Yuav ua li cas yog lub square hauv paus hniav?

Ntawm cov txheej ntawm kev txawj ntse, uas yog ib tug kos npe rau ntawm kev kawm ntawv nyob rau hauv thawj qhov chaw yog tus niam ntawv. Tom ntej no, nyob rau hauv tib "tseem ceeb" lub caij yog qhov sib ntxiv-npaug txawj thiab nyob ib sab mus rau lawv, tab sis qhov rov qab lub ntsiab lus, kev laij lej rho, division. Cov tshooj lus nyob rau hauv lub deb thaum yau lub tsev kawm ntawv kev txawj ntse, ua hauj lwm rau siab ntso ua hnub thiab hmo ntuj: TV, ntawv xov xwm, SMS invoice. Thiab qhov txhia chaw, peb nyeem ntawv, sau ntawv, saib, ntxiv, rho tawm, multiply. Thiab, qhia rau kuv, yuav ua li cas feem ntau uas koj muaj rau lub neej, tshem lub keeb kwm, tsuas yog raws li nyob rau hauv lub teb chaws? Piv txwv li, xws li ib entertaining ua hauj lwm, xws li, cov square hauv paus ntawm tus xov tooj 12345 ... Yog lub neej nyob rau hauv lub qub aub? Mastered? Yog, muaj yog tsis muaj dab tsi yooj yim! Qhov twg yog kuv tswvyim ... Thiab tsis muaj nws, txhais tes mus rau tes, me ntsis?

Ua ntej, peb kom meej li cas nws yog - lub square hauv paus ntawm ib tug xov tooj. Feem ntau hais lus, "mus rau extract lub square hauv paus ntawm tus xov tooj" txhais tau hais tias ua xam lag luam opposite exponentiation - uas yog koj thiab cov kev sib sau ntawm opposites nyob rau hauv lub neej daim ntawv thov. Exponentiation, cia hais tias, ib tug square, yog lub npaug ntawm ib tug xov tooj ntawm nws tus kheej, xws li, raws li qhia nyob rau ntawm lub tsev kawm ntawv, X * X = ib tug los yog lwm yam nkag X 2 = A, thiab cov lus - "X squared yog sib npaug zos rau A". Ces tus rov qab qhov teeb meem yog: lub square hauv paus ntawm A, X yog ib tug xov tooj uas yog tsa nyob rau hauv lub square yog sib npaug zos rau A.

square hauv paus hniav

Los ntawm ib tug lub tsev kawm ntawv chav kawm ntawm xam txoj kev paub xam "nyob rau hauv cov kem" uas pab kom ua tau tej suav siv cov thawj plaub arithmetical operations. Alas ... Mus square, thiab tsis tsuas yog lub square cov hauv paus hniav ntawm cov algorithms tsis muaj nyob. Thiab nyob rau hauv cov ntaub ntawv no, raws li cov square hauv paus tsis muaj ib tug lub tshuab xam zauv? Raws li lub ntsiab txhais ntawm ib tug square hauv paus tso zis - nws yog tsim nyog los xaiv cov nqi brute quab yuam tus xov tooj uas nws square txuas tus nqi ntawm cov radicand. Hais tias yog tag nrho! Tsis txhob muaj lub sij hawm kom dhau ib teev los yog ob tug, raws li nws yog tau los xam, siv ib tug zoo-paub txoj kev npaug nyob rau hauv lub "kem" ntawm tej square hauv paus. Yog hais tias koj yog xis txaus los mus ua ib tug ob peb feeb. Txawm tsis heev tshaj cov neeg siv lub tshuab xam zauv los yog PC ua rau nws nyob rau hauv ib tug fell swoop - kev kawm.

Tab sis tiag, lub square hauv paus yog feem ntau tau siv ib txoj kev "artillery tib rab diav rawg": thawj coj ib tug xov tooj uas nws square, roughly sau raws nkaus Ii lub radicals. Nws yog zoo dua yog hais tias "peb square" ib tug me ntsis tsawg tshaj li qhov no qhia. Ces, kho cov naj npawb ntawm lawv tus kheej muaj peev xwm, to taub, piv txwv li, multiplied by ob tug, thiab ... dua squared. Yog hais tias cov kev tshwm sim yog ntau tshaj tus xov tooj hauv qab no lub hauv paus successively kho cov thawj tus xov tooj yog maj nce nws "counterpart" nyob rau hauv lub hauv paus. Raws li koj tau pom - tsis muaj tshuab xam zauv, tsuas yog tus muaj peev xwm yuav tsum tau suav hais tias "nyob rau hauv ib kem". Ntawm cov hoob kawm, muaj ntau ntau kev thiab piav rau thiab optimized algorithms koj laij square cov hauv paus hniav, tab sis rau "siv hauv tsev" kom tsawg saum toj no muab 100% cog qoob loo nyob rau hauv cov kev tshwm sim.

Oh, kuv yuav luag tsis nco qab kom paub meej tias nws nce kev kawm ntawv, xam cov square hauv paus ntawm qhov yav tas los teev xov tooj 12345. Ua ib kauj ruam yog kauj ruam:

1. Siv intuitively, X = 100. Peb xam: X * X = 10,000 qhov ntawm qhov siab - cov no tsawg tshaj li 12345.

2. Sim kuj intuitively, X = 120. Ces: X * X = 14400.I dua nrog qhov kev txiav txim - qhov tshwm sim los ntawm ntau tshaj 12345.

3. Qhov saum toj no tau "diav rawg" ntawm 100 thiab 120. Xaiv ib tug xov tooj tshiab - 110 thiab 115. Peb tau, ntsig txog, 12100 thiab 13225 - diav rawg narrows.

4. Sim "random" X = 111. * Tau X X = 12321. Qhov no tus xov tooj yog nyob ze txaus rau 12345. Nyob rau hauv raws li qhov yuav tsum tau raug "haum" yuav mus los yog tso tseg rau qhov kev tshwm sim tau. Hais tias yog tag nrho. Raws li nws tau cog lus tseg - txhua yam yog yooj yim heev thiab tsis muaj ib tug tswvyim.

Heev me ntsis keeb kwm ...

Lawv ntaus li lub tswv yim mus siv rau hauv lub square hauv paus hniav tseem Pythagoreans, lub tsev kawm ntawv cov menyuam kawm ntawv thiab followers ntawm Pythagoras, 800 BC thiab ces "khiav" rau cov tshiab discoveries nyob rau hauv lub teb ntawm cov zauv. Thiab nyob qhov twg puas los ntawm?

1. Cov tshuaj ntawm qhov teeb meem nrog kev tshem tawm lub hauv paus, muab ib tug tshwm sim nyob rau hauv daim ntawv ntawm ib tug tshiab hauv chav kawm ntawv ntawm tus xov tooj. Lawv hu ua irrational, uas yog hais tias, "tsis yog zoo caij" vim hais tias lawv tsis kaw tag nrho tus naj npawb. Qhov tseem classic piv txwv ntawm no zoo - tus square hauv paus ntawm 2. Cov ntaub ntawv no sau raws nkaus Ii mus rau lub xam ntawm lub kab pheeb ces kaum ntawm ib tug square nrog ib tug sab sib npaug zos rau 1 - uas yog, tus ntawm lub tsev kawm ntawv ntawm Pythagoras. Nws muab tawm hais tias ib tug daim duab peb sab uas muaj ib qho loj ntawm ib tug tib sab, lub hypotenuse ntawm ib tug loj uas yog qhia los ntawm ib tug xov tooj, nyob rau hauv uas "muaj yog tsis muaj kawg." Yog li ntawd nyob rau hauv kev kawm txog zauv nyob irrational xov tooj.

2. Nws yog lub npe hu hais tias dashing teeb meem pib. Nws muab tawm hais tias qhov no xyuam xim lag luam muaj lwm ua kom yuam kev - noj cov square hauv paus, peb tsis paub lub square ntawm tus xov tooj, zoo los tsis zoo, yog ib tug tshaj dhau kev qhia. Qhov no tsis meej, lub ob tshwm sim ntawm ib tug ua lag luam, thiab kaw.

Txoj kev tshawb no txuam nrog rau qhov no tshwm sim tej kev txhawj xeeb yog cov kev taw qhia nyob rau hauv kev kawm txog zauv, hu ua lub hom phiaj ntawm txoj nce mus nce los, uas yog ntawm kuj zoo kawg tswv yim tseem ceeb nyob rau hauv lej physics.

Curiously, lub los ntawm lub hauv paus - ib tug - thov nyob rau hauv nws "Universal xam" yog tib yam ubiquitous Newton, thiab niaj hnub saib raws nraim cov ntaubntawv povthawj siv rau lub hauv paus tau paub txij li thaum 1690 los ntawm phau ntawv lub Frenchman Rolle "Coj algebra".