ื”ื™ืงืฃ: ืžืžื“ื™ื ื•ื™ื—ื™ื“ื•ืช

ืœืžื“ื• ื•ืชืจื’ืœื• ื—ื™ืฉื•ื‘ ื”ื™ืงืฃ ืขื ื”ืžืจื•ืช ื™ื—ื™ื“ื•ืช ืื•ืจืš, ื•ื”ื‘ื™ื ื• ืืช ื”ื”ื‘ื“ืœ ื‘ื™ืŸ ืงื ื” ืžื™ื“ื” ื—ื“-ืžืžื“ื™ ื•ื“ื•-ืžืžื“ื™.

ื ืคืชืจื•: 0

ืžืžื“ื™ื ื•ื™ื—ื™ื“ื•ืช

ื”ืฉืชืžืฉ ื‘ืื–ื•ืจ ื”ืขื‘ื•ื“ื”. ื›ืชื•ื‘ ืžืฉื•ื•ืื•ืช ื›ืžื• P = 24 ื›ื“ื™ ืœืคืชื•ืจ ืืช ื”ื”ื™ืงืฃ.

๐Ÿ“– ืžื“ืจื™ืš ืœืžื™ื“ื”: ื”ื™ืงืฃ

1. ืžื”ื• ืžืžื“?

ืžืžื“ ืžื’ื“ื™ืจ ื›ืžื” ื›ื™ื•ื•ื ื™ื ืขืฆืžืื™ื™ื ื ื“ืจืฉื™ื ืœืžื“ื™ื“ืช ืฆื•ืจื”. ืขื™ื™ื ื• ื‘ืžื“ืจื™ืš ืžืžื“ื™ื ื•ื™ื—ื™ื“ื•ืช ื‘ืขืžื•ื“ ื”ืฉื˜ื— ืœืงื‘ืœืช ืคืจื˜ื™ื ื ื•ืกืคื™ื ืขืœ ืžืžื“ื™ื ื•ื”ืฉื™ื˜ื” ื”ืžื˜ืจื™ืช ื•ื”ืืžืจื™ืงืื™ืช.
โ€ข ืงื• ืื• ื’ื‘ื•ืœ ื”ื•ื ื—ื“-ืžืžื“ื™ (1D) โ€” ื™ืฉ ืœื• ืจืง ืื•ืจืš.
โ€ข ืžืฉื˜ื— ืฉื˜ื•ื— ื”ื•ื ื“ื•-ืžืžื“ื™ (2D) โ€” ื™ืฉ ืœื• ืจื•ื—ื‘ ื•ื’ื•ื‘ื”.
โ€ข ื’ื•ืฃ ืžื•ืฆืง ื”ื•ื ืชืœืช-ืžืžื“ื™ (3D).

2. ื™ื—ื™ื“ื•ืช ื”ื™ืงืฃ

ืžื›ื™ื•ื•ืŸ ืฉื”ื”ื™ืงืฃ ืžื•ื“ื“ ืืช ื’ื‘ื•ืœ ื”ืฆื•ืจื” (ืื•ืจืš ื—ื“-ืžืžื“ื™), ื”ื•ื ืชืžื™ื“ ื ืžื“ื“ ื‘ื™ื—ื™ื“ื•ืช ืœื™ื ื™ืืจื™ื•ืช (ืœืžืฉืœ mm, cmcm, ftft, inin), ื•ืœืขื•ืœื ืœื ื‘ื™ื—ื™ื“ื•ืช ืจื™ื‘ื•ืขื™ื•ืช (ื”ืžืฉืžืฉื•ืช ืœืฉื˜ื—). ืœื“ื•ื’ืžื”, ืื ืœืžืœื‘ืŸ ื™ืฉ ืฆืœืขื•ืช ืฉืœ 5ย ืžโ€™5\text{ ืž'} ื•-3ย ืžโ€™3\text{ ืž'}, ื”ื”ื™ืงืฃ ืฉืœื• ื”ื•ื 16ย ืžโ€™16\text{ ืž'} (ืœื™ื ื™ืืจื™), ื‘ืขื•ื“ ืฉื”ืฉื˜ื— ืฉืœื• ื”ื•ื 15ย ืžโ€™215\text{ ืž'}^2 (ืจื™ื‘ื•ืขื™).
ืžืœื‘ืŸ (5m ร— 3m)5 m3 mืฉื˜ื— = 15 mยฒ(5 ร— 3 = 15)[2D Surface]ื”ื™ืงืฃ = 16 m(5 + 3 + 5 + 3 = 16) [1D Line]
ืžืฉื•ืœืฉ (3m - 4m - 5m)3 m4 m5 mืฉื˜ื— = 6 mยฒ(ยฝ ร— 4 ร— 3)[2D Surface]ื”ื™ืงืฃ = 12 m(3 + 4 + 5 = 12) [1D Line]
ืžืขื’ืœ (r = 3m)3 mืฉื˜ื— โ‰ˆ 28.27 mยฒ(ฯ€ ร— 3ยฒ)[2D Surface]ื”ื™ืงืฃ โ‰ˆ 18.85 m(2 ร— ฯ€ ร— 3) [1D Line]

3. ื”ืžืจืช ื™ื—ื™ื“ื•ืช ืื•ืจืš

ื›ื“ื™ ืœื”ืžื™ืจ ื”ื™ืงืฃ, ื”ืฉืชืžืฉื• ื‘ื ื•ืกื—ืื•ืช ื”ืžืจืช ื”ืื•ืจืš ื”ืกื˜ื ื“ืจื˜ื™ื•ืช ืžื“ืฃ ื”ื ื•ืกื—ืื•ืช:
โ€ข ืžื˜ืจื™: 1ย ืžโ€™=100ย ืก"ืž=1,000ย ืž"ืž1\text{ ืž'} = 100\text{ ืก"ืž} = 1{,}000\text{ ืž"ืž}, 1ย ืก"ืž=10ย ืž"ืž1\text{ ืก"ืž} = 10\text{ ืž"ืž}, 1ย ื“"ืž=10ย ืก"ืž1\text{ ื“"ืž} = 10\text{ ืก"ืž}.
โ€ข ืืžืจื™ืงืื™: 1ย ืžื™ื™ืœ=1,760ย ื™ืืจื“1\text{ ืžื™ื™ืœ} = 1{,}760\text{ ื™ืืจื“}, 1ย ื™ืืจื“=3ย ืจื’ืœ1\text{ ื™ืืจื“} = 3\text{ ืจื’ืœ}, 1ย ืจื’ืœ=12ย ืื™ื ืฅโ€™1\text{ ืจื’ืœ} = 12\text{ ืื™ื ืฅ'}.
โ€ข ื”ื›ืคื™ืœื• ื›ืืฉืจ ืืชื ืžืžื™ืจื™ื ืžื™ื—ื™ื“ื” ื’ื“ื•ืœื” ืœืงื˜ื ื” (ืœืžืฉืœ 3ย ืจื’ืœร—12=36ย ืื™ื ืฅโ€™3\text{ ืจื’ืœ} \times 12 = 36\text{ ืื™ื ืฅ'}). ื—ืœืงื• ื›ืืฉืจ ืขื•ื‘ืจื™ื ืžื™ื—ื™ื“ื” ืงื˜ื ื” ืœื’ื“ื•ืœื”.

4. ืฉื™ื ื•ื™ ืงื ื” ืžื™ื“ื”: ื”ื™ืงืฃ ืœืขื•ืžืช ืฉื˜ื—

ื›ืืฉืจ ืžื’ื“ื™ืœื™ื ืฆื•ืจื” ื‘ืื—ื•ื– ืžืกื•ื™ื (ื”ื›ืคืœืช ื›ืœ ื”ืžืžื“ื™ื ืฉืœื” ื‘ื’ื•ืจื ืงื ื” ืžื™ื“ื” kk):
โ€ข ื”ื™ืงืฃ (1D) ืžืฉืชื ื” ืœื™ื ื™ืืจื™ืช ืœืคื™ kk. ื™ื—ืก ื”ื”ื™ืงืฃ ื”ื—ื“ืฉ ืœื™ืฉืŸ ื”ื•ื k:1k:1.
โ€ข ืฉื˜ื— (2D) ืžืฉืชื ื” ืจื™ื‘ื•ืขื™ืช ืœืคื™ k2k^2. ื™ื—ืก ื”ืฉื˜ื— ื”ื—ื“ืฉ ืœื™ืฉืŸ ื”ื•ื k2:1k^2:1.

ื“ื•ื’ืžื”: ืื ืชื’ื“ื™ืœื• ืืช ื›ืœ ืฆืœืขื•ืช ื”ืฆื•ืจื” ื‘-50%50\%, ื’ื•ืจื ืงื ื” ื”ืžื™ื“ื” ื”ื•ื 1.5=3/21.5 = 3/2.
โ€ข ื™ื—ืก ื”ื”ื™ืงืฃ ื”ื—ื“ืฉ ืœื”ื™ืงืฃ ื”ื™ืฉืŸ ื”ื•ื 3:2\mathbf{3:2}.
โ€ข ื™ื—ืก ื”ืฉื˜ื— ื”ื—ื“ืฉ ืœืฉื˜ื— ื”ื™ืฉืŸ ื”ื•ื (3/2)2=9:4(3/2)^2 = \mathbf{9:4}.

5. ืกืงืจื ื•ืช: ื”ื—ื‘ืœ ืกื‘ื™ื‘ ื›ื“ื•ืจ ื”ืืจืฅ

ืชืืจื• ืœืขืฆืžื›ื ืฉืืชื ื›ื•ืจื›ื™ื ื—ื‘ืœ ื‘ืฆื•ืจื” ื”ื“ื•ืงื” ืกื‘ื™ื‘ ืงื• ื”ืžืฉื•ื•ื” ืฉืœ ื›ื“ื•ืจ ื”ืืจืฅ (ื‘ื”ื ื—ื” ืฉื›ื“ื•ืจ ื”ืืจืฅ ื”ื•ื ื›ื“ื•ืจ ืžื•ืฉืœื ื‘ืขืœ ืจื“ื™ื•ืก RR). ืื•ืจื›ื• ื”ื•ื ื”ื”ื™ืงืฃ C1=2ฯ€RC_1 = 2\pi R.
ื›ืขืช, ื ื ื™ื— ืฉืืชื ืจื•ืฆื™ื ืœื”ื•ืกื™ืฃ ื‘ื“ื™ื•ืง ืžืกืคื™ืง ื—ื‘ืœ ื›ืš ืฉื”ื—ื‘ืœ ื™ืจื—ืฃ ื‘ื“ื™ื•ืง ื‘ื’ื•ื‘ื” 1ย ืžื˜ืจ1\text{ ืžื˜ืจ} ืžืขืœ ืคื ื™ ื”ืงืจืงืข ืœืื•ืจืš ื›ืœ ื”ื“ืจืš. ื”ืจื“ื™ื•ืก ื”ื—ื“ืฉ ื”ื•ื R+1ย ืžโ€™R + 1\text{ ืž'}, ื•ื”ื”ื™ืงืฃ ื”ื—ื“ืฉ ื”ื•ื C2=2ฯ€(R+1)=2ฯ€R+2ฯ€C_2 = 2\pi(R + 1) = 2\pi R + 2\pi.
ืื•ืจืš ื”ื—ื‘ืœ ืฉืฆืจื™ืš ืœื”ื•ืกื™ืฃ ื”ื•ื:
C2โˆ’C1=2ฯ€(R+1)โˆ’2ฯ€R=2ฯ€โ‰ˆ6.28ย ืžื˜ืจื™ืC_2 - C_1 = 2\pi(R + 1) - 2\pi R = 2\pi \approx 6.28\text{ ืžื˜ืจื™ื}

ื‘ืื•ืคืŸ ืžืคืชื™ืข, ื–ื” ื›ืœืœ ืื™ื ื• ืชืœื•ื™ ื‘ืจื“ื™ื•ืก ืฉืœ ื›ื“ื•ืจ ื”ืืจืฅ! ื‘ื™ืŸ ืื ืืชื ืžืงื™ืคื™ื ื›ื“ื•ืจ ื˜ื ื™ืก ืื• ืืช ื›ื“ื•ืจ ื”ืืจืฅ ื›ื•ืœื•, ืขืœื™ื›ื ืœื”ื•ืกื™ืฃ ืจืง ื›-6.28ย ืžโ€™6.28\text{ ืž'} ืฉืœ ื—ื‘ืœ. ื”ืกื™ื‘ื” ืœื›ืš ื”ื™ื ืฉื”ืงืฉืจ ื”ื•ื ืœื™ื ื™ืืจื™ (ื—ื“-ืžืžื“ื™), ืžื•ืฉื’ ืฉื ื—ืงื•ืจ ื‘ื ื•ืฉืื™ื ืขืชื™ื“ื™ื™ื.

ืฉืœื™ื˜ื” ื‘-SealMath: ืชืฉื•ื‘ื•ืช ื™ื—ืก ื•ื™ื—ื™ื“ื•ืช

โ€ข ืœืฉืืœื•ืช ื™ื—ืก: ื”ื–ื™ื ื• ืืช ื”ืชืฉื•ื‘ื” ื‘ืคื•ืจืžื˜ a:b (ืœืžืฉืœ, 3:2 ืื• 9:4). ื•ื“ืื• ืฉื”ื™ื—ืก ืžืฆื•ืžืฆื ืœื—ืœื•ื˜ื™ืŸ (ืœืœื ื’ื•ืจืžื™ื ืžืฉื•ืชืคื™ื).
โ€ข ืœืฉืืœื•ืช ื—ื™ืฉื•ื‘: ื”ื–ื™ื ื• ืืช ื”ืชืฉื•ื‘ื” ื”ืžืกืคืจื™ืช ื‘ืฆื•ืจื” P = ืขืจืš. ื”ื™ื—ื™ื“ื” ืžื•ืฆื’ืช ื‘ืฉืืœื”, ืœื›ืŸ ืื™ืŸ ืœื”ืงืœื™ื“ ืื•ืชื”.
ื ื•ืฉืื™ ืœื™ืžื•ื“

ืฉืืœื•ืช ื ืคื•ืฆื•ืช

ืžื”ื• ื”ื™ืงืฃ?

ื”ื™ืงืฃ ื”ื•ื ืื•ืจืš ื”ื’ื‘ื•ืœ ื”ื›ื•ืœืœ ืฉืœ ืฆื•ืจื” ื“ื•-ืžืžื“ื™ืช. ื”ื•ื ื›ื•ืœืœ ื”ืŸ ืืช ื”ื’ื‘ื•ืœ ื”ื—ื™ืฆื•ื ื™ ื•ื”ืŸ ืืช ื”ื’ื‘ื•ืœื•ืช ื”ืคื ื™ืžื™ื™ื (ื›ืžื• ื’ื‘ื•ืœื•ืช ืฉืœ ื—ื•ืจื™ื ื‘ืชื•ืš ื”ืฆื•ืจื”).

ื›ื™ืฆื“ ืžื—ืฉื‘ื™ื ื”ื™ืงืฃ ืžืœื‘ืŸ?

ื”ื”ื™ืงืฃ ืฉืœ ืžืœื‘ืŸ ื”ื•ื ืกื›ื•ื ื›ืœ ืืจื‘ืข ืฆืœืขื•ืชื™ื•: P = 2w + 2h ืื• P = 2(w + h), ื›ืืฉืจ w ื”ื•ื ื”ืจื•ื—ื‘ ื•-h ื”ื•ื ื”ื’ื•ื‘ื”.

ืžื“ื•ืข ื ื•ืกื—ืช ื”ื™ืงืฃ ื”ืจื™ื‘ื•ืข ื”ื™ื P = 4s?

ืจื™ื‘ื•ืข ื”ื•ื ืžืงืจื” ืžื™ื•ื—ื“ ืฉืœ ืžืœื‘ืŸ ืฉื‘ื• ื”ืจื•ื—ื‘ ื•ื”ื’ื•ื‘ื” ืฉื•ื•ื™ื (w = h = s). ื”ืฆื‘ื” ื‘ื ื•ืกื—ืช ื”ืžืœื‘ืŸ ื ื•ืชื ืช P = 2(s + s) = 4s.

ื›ื™ืฆื“ ืžืฉืคื™ืข ื—ื•ืจ ืขืœ ื”ื”ื™ืงืฃ?

ืžื›ื™ื•ื•ืŸ ืฉื”ื”ื™ืงืฃ ืžื•ื“ื“ ืืช ื›ืœ ื’ื‘ื•ืœื•ืช ื”ืฆื•ืจื”, ื—ื•ืจ ืžื•ืกื™ืฃ ืœื”ื™ืงืฃ. ื”ื”ื™ืงืฃ ื”ื›ื•ืœืœ ื”ื•ื ื”ื”ื™ืงืฃ ื”ื—ื™ืฆื•ื ื™ ื•ืขื•ื“ ื”ื”ื™ืงืฃ ื”ืคื ื™ืžื™ (ื”ื™ืงืฃ ื”ื—ื•ืจ).

ื›ื™ืฆื“ ืžื•ืฆืื™ื ื”ื™ืงืฃ ืฉืœ ืžืฉื•ืœืฉ ื™ืฉืจ ื–ื•ื•ื™ืช ืื ืื—ืช ื”ืฆืœืขื•ืช ื—ืกืจื”?

ืžื›ื™ื•ื•ืŸ ืฉื›ื‘ืจ ืœืžื“ื ื• ืืช ืžืฉืคื˜ ืคื™ืชื’ื•ืจืก (aยฒ + bยฒ = cยฒ), ืื ื• ื™ื›ื•ืœื™ื ืœื—ืฉื‘ ืชื—ื™ืœื” ืืช ืื•ืจืš ื”ืฆืœืข ื”ื—ืกืจื” ื•ืœืื—ืจ ืžื›ืŸ ืœื—ื‘ืจ ืืช ื›ืœ ืฉืœื•ืฉ ื”ืฆืœืขื•ืช ื›ื“ื™ ืœืงื‘ืœ ืืช ื”ื”ื™ืงืฃ.

ื‘ืื™ืœื• ื™ื—ื™ื“ื•ืช ืžืฉืชืžืฉื™ื ืœื”ื™ืงืฃ?

ืžื›ื™ื•ื•ืŸ ืฉื”ื”ื™ืงืฃ ื”ื•ื ืื•ืจืš ื—ื“-ืžืžื“ื™ (ื’ื‘ื•ืœ), ื”ื•ื ื ืžื“ื“ ื‘ื™ื—ื™ื“ื•ืช ืื•ืจืš ืœื™ื ื™ืืจื™ื•ืช ื›ืžื• ืžื˜ืจื™ื (m), ืกื ื˜ื™ืžื˜ืจื™ื (cm), ืจื’ืœ (ft), ืื• ืื™ื ืฅ' (in). ื”ื•ื ืœืขื•ืœื ืื™ื ื• ื ืžื“ื“ ื‘ื™ื—ื™ื“ื•ืช ืžืจื•ื‘ืขื•ืช, ื”ืฉืžื•ืจื•ืช ืœืฉื˜ื—.

ื›ื™ืฆื“ ื”ื›ืคืœืช ืฆืœืขื•ืช ืฉืœ ืฆื•ืจื” ืžืฉืคื™ืขื” ืขืœ ื”ื”ื™ืงืฃ ื•ื”ืฉื˜ื— ืฉืœื”?

ื”ื›ืคืœืช ื›ืœ ื”ืžืžื“ื™ื (ื’ื•ืจื ืงื ื” ืžื™ื“ื” ืฉืœ 2) ืžื›ืคื™ืœื” ืืช ื”ื”ื™ืงืฃ (ื™ื—ืก 2:1) ืžื›ื™ื•ื•ืŸ ืฉื”ื”ื™ืงืฃ ืœื™ื ื™ืืจื™ (1D). ืขื ื–ืืช, ื”ื™ื ืžื’ื“ื™ืœื” ืคื™ ืืจื‘ืขื” ืืช ื”ืฉื˜ื— (ื™ื—ืก 4:1) ืžื›ื™ื•ื•ืŸ ืฉื”ืฉื˜ื— ื“ื•-ืžืžื“ื™ (2D) ื•ืžืฉืชื ื” ื‘ืจื™ื‘ื•ืข (2ยฒ = 4).

ื”ื™ืงืฃ: ืžืžื“ื™ื ื•ื™ื—ื™ื“ื•ืช | SealMath