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Serbian to English - Standard rate: 0.12 USD per word / 30 USD per hour English - Standard rate: 0.12 USD per word / 30 USD per hour
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Sample translations submitted: 1
Serbo-Croat to English: Podjela duži na tri jednaka dijela General field: Science Detailed field: Mathematics & Statistics
Source text - Serbo-Croat
1. APSTRAKT
Sadržaj ovog rada se, kao što to i naziv rada kaže, bavi problemom podjele duži na tri jednaka dijela korištenjem samo šestara i lenjira bez mjerne skale. Ovo do sada nije bilo moguće.
U uvodu ovog rada autor iznosi kratak opis problema, kao i motivaciju za bavljenje ovim problemom. Glavni dio ovog rada donosi jednostavan postupak za njegovo rješavanje. Ovaj postupak je grafički predstavljen i matematičkim jezikom objašnjen korak po korak.
Doprinos ovog rada je u tome što donosi jednostavan postupak kojim se duž može podijeliti na tri jednaka dijela upotrebom samo žestara i lenjira bez podioka.
2. KLJUČNE RIJEČI I KLASIFIKACIJA PO OBLASTI
Geometrija, konstruisanje,duž, prava, podjela, dizajniranje, uglovi, stepeni, šestar, lenjir, metoda, postupak, construction, design, angles, degrees, a pair of compasses, ruler, method,length,
Prema AMS Mathematical Subject Classification ovaj rad spada u oblast 51(geometrija).
3. UVOD
Tokom konstruisanja uglova neke uglove je jednostavno konstruisati uz korištenje samo osnovnih sredstava tj. pomoću šestara i lenjira bez podioka, odnosno brojne skale . Za konstruisanje uglova je veoma važno znati da se kružnica može podijeliti na šest jednakih dijelova (tako što nacrtamo kružnicu, a zatim tim zahvatom šestara dijelimo tu kružnicu). Tako dobivamo šest jednakih dijelova od kojih svaki ima 60 stepeni. Takođe bilo koji ugao možemo podijeliti na dva jednaka dijela. Kombinovanjem ova dva postupka možemo dobiti veliki broj uglova različitih vrijednosti. Problem nastaje kada pokušamo da konstruišemo uglove od 40, 20, 10 i 5 stepeni(kao i druge uz pomoć ovih navedenih uglova). Autor ovog rada se sa ovim problemom susreo još u toku osnovne škole gdje je dobio zadatak da konstruiše ugao od 5 stepeni. Nakon mukotrpnog više sedmičnog rada na ovom problemu nije uspio da ga riješi, te je smatrao da je to nemoguće. S druge strane zašto bi nastavnik dao takav zadatak ako ga je nemoguće riješiti. Možete zamisliti razočarenje kada je od nastavnika saznao da treba da konstruiše ugao od 15 stepeni, a zatim da „otprilike“ uzme trećinu tog ugla.
Nakon dužeg rada na ovom problemu autor ovog rada je takođe naišao na problem kako podijeliti duž na tri jednaka dijela koristeći samo šestar i lenjir bez podioka. U ovom radu je predstavljeno rješenje ovog problema. Radi se o veoma jednostavnom postupku.
Postupak odnosno metoda za podjelu duži je grafički predstavljena i matematičkim jezikom objašnjena korak po korak u glavnom dijelu ovog rada.
Translation - English
1. ABSTRACT
This work deals with the problem how to devide a length by using pair of compasses and a ruler. This was not possible until now.
In the introduction of this work the author brings a short description of the problem and motivation to deal with this problem. The main part of this work brings a simple method to solve the problem. This method is presented by a graphic, but also described step by step in math language.
The contribution of this work is the method, that it brings, how to devide a length by using pair of compasses and a ruler.
2. KEY WORDS AND SUBJECT CLASSSIFICATION NUMBER
Geometry, construction, design, angles, a pair of compasses, ruler, method, length, straight line, divide, three parts, etc.
The subject classificiation number is 51(Geometry).
3. INTRODUCTION
When constructing angles some of them are easy to construct by using a pair of compases and a ruler. To construct angles it is important to know that circumference can be divided to six equal parts (first we construct circumference , and with the same reach of the pair of compases simply divide the circumference). This way we get six eqyal angles, sixty degrees each. Also every angle we can divide in two equal parts. By combining these two methods we can get various angles. The problem occurs when we try to construct 40⁰,20⁰,10⁰ and 5⁰ angles (so as others with the use of the stated angles). The author of this work faced this problem during elementary school. He got the assignment to construct 5 degrees angle. After many weeks of hard work he realised he can not solve this problem and considered the task impossible. On the other hand why would the teacher give him an impossible task. You can imagine his surprise when the teacher told him he should construct 15 degrees angle, and then „approximately“ take a third of the angle.
After a long work on this problem the author also encountered a the problem How to divie a length on three equal parts using only a ruler and a pair of compases.
The solution i.e. the method is presented in this work. It is a simple method.
This method is presented by a graphic, but also described step by step in math language in the main part of this work.
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