Iyiv numerals. Keeb kwm, piav qhia, zoo thiab tsis zoo, piv txwv ntawm ancient Iyiv tooj system

Ob peb cov neeg xav hais tias cov hom kev kawm thiab cov qauv uas peb siv los mus xam yooj yim los yog lej, tsim tau ntau centuries, thiab nyob rau hauv ntau qhov chaw ntawm lub ntiaj teb no. Advanced lej uas kos npe rau, txawm ib tug thawj voom, tau yav tas los lawm prohibitive rau lub smartest neeg. Ib tug enormous pab mus rau txoj kev loj hlob ntawm lub lag luam muaj ua lub Egyptian tooj system, ib co ntsiab uas peb tseem siv nyob rau hauv lawv cov thawj daim ntawv no.

nyuag txhais

Historians paub tej yam uas tej ancient civilization hloov zuj zuj mas sau ntawv thiab zauv tseem ceeb twb yeej ib txwm nyob rau hauv ob qhov chaw. Vim li no, nyob rau hauv lub yav dhau los millennia kev kawm txog zauv ntau inaccuracies thiab tej zaum niaj hnub ua hauj lwm khawb lawv lub taub hau nyob rau hauv cov learn. Nws yog tsis muaj kev zam thiab lub Egyptian numerals, uas, incidentally, yog tseem nonpositional. Qhov no txhais tau hais tias txoj hauj lwm ntawm ib tug tib tooj nyob rau hauv cov ntaub ntawv tus xov tooj tsis hloov tus nqi tag nrho. Raws li ib qho piv txwv, xav txog ib tug nqi ntawm 15, nyob rau 1 - thawj qhov chaw, thiab 5 - nyob rau hauv lub thib ob. Yog hais tias peb hloov cov xov tooj, kom tau ib tug loj npaum li cas tus xov tooj. Tab sis lub ancient Iyiv tooj system cov kev pauv yuav tsis xav. Txawm nyob rau hauv loj tus xov tooj tag nrho nws cov Cheebtsam raug kaw nyob rau hauv random order.

Cia li nco ntsoov tias tus niaj hnub inhabitants ntawm no kub lub teb chaws txaus siab rau cov tib Arabic numerals, raws li peb sau ntawv rau lawv nyob rau hauv nruj raws li qhov tseeb txoj kev thiab sab laug mus rau sab xis.

Yuav ua li cas yog cov tej yam tshwm sim?

Yuav kom sau tus xov tooj Egyptians siv Hieroglyphs, thiab nyob rau tib lub sij hawm tsis muaj ntau yam thiaj li. Duplicating lawv nyob rau ib txoj cai, nws yog tau txais lub xov tooj ntawm tag nrho cov ntau thiab tsawg pab, Txawm li cas los, qhov no yuav tsum tau ib tug loj tus naj npawb ntawm papyrus. Thaum thawj zaug rau theem ntawm cov hav zoov ntawm cov neeg Iyiv hieroglyphic tooj system muaj cov zauv 1, 10, 100, 1000 thiab 10000. Tom qab ntawd, muaj ib tug tseem ceeb pes tsawg tus uas yog cov zauv ntawm 10. Yog hais tias ib tug yuav tau sau ib tug ntawm cov saum toj no indicators, As, siv xws li cim:

Yuav kom sau cov xov tooj uas tsis yog ib tug ntau yam ntawm kaum, siv cov txheej txheem no ingenuous:

deciphering cov zauv

Raws li ib tug tshwm sim ntawm cov piv txwv saum toj no, peb pom hais tias nyob rau hauv thawj qhov chaw peb tau xaiv rau puas, ua raws li los ntawm ob xyoo lawm thiab nyob rau thaum xaus ntawm lub ob units. Ib yam li ntawd, lwm yam pes tsawg yog kaw, uas yuav siv tau txhiab thiab vam leej. Txawm li cas los, qhov no piv txwv yog sau sab laug mus rau sab xis, yog li ntawd cov niaj hnub nyeem ntawv yuav zoo to taub nws, tab sis hais tias yog ua tau Iyiv numerals tsis yog raws li muaj tseeb. Cov nqi yuav tsum raug muab sau los ntawm txoj kev mus rau sab laug, to taub qhov twg pib, thiab qhov twg yog qhov kawg, nws yog tsim nyog, raws li nyob rau hauv cov duab nrog lub siab tshaj plaws muaj nqis. Ib tug zoo xws li cov benchmark yuav tsum tau thiab yog hais tias cov xov tooj nyob rau hauv ib tug loj tus naj npawb ntawm across kaw (raws li lub system nepozitsionnyh).

Cov zauv yog tseem ceeb heev

Egyptians ua ntej ntawm muaj ntau lwm yam tswv lej. Vim li no, qee lub sij hawm nyob ib leeg nuj nqis nws yog tsis txaus, thiab cov zauv feem tau maj ua tswvcuab. Txij ancient Iyiv hieroglyphic tooj system yog pom tias yuav sau lub numerators thiab denominators siv raws li cov cim. Rau ½ muaj ib tug tshwj xeeb thiab qhov kos npe rau, thiab tag nrho lwm yam tsiaj raug tsim nyob rau hauv tib txoj kev uas twb tau muab siv rau cov loj xov tooj. Lub numerator yog yeej ib txwm featured ib tug cim xyaum qhov zoo ntawm tus tib neeg lub qhov muag, thiab cov denominator yog twb tau hais tseg.

zauv ua hauj lwm

Yog hais tias muaj yog tus xov tooj, lawv ntxiv thiab rho tawm, muab thiab faib. Iyiv numerals tiv nrog no ua hauj lwm paug zoo, txawm hais tias muaj muaj nws tus kheej specifics. Qhov yooj yim txoj kev tau ua folding thiab sib rho. Ua li no, ob tug zauv raug kaw nyob rau hauv ib tug xov tooj ntawm cov cim, kev hloov ntawm lawv lees paub ntswg. Nws yog xav paub ntau yooj yim to taub yuav ua li cas lawv tau huaj vam coob vim tus txheej txheem yog ib tug me ntsis zoo ib yam li niaj hnub. Ob kab, ib tug ntawm lawv pib nrog ib tug thiab lwm yam - los ntawm lub thib ob tau. Tom qab ntawd nws pib dua zaum ob txhua tus ntawm cov xov tooj los ntawm cov ntaubntawv povthawj siv ib tug tshiab tshwm sim rau lub yav dhau los yog ib tug. Thaum cais los ntawm tus thawj kem ntawm cov zauv muaj kev tswj kom sau cov uas ploj lawm tau summed. Ntau precisely to taub tus txheej txheem no yuav ua tau, tab tom nrhiav rau ntawm lub rooj. Nyob rau hauv cov ntaub ntawv no 7 khoo los ntawm 22:

Cov tshwm sim nyob rau thawj kem 8 twb tshaj 7, li ntawd, ob npaug xaus ntawm 4. 1 + 2 + 4 = 7, thiab 22 + 44 + 88 = 154. Cov lus teb no yog muaj tseeb, tab sis tau txais li txawv txawv rau peb los ntawm.

Rho thiab division yog ua nyob rau hauv lub rov qab kev txiav txim ntawm ntxiv thiab npaug.

Yog vim li cas sawv Iyiv numerals?

Lub keeb kwm ntawm tshwm sim ntawm cov cim, yam tsawg, raws li vague li cov tsos ntawm cov tag nrho ntawm Iyiv civilization. Nws yug hnub ntawm lub thib ob ib nrab ntawm peb Millennium BC. Nws tau mus ntseeg hais tias xws li yog cov neeg nyob rau hauv cov hnub yog ib tug tsim nyog ntsuas. Tim lyiv teb chaws yog ib tug twb tau tag nrho-fledged lub xeev, thiab los ua ntau haib thiab wider txhua txhua xyoo. Nqa tawm kev tsim kho ntawm lub tuam tsev, twb sau npe nyob rau hauv lub ntsiab sawv cev, thiab nyob rau hauv thiaj li yuav muab tag nrho cov no, cov tub ceev xwm tau txiav txim siab yuav ua kom paub qhov no system account. Nws ntawd kub ntev li ib tug ntev lub sij hawm - kom txog rau thaum lub kaum xyoo pua AD, tom qab uas nws twb hloov ieratika.

Iyiv numerals: strengths and weaknesses

Lub ntsiab kev kawm tau ntawm cov ancient Egyptians nyob rau hauv kev kawm txog zauv - yog simplicity thiab precision. Nrhiav rau ntawm cov ua cim, ib txwm yuav tsum tau los mus txiav txim yuav ua li cas muaj ntau yam kaum, pua pua los yog txhiab sau rau ntawm papyrus. Qhov kom zoo dua ntawm lub system yog tseem xam tau tias yog mus ntxiv thiab muab xov tooj. Tsuas yog thaum xub thawj siab ib muag nws nkawd ruam tag, tab sis tob tob hauv lub essence, koj yuav pib sai sai thiab yooj yim daws tau xws learn. Lub disadvantage tau raug lees paub tias los ntawm ib tug ntau ntawm cov tsis meej pem. Numbers yuav raug kaw tsis tau tsuas yog nyob rau hauv cov kev taw qhia, tab sis cia li, yog li yuav tsum tau ntau lub sij hawm nyob rau hauv lawv cov ntawv tseem ceeb. Thiab kawg rho tawm, tej zaum, yog cov incredibly ntev kab ntawm cov cim, vim hais tias lawv yeej muaj tau theej tawm.