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TEXTO 1 
 
REDUCING WATER CONSUMPTION IN MINING 
Found in smartphones, modern cars, climate-friendly photovoltaic units and used in many other 
industries, hi-tech materials have become an indispensable constituent of everyday life. Although 
recycling can partially cover the demand for raw materials, most are still sourced from mining. The 
environmental impacts are well known: land use, the generation of additional traffic infrastructure 
and the industrialization of often remote areas. Mining also requires vast quantities of water and 
produces correspondingly large volumes of wastewater. Working in partnership with colleagues in 
Finland, a team of researchers at Helmholtz Institute Freiberg for Resource Technology (HIF) led by 
process engineer Bruno Michaux has developed a method of making water usage in the processing of 
mineral raw materials more sustainable. Taking the mineral fluorite as an example, they have shown 
how the water consumption can significantly be reduced by the aid of process simulation. 
Fluorite — also known in mineralogy as fluorspar and by its chemical name of calcium fluoride — is an 
important raw material for industry. It is used, for example, in the smelting of iron, in aluminum 
extraction and in the chemical sector as a raw material for producing fluorine and hydrofluoric acid. 
Probably the best-known product of fluorine chemistry is PTFE, a fluoropolymer which is sold in 
membrane form under the trade names Teflon and Gore-Tex. 
"The extraction of fluorite consumes a lot of water," explains Bruno Michaux. "Depending on the local 
climate, but even more so on the design of the mineral beneficiation plant, it can be up to 4,000 litres 
per tonne of ore." There is obviously nothing that the HIF researchers can do about the weather, but 
they can certainly contribute to optimizing the processing itself. In this step of the process, waste rock 
is separated from the extracted ore in order to raise the fluorite content from below 50 percent to 
around the 98 percent mark. 
"Mining companies are trying to reduce their consumption of water by using it multiple times," says 
Michaux. "However, used water contains substances that can interfere with the process performance, 
and that is something to be avoided." Examples of such substances would be calcium and magnesium 
ions, which hamper the hydrophobization of the fluorite surface. The potency of this effect depends on 
the concentration of the ions. The new method now takes into account the influence of the chemical 
composition of the water on the flotation. As a result of extensive laboratory experiments with a 
fluorite ore, the researchers obtained data that reflected the complex interaction of the dissolved 
substances and integrated them into the HSC Sim simulation software. HSC Sim is already used in the 
mining industry to map the processing plant and to control mineral beneficiation process. 
"With the additional features we developed, the software is now able to take into account the 
composition of the process water," explains Michaux. "This enables the possibility of recycling the 
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water without compromising the process efficiency." The simulation also allows operators to optimize 
the use of different water reservoirs in the vicinity of the mine such as lakes, rivers, aquifers or the sea. 
Further process steps, such as the grinding and dewatering of the ore, are to be integrated in the 
future. In an ideal scenario, water consumption could then fall below 1,000 litres per tonne of ore. 
The research team hopes to subject the new method to a practical test in an actual mining operation 
very soon. "As this requires a fully digitized treatment process in which sensors are continuously 
measuring and reporting the properties of the streams to process control, it is only larger mines that 
will venture such an investment at this early stage," adds Michaux. "The potential of digitization is, 
however, enormous: real-time monitoring and truly intelligent process simulation make it possible 
to extract more raw materials while using less energy and fewer natural resources." This applies to all 
ores and not just to the recycling of water in fluorite processing, for which the simulation method was 
developed by the HIF team. 
Fonte: Adaptado de: Helmholtz-Zentrum Dresden-Rossendorf. Reducing water consumption in mining. Disponível em: 
https://www.sciencedaily.com/releases/2019/03/190328102647.htm. Acesso em 23 jun 2019. 
 
TEXTO 2 
 
THE TWO CULTURES OF MATHEMATICS IN ANCIENT GREECE 
The notion of ‘Greek mathematics’ is a key concept among those who teach or learn about the Western 
tradition and, especially, the history of science. It seems to be the field where that which used to be 
referred to as ‘the Greek miracle’ is at its most miraculous. The works of, for example, Euclid or 
Archimedes appear to be of timeless brilliance, their assumptions, methods, and proofs, even after 
Hilbert, of almost eternal elegance. Therefore, for a long time, a historical approach that investigated 
the environment of these astonishing practices was not deemed necessary. Recently, however, a 
consensus has emerged that Greek mathematics was heterogeneous and that the famous 
mathematicians are only the tip of an iceberg that must have consisted of several coexisting and partly 
overlapping fields of mathematical practices. We describe as much of this ‘iceberg’ as possible, and the 
relationships between its more prominent parts, mainly during the most crucial time for the formation 
of the most important Greek mathematical traditions, the fifth to the third centuries BC. 
Let us begin with a basic observation. Whoever looks for the first time at a page from one of the giants 
of Greek mathematics, say, Euclid, cannot but realize an obvious fact: these theorems and proofs are 
far removed from practical life and its problems. They are theoretical. Counting, weighing, measuring, 
and in general any empirical methods, have no place in this type of mathematics. Somebody, however, 
must have performed such practices in daily life, for example, in financial or administrative fields such 
as banking, engineering, or architecture. Some of these fields demand mathematical operations of 
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considerable complexity, for example, the calculation of interest or the comparison of surface areas. 
Occasionally, ancient authors mention such mathematical practices in passing. What is known about 
these practical forms of Greek mathematics? 
Of the social elite who alone wrote and read for pleasure, most were less interested in practical 
mathematics, which was apparently not part of common knowledge. Occasionally, one comes across 
obvious arithmetical blunders, mostly by historians. On the other hand, in most cases the practitioners 
themselves left no texts. Therefore, of all the manifold forms of practical mathematics that must have 
existed, only two are known a little, partly through occasional references by authors interested in 
other topics, partly through preserved artifacts, and, rarely, through the textual traditions of the 
practitioners themselves. 
Pebble arithmetic was used in order to perform calculations of all kinds. ‘Pebbles’ that symbolized 
different numbers through different forms and sizes, were moved and arranged on a marked surface— 
what is sometimes called the ‘Western abacus’. Several of these have been found, and the practitioners 
themselves are mentioned occasionally. These must have been professionals that one could hire 
whenever some arithmetical problem had to be solved, not so different from professionals renting out 
theirliteracy. However, manipulating pebbles on an abacus can lead to the discovery of general 
arithmetical knowledge, for example the properties of even and odd, or prime numbers, or abstract 
rules of how to produce certain classes of numbers, for example, square numbers. I call this knowledge 
‘general’ because it no longer has any immediate application. Here ‘theoretical’ knowledge emerges 
from a purely practical-professional background. 
The second subgroup of mathematical practitioners was concerned with measuring and calculating 
areas and volumes. Unlike the pebble arithmeticians, they had textual traditions, of which traces are 
scarce for ancient Greece, but considerable throughout the ancient Near East. These textual traditions, 
however, were sub-literary, that is, they never made it into the traditions of Greek mathematical 
literature. Therefore, most of these texts have been found inscribed on papyri, mostly written in 
imperial times, extant only from the Greek population in Egypt because of the favorable conditions of 
preservation there. There is every reason to assume, however, that in antiquity such texts were 
widespread in the Greek speaking world, both earlier and later. Here is an example from a first-
century AD Greek papyrus, now in Vienna: 
Concerning stones and things needed to build a house, you will measure the volume according to the 
rules of the geometer as follows: the stone has 5 feet everywhere. Make 5 x 5! It is 25. That is the area of 
the surface. Make this 5 times concerning the height. It is 125. The stone will have so many feet and is 
called a cube. 
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The papyrus contained thirty-eight such paragraphs in sixteen columns, obviously meant to codify 
valid methods or, rather, approved procedures in textbook style. Obviously, these methods are what 
the text calls ‘the rules of the geometer’. 
Fonte: Adaptado de: M. Asper. The two cultures of mathematics in ancient Greece, in The Oxford Handbook of the History of 
Mathematics. Oxford: Oxford University Press, 2009, p. 107-10. 
 
QUESTÕES 
 
As questões de 1 a 5 referem-se ao TEXTO 1: 
 
1) O grupo de pesquisadores do HIF 
(A) adaptou a usina de beneficiamento às condições climáticas. 
(B) criou um meio de tornar a mineração menos agressiva à natureza. 
(C) descobriu que a fluorita poderia ser reciclada durante o processamento. 
(D) desenvolveu materiais hi tech para serem utilizados na mineração. 
 
2) Analise as afirmativas abaixo e assinale a seguir. 
I. O grupo do HIF contribuiu para a criação do fluoropolímero PTFE. 
II. O fluoropolímero PTFE já tem aplicação comercial estabelecida. 
III. Segundo Bruno Michaux, a extração da fluorita depende de condições climáticas específicas. 
IV. A forma de reaproveitamento de água, proposta pelo HIF, dependeu do uso da computação. 
 
(A) Apenas I e III estão corretas. 
(B) Apenas II e IV estão corretas. 
(C) Apenas I, II e IV estão corretas. 
(D) I, II, III e IV estão corretas. 
 
3) Quais foram os métodos utilizados por Bruno Michaux e o grupo do HIF a fim de atingirem 
seus objetivos? 
 
4) Por que Bruno Michaux conclui que "The potential of digitization is, however, enormous” (6º 
parágrafo)? 
 
5) É CORRETO o que se afirma em 
(A) “recycling” e “Taking”, destacados no 1º parágrafo, indicam atividades desempenhadas pelo grupo 
 do HIF. 
(B) “smelting” e “producing”, destacados no 2º parágrafo, referem-se a fatos ocorridos no passado. 
(C) “Depending” e “processing”, destacados no 3º parágrafo, podem ser substituídos, respectivamente, 
 por “to depend” e “processes”, sem comprometer o significado das orações. 
(D) “measuring” e “reporting”, destacados no 6º parágrafo, apontam ações realizadas pelos sensores. 
 
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As questões de 6 a 10 referem-se ao TEXTO 2: 
 
6) O texto afirma que há um novo consenso que altera o entendimento anterior sobre a 
matemática grega antiga. Explique a razão para esta afirmação. 
 
7) De acordo com as informações constantes no 2º parágrafo, os chamados “gigantes da 
matemática grega” NÃO 
(A) conheciam os princípios da engenharia e da arquitetura. 
(B) incluíam matemáticos relevantes, como Euclides. 
(C) se interessavam por aspectos práticos da vida. 
(D) utilizavam operações matemáticas complexas. 
 
8) Segundo o texto, o que se sabe sobre a pergunta “What is known about these practical forms 
of Greek mathematics?”, em destaque ao final do 2º parágrafo? 
 
9) A aritmética dos seixos (“pebble arithmetic”) 
I. baseava-se em princípios semelhantes aos de um ábaco. 
II. era praticada por matemáticos renomados. 
III. exigia aplicação teórico-prática nas operações. 
 
É CORRETO o que se afirma em 
 
(A) I e III, apenas. 
(B) I e II, apenas. 
(C) II, apenas. 
(D) III, apenas. 
 
10) O papiro que hoje se encontra em Viena 
(A) demonstra que as conjecturas dos “gigantes da matemática grega” estavam corretas. 
(B) foi, na realidade, escrito por matemáticos egípcios. 
(C) objetivava explicar noções básicas e teóricas de aritmética. 
(D) serve para ilustrar um dos tipos de interesse de um subgrupo de matemáticos gregos. 
 
 
 
 
 
 
 
 
 
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RASCUNHO