑐᒃ: ᐊᑕᐅᓯᖅ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᑦ ᖃᓄᖅ ᐊᖏᒡᓕᕐᓂᖏᓐᓂᒃ ᐅᖃᖅᑐᖅ, ᐊᓯᐊ ᐱᙳᐊᕈᑎ ᑕᒪᕐᒥᒃ ᓱᓇᒥᒃ ᐅᑎᖅᑎᑦᓯᓂᖓᓂᒃ ᐅᖃᖅᑐᖅ.
ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᑭᖑᐊᓂ ᖃᓄᑎᒋ ᐊᓯᐅᔾᔨᓯᒪᕙ?
ᒪᕐᕉᒃ ᓈᓴᐃᓂᒃᑯᑦ ᓱᓕᔪᒃ ᖁᓛᓂ ᓈᓴᐅᑎᓕᐊᓂᒃ ᖃᐅᔨᓴᕈᓐᓇᕐᓂᕐᒥᒃ ᐱᔪᓐᓇᐅᑎᑦᓯᔪᒃ. n ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᑭᖑᐊᓂ ᑲᑎᑕᐅᔪᑦ ᐊᓯᐅᔾᔨᓃᑦ (n + 2)-ᖓ ᕕᐳᓈᑦᓯ ᓈᓴᐅᑎ 1-ᒥᒃ ᐲᖅᓯᓪᓗᒍ, ᑕᐃᒪ 1, 2, 4, 7, 12, 20 ᐊᒻᒪ ᐊᓯᖏᑦ, ᑐᓪᓕᖓᓗ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ (n + 1)-ᖓ ᕕᐳᓈᑦᓯ ᓈᓴᐅᑎ. ᐳᓪᒪᓐ (Bollman) (2021) ᐊᔾᔨᒌᒃᑐᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖅ ᐃᓐᑕᒃᓴᓐᒃᑯᑦ (induction) ᑐᓪᓕᖅᑐᓄᑦ 1, 2, 3-ᒥᑦ ᐱᒋᐊᖅᑐᓄᑦ, ᓈᓴᐅᑎ ᑕᒪᕐᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ ᐃᓂᒥᒃ ᓅᑦᑎᓪᓗᒍ. 500 ᐊᑦᔨᐅᑎᓂᒃ ᑭᒡᓕᖃᖅᑎᓪᓗᒍ 1 ᐊᑦᔨᐅᑎᒥᑦ ᐱᒋᐊᖅᑐᖅ, ᒫᑎᓐᒐᐃᓪ 10-ᖓᓂᒃ ᐱᙳᐊᕈᑎᒥᒃ, 512 ᐊᑦᔨᐅᑏᑦ, ᐃᓕᔾᔪᓐᓇᙱᑦᑐᖅ. ᕕᐳᓈᑦᓯ 14-ᖓᓂᒃ ᐃᓕᔾᔪᓐᓇᖅᑐᖅ, 377 ᐊᑦᔨᐅᑏᑦ, 15-ᖓᓂᒃ ᐃᓕᔾᔪᓐᓇᙱᑦᑐᖅ, 610.
ᑕᓴᓐᒥ ᓇᑉᐸᖅᑐᒥᓗ ᓱᓇ ᐊᓯᑦᑐᖅᐸ?
ᑕᓴᓐᒥᐱᙳᐊᕈᑎᑕᓴᓐ1–12, 13–24 ᐅᕝᕙᓘᓐᓃᑦ 25–36, ᐊᑭᓕᐅᑎ 2:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐅᕝᕙᓘᓐᓃᑦ ᓇᑉᐸᖅᑐᒥᐱᙳᐊᕈᑎᓇᑉᐸᖅᑐᖅᖁᓕᑦ ᒪᕐᕉᒡᓗ ᓈᓴᐅᑏᑦ ᐱᙳᐊᕈᑎᓕᕆᕝᕕᐅᑉ ᓇᑉᐸᖅᑐᖓᓂ ᐊᑕᐅᓯᕐᒥ, ᐊᑭᓕᐅᑎ 2:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →, 2, 1-ᒧᑦ ᐊᑭᓕᐅᑎᓕᒻᒥ, ᐅᑎᕐᓂᖅ ᐱᔭᕆᐊᖃᙱᑦᑐᖅ. F ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖃᖅᑎᓪᓗᒍ ᐊᔪᒐᕐᓂᖅ 2F-ᒥᒃ ᐊᑭᓕᐅᑎᖃᖅᑐᖅ, ᓯᕗᓂᐊᓂ ᐊᓯᐅᔾᔨᓯᒪᔪᓂᑦ ᐊᖏᓂᖅᓴᐅᐃᓐᓇᖅᑐᖅ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ ᐊᔪᒐᕐᓂᖅ ᑕᒪᕐᒥᒃ ᑐᓪᓕᖅᑐᓂᒃ ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒥᒃ ᐃᓱᓕᑦᑎᔪᖅ. ᐊᑭᖓ ᐅᓇᐅᔪᖅ: ᑕᓴᓐ 37-ᓂ 12-ᓂ ᑭᓯᐊᓂ ᐊᔪᒐᖅᐸᒃᑐᖅ, ᑕᐃᒪᓐᓇᐃᑦᑐᖅ ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᐊᑯᓂᐅᔪᑦ ᐊᒥᓱᐊᓗᐃᓂᖅᓴᐅᔪᑦ: ᖁᓕᑦ ᓯᑕᒪᓪᓗ ᑕᓴᓐ ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ 242 ᐱᓕᕆᐊᓂ ᐊᑕᐅᑦᑎᒃᑯᑦ ᖃᓂᒋᔭᖓᓂ ᐱᑕᖃᖅᐸᒃᑐᑦ, ᐊᐅᐸᓗᒃᑐᒥᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → 11,000-ᓂ ᐊᑕᐅᑦᑎᒃᑯᑦ ᖃᓂᒋᔭᖓᓂ.
ᒪᕐᕉᒃ ᐊᔪᒐᕐᓃᒃ ᑐᓪᓕᖅᑐᒃ ᑭᖑᐊᓂ ᑭᓯᐊᓂ ᓄᖅᑲᒃᐸᑦ?
ᐊᓯᐊ ᐊᔾᔨᒋᙱᑦᑐᖅ ᑲᐃᕙᕐᓂᖅ ᑕᒪᕐᒥᒃ ᑭᖑᐊᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᐊᖅᑐᖅ, ᐊᔪᒐᒃᐸᑦ ᐊᓯᐅᔾᔨᒃᐸᓪᓘᓐᓃᑦ, ᒪᕐᕉᒃ ᐊᔪᒐᕐᓃᒃ ᑐᓪᓕᖅᑐᒃ ᑭᖑᐊᓂ ᑭᓯᐊᓂ ᓄᖅᑲᖅᑐᖅ. n ᐊᓯᐅᔾᔨᓃᑦ ᒪᕐᕉᒃ ᐊᔪᒐᕐᓃᒃ ᓯᕗᓂᐊᓂ ᐱᑕᖃᖅᑎᓪᓗᒋᑦ, ᑮᓇᐅᔭᒃᓴᕐᓂᖅ (n + 1)-ᖓ ᕕᐳᓈᑦᓯ ᓈᓴᐅᑎ 1-ᒥᒃ ᐃᓚᓪᓗᒍ: ᒥᑭᔪᖅ ᐊᔪᒐᕐᓃᒃ ᓯᕗᓪᓗᐊᖅᑐᒥᒃ ᑎᑭᒃᐸᑕ, ᐊᖏᓂᖅᓴᖅ ᑭᖑᓪᓕᖅᑐᒥᒃ ᑎᑭᒃᐸᑕ, ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᓐᓂᒡᓗ ᐊᖏᒡᓕᓯᒪᔪᓂᒃ ᐱᔭᐅᔪᖅ. ᓯᕗᓪᓗᐊᖅᑐᒃ ᐊᔪᒐᕐᓃᒃ ᒥᑭᔪᓂ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖏᓐᓂ ᑎᑭᐃᓐᓇᖅᑐᒃ; ᑭᖑᓪᓕᖅᑐᒃ ᐊᖏᔪᒥᒃ ᐱᙳᐊᕈᑎᒥᒃ ᐱᔭᕆᐊᖃᖅᑐᓐᓇᖅᑐᒃ ᐱᙳᐊᖅᑕᐅᓂᖓ ᓯᓚᑦᑐᓂᖅᐹᖑᑎᓪᓗᒍ.
ᐊᔾᔨᐅᖅᑕᐅᑎ · ᕕᐳᓈᑦᓯ
2,000 ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎᓂᒃ, $1,000 ᐱᙳᐊᕈᑎᒃᓴᓂᑦ ᐱᒋᐊᕐᓗᓂ.
ᐱᒋᐊᕈᑎ ᐱᙳᐊᕈᑎ $10 · ᐱᙳᐊᕐᕕᐅᑉ ᑭᒡᓕᖓ $500 · 100 ᑲᐃᕙᕐᓃᑦ ᐱᙳᐊᖅᑕᐅᓂᖓᓂ
ᖃᔅᓯᓪᓗᐊᖅᑐᒥᒃ ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ ᓴᖅᑭᕙᑦᑐᑦ
ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ ᐊᑕᐅᓯᖅ ᓯᕉᓕᖕᒥ ᐊᒃᓴᓗᐊᕐᒥ ᐊᓯᐅᔾᔨᕙᑦᑐᖅ 19 ᑲᐃᕙᕐᓂᕐᓂ 37-ᓂ. ᑐᑭᓕᐊᑕᒫᑦ ᑕᑯᑎᑦᓯᔪᑦ ᐱᔪᓐᓇᕐᓂᕐᒥᒃ ᑲᐃᕙᕐᓃᑦ ᑐᓪᓕᖅᑐᑦ ᐃᓘᓐᓇᖏᑦ ᐊᓯᐅᔾᔨᓂᐊᕐᒪᖔᑕ, ᐊᒻᒪ ᖃᔅᓯᓂᒃ ᕕᐳᓈᑦᓯ ᐱᙳᐊᖅᑎᐅᑉ, ᐊᓯᐅᔾᔨᑐᐊᕋᒥ ᑐᓪᓕᕆᐊᖏᑎᒍᑦ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᐊᖅᑐᑉ, ᐊᓯᐅᔾᔨᓯᒪᓂᖓ ᑕᐃᑲᓂ.
| ᐊᓯᐅᔾᔨᓃᑦ ᑐᓪᓕᖅᑐᑦ | ᐱᔪᓐᓇᕐᓂᖅ | ᖃᓂᒋᔮᓂ 1 / | ᒫᓐᓇᒧᑦ ᐊᓯᐅᔾᔨᓯᒪᔪᑦ | ᑐᓪᓕᐊ ᐱᙳᐊᕈᑎ |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $1 |
| 2 | 26.4% | 4 | $2 | $2 |
| 3 | 13.5% | 7 | $4 | $3 |
| 4 | 7.0% | 14 | $7 | $5 |
| 5 | 3.6% | 28 | $12 | $8 |
| 6 | 1.8% | 55 | $20 | $13 |
| 7 | 0.94% | 106 | $33 | $21 |
| 8 | 0.48% | 207 | $54 | $34 |
| 9 | 0.25% | 403 | $88 | $55 |
| 10 | 0.13% | 784 | $143 | $89 |
| 11 | 0.065% | 1527 | $232 | $144 |
| 12 | 0.034% | 2974 | $376 | $233 |
| 13 | 0.017% | 5792 | $609 | $377 |
| 14 | 0.0089% | 11279 | $986 | $610 |
| 15 | 0.0046% | 21965 | $1,596 | $987 |
ᐱᔪᓐᓇᕐᓂᖅ ᑕᒪᓐᓇ 19/37 ᐃᒻᒥᓂᒃ ᐊᒥᓱᕆᐊᖅᑎᑕᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᑕᒫᑦ, ᑲᐃᕙᕐᓂᕐᒥᑦ ᐊᑕᐅᓯᕐᒥᑦ ᓈᓴᐃᓪᓗᓂ. ᐊᑯᓂᐅᔪᖅ ᐱᙳᐊᖅᑕᐅᓂᖓ ᑲᐃᕙᕐᓂᖃᖅᑐᖅ ᐊᒥᓱᓂᒃ ᑕᒪᒃᑯᓂᖓ ᑐᓪᓕᖅᑐᑦ ᐱᒋᐊᕐᕕᒋᔪᓐᓇᖅᑕᖏᓐᓂᒃ, ᑕᐃᒪᓐᓇ ᐅᓐᓄᒃᑯᑦ ᐱᙳᐊᕐᓗᓂ ᑕᐃᒪᐃᓐᓂᖓ ᐱᔪᓐᓇᕐᓂᖅᓴᐅᓪᓚᕆᒃᑐᖅ ᑐᑭᓕᐊᖅ ᐊᑕᐅᓯᖅ ᑕᑯᑎᑦᓯᔭᖓᓂᑦ.
ᐊᐱᖅᑯᑏᑦ
ᐄ: ᐊᔪᒐᕐᓂᐅᑉ ᑭᖑᐊᓂ ᓯᕗᒧᐊᖅᑐᖅ, ᐊᓯᐅᔾᔨᓂᐅᑉ ᑭᖑᐊᓂ ᐅᑎᖅᑐᖅ. ᓱᒃᑲᐃᓂᖅᓴᑎᑐᑦ ᐸᕈᓕᑎᑐᑦᐸᕐᓇᐅᑎᐸᕈᓕᐱᐅᔪᖅ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ: ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᖓᓂ ᒪᕐᕉᕆᐊᖅᓗᒍ, ᐊᓯᐅᔾᔨᓂᖅ ᑭᖑᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᖓᓱᑦ ᐊᔪᒐᕐᓃᑦ ᑐᓪᓕᖅᑐᑦ ᑭᖑᓂᖏᓐᓂ ᐱᒋᐊᖅᑭᓪᓗᒍ. ᐊᓯᐊᓂ ᐊᑎᖓ: ᐅᑎᖅᑕᖅ ᒫᑎᓐᒐᐃᓪ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᐅᓚᑦᑎᔪᖅ.
ᓈᓴᐃᓂᕐᒥᒃ ᐱᙳᐊᕐᓂᖅ
ᓯᕗᓪᓕᐅᓪᓗᓂ ᐃᓕᖕᓂᒃ ᐆᒃᑐᕐᓗᑎᑦ. ᑭᐅᔾᔪᑏᑦ ᐃᓗᓕᖏᑦ ᒪᑐᔭᐅᓯᒪᔪᑦ; ᐅᐸᒍᓐᓇᕈᕕᑦ ᒪᑐᐃᖅᓯᓗᒍ.
ᐊᔾᔨᒋᙱᑦᑐᖓ ᐱᙳᐊᕐᓗᒍ ᑐᓪᓕᖅᑲᑕᐅᔪᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᐊᖅᑐᖅ ᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓇ ᑭᖑᓂᐊᒍᑦ, ᐊᔪᒐᕈᓂ ᐊᓯᐅᔾᔨᒍᓂᓘᓐᓃᑦ, ᓄᖅᑲᖅᑐᕐᓗ ᒪᕐᕉᓂᒃ ᐊᔪᒐᕐᓃᓂᒃ ᑐᓪᓕᖅᑲᑕᐅᔪᓂᒃ ᑭᖑᓂᐊᒍᑦ: ᐱᙳᐊᕈᑏᑦ 1, 1, 2, 3, 5, 8 ᐊᓯᖏᓪᓗ. ᓯᕗᓪᓕᖅᐹᑦ ᖁᓕᑦ ᓯᑕᒪᓪᓗ ᐃᓱᓕᑦᑎᓃᑦ (ᐊ = ᐊᔪᒐᖅᑐᖅ, ᓯ = ᐊᓯᐅᔾᔨᔪᖅ) ᐊ ᓯ ᐊ ᓯ ᓯ ᓯ ᐊ ᓯ ᓯ ᓯ ᐊ ᓯ ᓯ ᐊ. ᓇᐅᓐᓃᑦᑐᑎᑦ, ᑐᓪᓕᐊᓂᓗ ᐱᙳᐊᕈᑎ ᖃᓄᑎᒋᕙ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ 22 ᐊᑦᔨᐅᑏᓂᒃᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᓯᐅᔾᔨᓯᒪᔪᑎᑦ. ᑐᓪᓕᐊᓂ ᐱᙳᐊᕈᑎ 610 ᐊᑦᔨᐅᑏᑦ, ᐊᔪᒐᕐᓂᕐᓗ ᐱᙳᐊᖅᑕᐅᓂᖓᓂᒃ 588-ᒥᒃ ᑮᓇᐅᔭᒃᓴᖅᓯᓪᓗᓂ ᐃᓱᓕᑦᑎᓂᐊᖅᑐᖅ.
ᐱᙳᐊᕈᑏᑦ ᓯᕗᓪᓕᖅᐹᑦ ᖁᓕᑦ ᓯᑕᒪᓪᓗ ᕕᐳᓈᑦᓯᐸᕐᓇᐅᑎᕕᐳᓈᑦᓯᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᖅ ᓈᓴᐅᑏᑦ 1, 1, 2, 3, 5, 8, 13… ᑐᓪᓕᐊᓂᖏᓐᓂᒃ ᒪᓕᒃᑐᖅ: ᐊᓯᐅᔾᔨᓂᖅ ᑭᖑᓂᖓᓂ ᐊᑕᐅᓯᕐᒥᒃ ᓯᕗᒧᑦ, ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᖓᓂ ᒪᕐᕉᓂᒃ ᑐᓄᒧᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓈᓴᐅᑏᑦ: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ᐊᒻᒪ 377. ᐊᔪᒐᕐᓃᑦ ᑲᑎᓗᒋᑦ ᐊᓯᐅᔾᔨᓃᓪᓗ ᐲᖅᓯᓗᒋᑦ: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22.
ᑭᖑᓪᓕᖅᐹᖅ ᐃᓱᓕᑦᑎᓂᖅ ᐊᔪᒐᕐᓂᐅᔪᖅ, ᑕᐃᒪ ᐊᔪᒐᕐᓂᖅ ᐊᑕᐅᓯᖅ ᐃᓱᓕᑦᑎᓂᐊᖅᑐᖅ. ᑐᓪᓕᐊᓂ ᐱᙳᐊᕈᑎ 610: ᐊᔪᒐᕐᓂᖅ +588-ᒥᒃ ᐱᑕᖃᖅᑎᑦᓯᔪᖅ, ᐊᓯᐅᔾᔨᓂᖅ −632-ᒥᒃ ᑐᓪᓕᐊᓂᒡᓗ ᐱᙳᐊᕈᑎᒥᒃ 987-ᒥᒃ.
ᐊᔾᔨᒋᙱᑦᑐᖓ ᑕᒪᑦᑕᐃᓐᓇ ᓯᕗᓪᓕᐅᓪᓗᓂ ᐃᓱᓕᑦᑎᕙᒃᑐᖅ, ᑕᒫᓂᓕ 610 ᐊᑦᔨᐅᑎᓕᒻᒥᒃ ᐱᙳᐊᕈᑎᒥᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ. ᒪᓕᒐᐃᑦ ᓇᓕᓐᓇᐅᙱᑦᑐᑦ ᒪᓕᒃᑕᐅᒍᑎᒃ, ᐊᔪᒐᕐᓂᖅ ᑭᖑᓂᐊᒍᑦ ᒪᕐᕉᓂᒃ ᑐᓄᒧᑦ, ᐊᔾᔨᒌᒃᑐᑦ ᖁᓕᑦ ᓯᑕᒪᓪᓗ ᐃᓱᓕᑦᑎᓃᑦ 1 ᐊᑦᔨᐅᑎᒥᒃ ᑭᓯᐊᓂ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᑦ ᑐᓪᓕᐊᓂᒡᓗ ᐱᙳᐊᕈᑎᒥᒃ 2-ᒥᒃ. ᐳᓪᒪᓐ (Bollman, 2021), ᑐᓪᓕᖅᑲᑕᐅᔪᓂᒃ 1, 2, 3-ᒥᒃ ᐱᒋᐊᖅᓯᔪᖅ, 1-ᒥᒃ ᐊᓯᐅᔾᔨᓂᕐᒥᒃ ᑐᓪᓕᐊᓂᒡᓗ ᐱᙳᐊᕈᑎᒥᒃ 3-ᒥᒃ ᐱᔪᖅ. ᒪᓕᒐᐃᑦ ᓇᓕᓐᓇᐅᙱᑦᑐᑦ ᑕᒫᓂ ᒥᑭᓂᖅᓴᒥᒃ ᐊᓯᐅᔾᔨᑎᑦᓯᔪᑦ ᐊᔪᒐᕐᓂᖅ ᑕᒪᐃᓐᓇ ᐱᙳᐊᕈᑏᑦ ᒥᑭᓕᒋᐊᖅᑎᑦᓯᒻᒪᒋᑦ.
ᑲᐃᕙᕐᓂᖅᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᐃᓱᓕᑦᑎᓂᖅᑲᑎᑕᐅᓂᖏᑦ ᒫᓐᓇᐅᔪᖅ11ᐊᔪᒐᖅᑐᖅ+121ᐊᓯᐅᔾᔨᔪᖅ032ᐊᔪᒐᖅᑐᖅ+243ᐊᓯᐅᔾᔨᔪᖅ−155ᐊᓯᐅᔾᔨᔪᖅ−668ᐊᓯᐅᔾᔨᔪᖅ−14713ᐊᔪᒐᖅᑐᖅ−1821ᐊᓯᐅᔾᔨᔪᖅ−22934ᐊᓯᐅᔾᔨᔪᖅ−561055ᐊᓯᐅᔾᔨᔪᖅ−1111189ᐊᔪᒐᖅᑐᖅ−2212144ᐊᓯᐅᔾᔨᔪᖅ−16613233ᐊᓯᐅᔾᔨᔪᖅ−39914377ᐊᔪᒐᖅᑐᖅ−22ᐊᔾᔨᒌᒃᑐᒥ ᐊᔾᔨᒋᙱᑦᑐᒥ, ᓱᒻᒪᑦ n ᐊᓯᐅᔾᔨᓃᑦ ᒪᕐᕉᓂᒡᓗ ᐊᔪᒐᕐᓃᓂᒃ ᑐᓪᓕᐊᓂ ᑕᒪᑦᑕᐃᓐᓇ ᑮᓇᐅᔭᒃᓴᕐᓂᕐᒥᒃ ᐱᑕᖃᖅᑎᑦᓯᕙᑦ (n + 1)-ᖓᓄᑦ ᕕᐳᓈᑦᓯ ᓈᓴᐅᑎᒧᑦ 1-ᒥᒡᓗ ᐃᓚᓗᒍ?
ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ
ᑭᐅᔾᔪᑎ n ᐊᓯᐅᔾᔨᓃᑦ ᑲᑎᓪᓗᒋᑦ (n + 2)-ᖓ ᕕᐳᓈᑦᓯ ᓈᓴᐅᑎ 1-ᒥᒃ ᐲᖅᓯᓗᒍ, ᒪᕐᕉᒡᓗ ᐊᔪᒐᕐᓃᒃ ᑐᓪᓕᐊᓂ ᓈᓴᐅᑏᒃ ᒪᕐᕉᒃ, ᑕᐃᒃᑯᓂᖓ ᑲᑎᓪᓗᒋᒃ (n + 1)-ᖓᓂᒃ ᓈᓴᐅᑎᒥᒃ 1-ᒥᒡᓗ ᐅᖓᑖᓄᑦ.
F₁, F₂, F₃ … ᑎᑎᕋᕐᓗᒋᑦ 1, 1, 2, 3, 5 …-ᒧᑦ. ᓈᓴᐅᑎ ᑕᒪᐃᓐᓇ ᓯᕗᓂᐊᓂ ᒪᕐᕉᒃ ᑲᑎᓪᓗᒋᒃ.
ᐊᓯᐅᔾᔨᓃᑦ: F₁ + F₂ + … + Fₙ. ᑕᒪᓐᓇ ᑲᑎᑕᐅᓂᖓ 1-ᒥᒃ ᐃᓚᓗᒍ, F₂-ᒥᒃ ᑎᑎᕋᖅᓯᒪᔪᖅ, ᓇᐃᓈᖅᐸᓪᓕᐊᔪᖅ: F₂ + F₁ = F₃, ᑕᐃᒪ F₃ + F₂ = F₄, ᐊᓯᖏᓪᓗ, ᑲᑎᑕᐅᓂᖓ ᐃᓘᓐᓇᖓ Fₙ₊₂-ᐅᓕᖅᑎᓪᓗᒍ. ᑕᐃᒪ ᐊᓯᐅᔾᔨᓃᑦ ᑲᑎᓪᓗᒋᑦ Fₙ₊₂ − 1.
ᐊᔪᒐᕐᓃᒃ ᑐᓪᓕᐊᓂ ᐱᙳᐊᕈᑏᒃ ᒪᕐᕉᒃ, Fₙ₊₁ ᐊᒻᒪ Fₙ₊₂. ᑮᓇᐅᔭᒃᓴᕐᓂᖅ: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1. ᓯᑕᒪᓂᒃ ᐊᓯᐅᔾᔨᓃᓂᒃ, ᑕᒪᓐᓇ F₅ + 1 = 6 ᐊᑦᔨᐅᑏᑦ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᑰᓪᑦ ᓈᓴᐅᑎ ᐱᙳᐊᕈᑎ ᐊᖏᓛᖅ ᓇᓗᓇᐃᒃᑯᑕᖓᓂᒃ ᑐᑭᓯᓐᓂᐊᖅᑐᖅ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- RouletteDoc. Strategy description and examples.
- Roulette77. Strategy description and examples.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Sigler, L. E. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation.
- Singh, P. The so-called Fibonacci numbers in ancient and medieval India.