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By Reece Kurre, Gabriel Walton

"Roof bolting has long been used in underground mines across the world to provide ground support. Modern roof bolts are cheap and easy to install with the use of specialized machines as a part of the production cycle. Lhoist North America’s Crab Orchard Mine is an underground room and pillar limestone mine that uses mechanically anchored roof bolts for ground support. The mine currently employs two different roof bolting patterns: a standard 5 × 5 foot pattern, and a 2.5 × 2.5 foot pattern for use in areas with particularly hazardous roof conditions. The purpose of this study is to evaluate the relative effectiveness of each bolting pattern.A series of numerical models were created using RocScience’s RS2. The models were based on a symmetrical section of the mine at its deepest point, and were modeled using Generalized Hoek-Brown failure criterion along with a discrete fracture network. A series of sensitivity analyses were performed on the models by varying parameters such as joint friction angle, crack persistence, joint randomization, and tensile strength of the limestone. Based on the results of the original models and sensitivity analyses, it appears that the standard bolting pattern provides sufficient roof support capacity under almost all the expected conditions at the mine, since factors of safety below the design value of 1.5 were only found for individual bolts in a few of the worst test cases considered. These results can help improve the Mine’s productivity and reduce operating costs without compromising safety.INTRODUCTION AND CASE STUDY DESCRIPTIONLhoist North America’s Crab Orchard Mine is an underground limestone mine located in Crab Orchard, Tennessee. The mine is located under an 800-foot-high mountain, and outcrops on three sides. The mine is accessed through three separate portals and has two main levels, along with a partially developed third level. Extraction is accomplished by the room and pillar method using 50 × 50 feet pillars and 50 × 50 feet rooms. The mining height is limited to 50 feet to keep the pillar width to height ratio around 1.0. Each heading is excavated in a two-stage process that consists of a 30-foot-tall top heading and a 20-foot-tall bench. A distance of at least 30 feet is maintained between the two levels at all times (Crab Orchard Mine Technical Staff, 2017)."

Jan 1, 2019

By D. Keech

The Conveyor Equipment Manufacturers Association (CEMA) specification B105.1 “Welded Steel Conveyor Pulleys” adequately defines standard pulleys for most aggregate material handling applications. However, many aggregate applications demand pulleys of higher capacity and reliability than that offered by CEMA pulleys. This paper examines the CEMA Pulley Standard and pulley specifications for aggregate applications requiring greater capacity and reliability than the CEMA Pulley Standard. Higher reliability increases the uptime and has a lower total cost of ownership.

Jan 1, 2003

By R. M. Imhof, M. J. G. Battersby, G. Ciernioch

Pneumatic flotation is rapidly becoming accepted in the main stream of flotation techniques. Imhoflot is a pneumatic flotation process that in recent years has undergone progressive development. It combines short flotation times with excellent selectivity by employing intense pre-aeration and dispersion. K+S GmbH (K+S), Germany, has installed a complete Imhoflot flotation plant at its Sigmundshall plant. The plant treats hard salt consisting of sylvine, halite, anhydrite and kieserite. The reason for selection was that Imhoflot achieves the required grades of plus 60 weight percent K2O whilst offering lower operating costs than conventional flotation installations.

Jan 1, 2002

By F. Habashi

Asbestos, an extremely useful natural resource, has been studied extensively mineralogically and for industrial application. Its extraction from ores has been greatly improved with respect to safety in the work place. In spite of that, there is a decisive effort in many countries to ban its use on the grounds that it is a toxic substance. This action resulting in drastic decrease in production and the possibility of destroying the industry. The chelation of asbestos with organic dyes seems to be a promising way to abate its toxicity. Dyeing can be done when the fibers are slurred in water at ambient conditions in the same way as textile fibers.

Jan 1, 2009

By P. Rostami

It is important to study the ventilation system in order to better design and control of the working environment in deep underground mines. With increasing depth, heat, and humidity performance may be reduced and impair the attention of workers. The purpose of this paper is to apply a complex; development-end model configured in the MULTIFLUX program, developed at the University of Nevada, Reno, USA. The MULTIFLUX development-end model template has been benchmarked against measurement results from two UK coal mines in previous studies. The present study is a test of MULTIFLUX application in a metal mine. The model incorporates the simulation of the air flow field in the drift and the auxiliary air duct; simultaneous heat and humidity transport from the drift wall; heat and mass exchange between the air in the drift and the ducts; and the evaporation of process water and/or condensation of vapor as governed by the psychometric conditions. The results are compared with field data, measured at the Lucky Friday Mine (LF) in Idaho, USA, an underground mine and also shown between the results from the MULTIFLUX-based model, and those from another program, Kduct, developed at the Kyushu University in Japan.. Gao, K. Uchino & M. Inoue Fukuoka, Japan (2002)?

Jan 1, 2011

By R. Heersink, C. H. Wells

Innovations in communications and real-time information systems are providing industry opportunities to improve profitability. Real-time operating data is collected from equipment across a site or even several sites into a central server for secure PC and PDA-based Internet access. This paper includes discussion of how operating staff can use wireless devices to see equipment and processing data from anywhere throughout the mines and concentrators, and how management can view results from multiple mines, all in real time. Additional opportunities enabled through the remote access by equipment vendors or mining consultants is also presented, as well as an overview of typical benefits and current installations.

Jan 1, 2002

By Russell Barr

Strategic alignment throughout a mining organization is critical to effective strategic execution and good business performance. The alignment of strategic goals and objectives in the different operations and functions in a large global operation is a challenge facing executive management in light of legacy organizational structure and processes. An additional confounding factor in strategic alignment of acquisition and new project expansion is that mining projects and operations are frequently multi-cultural in terms of country origin as well as organizational culture. This brings together many cultures to accomplish the project or complete an acquisition (Financial Times, 2006). The mining industry presents numerous challenges to executives and mine management by the nature of the operation and organizational processes used in running it. For example, there seems to be an inherent conflict between the individual goals of the components that constitute a mineral processing operation (the mine, the mill, the smelter and the refinery), and lowest cost production of the final product. Managers of these component operations have specific objectives passed down from the corporate executives. Those site managers tend to be compensated based on throughput and perform to this main metric. This tendency to maximize throughput for an individual operation can contradict the general process flow of a best-fit solution to producing the final product at the lowest cost. In an effort to become more aligned, firms are increasingly using balanced scorecard derivatives at great cost and effort (whether internally or externally sourced) in an attempt to help with strategic alignment. Balanced score-cards have been effective in providing a good strategic scorecard to companies with some measure of strategic alignment. Many firms make this effort of using balanced scorecards. However, most firms are not strategically aligned or, at best, are sub-optimized, in terms of strategic alignment (Kaplan and Norton, 2006). The tendency in mining operations is to focus on operating individual components as optimally as possible and stretching existing assets to the best possible production rates. ?Making tons? is the common operational focus. Numerous factors underpin this focus and can affect the ability of the operation?s ability to align properly with the corporate strategy and strategic goals. Critical factors are legacy organizational structure, culture, processes and performance measurement systems. Changing anyone of these factors to affect better strategic alignment requires significant attention to managing change.

Jan 1, 2008

By R. W. Waytulonis

This paper is an update of the activities of the U.S. Bureau of Mines, other government agencies, and the automotive and truck industry concerning diesel emission control. Enacted and proposed regulations from the U.S. Mine Safety and Health Administration (MSHA) and developments in diesel emission control are presented in terms of their impact on underground coal, metal, and nonmetal mines. Mine air quality regulations proposed by MSHA may require the underground mining industry to comply with new standards. Some mines may be required to take additional actions to meet new diesel particulate and lower nitrogen dioxide exposure standards; however, the mining industry is in a position to benefit from emission controls developed for the on-highway diesel engine market. The U.S. Environmental Protection Agency (EPA) has enacted regulations to reduce emissions from on-highway diesel trucks and buses. Engine manufacturers have responded by developing cleaner burning engines. Fuel producers have responded by providing cleaner burning reformulated diesel fuel, and exhaust aftertreatment devices have been developed to provide additional emissions reductions. Bureau research and development projects seek to determine the advantages of using modern engines and fuels, and to evaluate the efficacy of new exhaust control devices on mining machines. It appears that the diesel engine will continue to be a practical power source for use in confined environments because no other available power source is as mobile and efficient.

Jan 1, 1993

By Yukika Miyashita, Takahiro Inoue, Kenji Namikawa, Masashi Matsumoto, Junichi Koseki, Yoshihiro Terashima

"In order to construct an underground two-layer expressway branch junction structure with a height of 14.7 m and a width of 22.3 m, two shield tunnels in each layer were combined by using a non-cut-and-cover enlargement method in sedimentary soft rock. Before and during the construction work, preliminary analysis, in-situ investigations and laboratory tests were conducted to ensure the construction safety and to evaluate the deformation characteristics of sedimentary soft rock. The construction project was safely executed without any water leakage or collapse of tunnel working face. The predicted results from preliminary analysis were almost similar to the measured values. From the detailed investigation of measured results, it was confirmed that the deformation characteristic of the sedimentary soft rock was observed to a small extent as the ground deformation derived from construction work. INTRODUCTION In recent years, some newly constructed urban expressways in Japan are being planned as underground structures due to the consideration of roadside environment. The construction of such underground expressways is frequently conducted using a shield tunneling, a typical one of non-cut-and-cover methods, to prevent any adverse effect to traffic in arterial roads, operation of nearby commercial establishments, and daily lives of local residents during construction work. For underground urban expressway, the connections with existing road network on ground surface or on elevated sections are indispensable, which require the construction of an underground branch junction with large cross-section. This raises a technical difficulty regardless of the open-cut or non-open-cut construction method."

Jan 1, 2016

By Marco Aurelio Piangatelli, Massimiliano Bringiotti, Ferdinando De Angelis

"The construction of the three connecting tunnels between the east side and the west side of station C13, adjacent to the Vistula river, has a long and complex history, as they cross beneath one of Warsaw’s main road arteries (Wislostrada). After the attempt to excavate the first tunnel, the face of the tunnel collapsed on the night of August 13, 2012, and a volume of about 10,000 cubic meters of liquid mass (water, silty soil and sand) entered and flooded the west side of the station, which was filled with more than seven meters of material. Fortunately, the workers managed to escape, but machines and equipment were lost. This is the story of how the tunnels were completed, by adopting soil improvement, jet grouting, GRP bars, ground freezing and a careful choice of work steps. INTRODUCTION The Centrum Nauki Kopernik station on Line II of the Warsaw Underground is located alongside to the Vistula river (Figure 1). This station hereinafter is referred to as station C13.The station consist of three parts: the east and west part, and three connecting tunnels 40 meters in length with a large cross section (170 m2).. It includes the rails along the sides and the platform along the centre. The reason for the underground connection of two shafts with a tunnel is due to the presence of a road tunnel (Wislostrada, hereinafter called WS), which must be underpassed by the new metro line (Figure 2).The existing tunnel (Wislostrada) was built many years before, between diaphragm walls, and some foundation structures interfere with the underground tunnel. The challenge was to build the connectors without stopping the traffic of vehicles along the highway above. All works took place in very difficult geological and groundwater conditions due to the presence of Vistula alluvial deposits with poor mechanical characteristics. The soil profile consists of relatively loose sands on top, and silts overlying high plasticity Pliocene clays highly disturbed by the effects of the repeated over-sliding of glacial moraine deposits."

Jan 1, 2016

Placing a detonating explosive inside a volume of rock is an efficient method of rock fragmentation. The explosion generates internal tensile stresses in the rock, and because rock is a brittle material, this brings about crack propagation and fragmentation far more efficiently than does application of explosive on the surface. To get the explosive inside, we drill a pattern of boreholes and charge the explosive into the holes. This is really the one and only purpose of making blastholes in mining: to give access for the explosive to the interior of the rock. No matter how big and expensive a drilling jumbo we stand up in front of a rock face, and no matter how many boreholes we let it drill, the rock does not fall apart by itself without blasting. It is the action of the explosive in the boreholes that does it. When we consider that we need a pound or two of explosive for every cubic yard of rock to be fragmented, and a pint of borehole volume for each pound of explosive, we see that the process of blasthole charging is an important element in the whole process of rock blasting.

Jan 1, 1975

By Cayo Soto

Mining activity is important for the development of humanity. This development must be understood from the Academy where it allows showing alternatives for the industry performance. Likewise, these mining companies need to improve their results. Historically, a few years ago the application of the ESG (Environmental, Social and Governance) criterion was verified, which is positioned as a factor/regulator in the design of the performance of industries in general. ESG as an integral part of the concept of sustainability serves as a tool to conceive mining without conflicts and with a reputation based on trust in the interrelation of the university, industry and society. Therefore, the academy must strive for new knowledge in a way that allows it to continue in the virtuous circle of constantly feeding it. In this context, the best mining practices are implemented in constant questioning of their activities. The scientific essence of the industry supported by the academy developed in an operational dynamic is addressed. Finally, the objective of this research work is to interrelate 3 variables: ESG, Academia, and the Mining Industry, where the transition of knowledge and the role of each variable in relation to each one can be understood. This allows for an additional understanding of mining in the future with new mental attention.

Feb 1, 2025

By Bruce Gellar

For the past six years, the author has made it a priority to attend the Prospectors and Developers Association of Canada’s (PDAC) annual conference. This most recent meeting took place March 10-13, 2002in Toronto, Ontario. In the three years since the author’s last PDAC report, the mining industry has undergone a severe trough. Some the industry’s woes included deeply discounted commodity prices, rampant layoffs, mergers, and overall avoidance by the investment community. However, at each of the PDAC conferences, the author has felt a heightened sense of excitement about the mining industry, more so than at other similar gatherings.

Jan 1, 2002

By Greg Sanders, Michael Gilbert, James G. Shaughnessy

"A new raw water intake from the South Holston River to the Kingsport water treatment plant is under construction. The exploration for the 335 meter long horseshoe shaped tunnel design took advantage of the site topography along the alignment to better define the complex geology consisting of Knox Limestone and Sevier Shale formations separated by a fault zone. To assess the geological conditions and to determine the extent of the fault zone, a 183 meter long horizontal boring and geophysical investigation was performed along a portion of the tunnel’s horizontal alignment. Explorations defined the fault zone width at approximately 5 meters and packer testing along the alignment provided a means of estimating groundwater inflows. As the tunnel excavation advances, comparisons of exploratory data versus encountered conditions will be made. This paper provides details on the geotechnical investigation, lessons learned, and the influence of the geology on the tunnel design. PROJECT OVERVIEW The Kingsport WTP is supplied with raw water via the South Holston River. The City of Kingsport (City) owns and operates the Kingsport Water Treatment Plant (WTP). The existing raw water intake system, consisting of pumps, power supply, raw water piping and appurtenant facilities has been determined to be vulnerable to failure. The original Raw Water Pump Station (RWPS) was constructed in 1928 as part of the original Kingsport WTP project. The 1928 RWPS operated until 1970 when it was replaced by the existing RWPS. This existing system still utilizes the 1928 piping and piping tunnel. Improvements to the RWPS hydraulics and capacity are required to meet the City’s future water treatment needs. The system extracts water from the South Fork of the Holsten River and coveys it via three pressure pipelines to the WTP. The conveyance piping exits the RWPS, ascends approximately 23 m up a near vertical rock outcropping then enters a 120 m long tunnel. Upon exiting the tunnel the piping continues underground to the WTP. The drill and blast tunnel is horseshoe shaped and nominally 3.3 m high by 3.3 m wide. The easternmost 62.3 m of the tunnel is without any type of support. The remainder is lined with concrete. According to the City of Kingsport, the concrete lining was installed in the 1970’s as part of upgrades to the facility. An evaluation of the current facilities concluded that the conveyance piping was in poor condition and required replacement."

Jan 1, 2016

By Norman Weiss

The design of an ore-processing plant requires a high degree of cooperation among the geological, mining and metallurgical engineers. The purposes of this section are to provide mill design information most commonly needed by the mine planners and management, and to summarize the kinds of information that must be supplied to the mill designer to enable him to provide a suitable plant. 28.1-BASIS OF DESIGN NORMAN WEISS 28.1.1-SIZE OF PROJECT The size of the project generally is expressed in tons of ore milled per day, but company policies differ widely in this respect, a few adhering to this set figure but many expecting the design capacity to be liberal. To some companies that follow the latter practice a 25,000-tpd milling plant that cannot reach 30,000 or 35,000 tpd without major additions is a disappointment. The engineers responsible for planning the operation must know what is intended. Equally important are operating schedules, particularly the number of operating days per week and shifts per day for ore delivery, crushing, grinding and processing. Hours per shift also are an important factor in design, particularly in the case of ore delivery, and the percentage lost time expected for maintenance, cleanup, inspection, preventive maintenance shutdowns, and many others, has to be taken into account. Frequently, the ore deposit will vary in hardness and grade to such a degree that the capacity of the mill will vary widely from year to year and cannot be expressed as a fixed figure. but rather as an average over a calculable period, such as 10 yr, or as a specific daily capacity over the first 2 yr, next 4 yr, etc., or some similar projection. A good example of this kind of situation is Asarco's Mission operation 15 mi southwest of Tucson, Ariz., described by Weiss and Vincent.' where the major rock types differed widely in hardness, so that a change in the proportion of these types in the mill feed could have imposed difficult design problems if a constant tonnage rate had been expected. 28.1.2-EXPECTED LIFE The life of a mining operation depends upon the size of the deposit and the rate of mining. The latter is a policy decision based on an economic analysis which, in turn, is based on many factors.' From the point of view of mill planning, the estimated life of the operation determines many criteria and affects many decisions on strength of structures and degree of protection of men and materials, the quality of the materials-handling and process machinery, the type of delivery systems for ore to the mill and concentrates to the smelter or market, and many others. Costly installations that may be excellent investments for a 20-yr project may be wasteful for a 5-yr operation. An example is the comparison of different methods of crushing or grinding. Take single- vs. multiple-stage grinding-the former may be found more economical for a 5-yr operation, and the other, more costly, method more economical for a 15 to 20-vi- life.

Jan 1, 1973

By William A. Vogely, Robert T. Deacon, Walter J. Mead

Oil and gas together are the most important energy sources consumed in the United States. In 1983, 67% of total energy consumption was represented by these two resources (43% was oil and 25% natural gas), while coal accounted for only 23% of U.S. energy use. All other sources (hydroelectric, nuclear, geothermal, wood and other waste products) accounted for only 10% (U.S. Department of Energy, 1983, p. 1). In this chapter we address the issue of regulation in the oil and natural gas sectors of the U.S. energy industry. In addition, we analyze the cartel characteristics of the Organization of Petroleum Exporting Countries (OPEC). If OPEC is an effective cartel, then U.S. oil as well as substitute energy prices, production, and consumption will be affected by cartel action. Further, as the nation learned in the 1970s, major changes in oil prices produced major disturbances in other sectors of the U.S. and world economies. Consequently, it is important to determine whether the roughly ten-fold increase in nominal prices that occurred in the 1970s was the result of cartel action, the result of normal economic forces adjusting to the fact that the world was running out of cheap oil, or some combination of the two. Furthermore, the presence of OPEC- associated oil price increases is related to regulations that were imposed on the energy sector during the decade of the 70s. THE RATIONALE FOR GOVERNMENT INTERVENTION Economists have traditionally judged the state of an economy to be efficient if it is impossible to improve the welfare of any one member of society without harming someone else. Any economy that satisfies this condition is said to be Pareto efficient, after the Italian economist Vilfredo Pareto who first gave rigorous attention to such questions (see Chapter 4.10). It is easy to see why an economy that fails to satisfy this condition could not be efficient; by definition, it would be possible to alter the allocation of resources in a way that improves everyone's welfare.' Much of the appeal of this weak efficiency criterion is that it avoids comparisons of levels of well being among different individuals. The cost of such generality, however, is that in any given economic system a wide array of different Pareto efficient states will typically be attainable. In the simple Robinson Cursoe economy of the undergraduate textbook, for example, efficiency could just as easily be attained in the case where most of the island's resources are owned by Friday as in the case where they are under Crusoe's control. However, the distribution of welfare among the two inhabitants would obviously be quite different in the two situations. Such equity issues cannot be settled on objective or scientific grounds. To decide which distribution of welfare is socially "best" an explicit value judgment is needed. It is useful to keep in mind the preceding distinction between efficiency and equity issues when analyzing the role of government in a market economy. Decentralized market processes will not necessarily result in a distribution of welfare that society considers just. For this reason a potential role for government lies in the redistribution of income among individuals. In some circumstances, however, market pro-

Jan 1, 1985

By J. W. Stevenson

At this 5th U.S. Mine Ventilation Symposium I would like to focus your attention on safety and the contribution of the ventilation engineer over the past 50 years. This conference affords us the opportunity to express, to listen, and to learn. As ventilation engineers it is indeed an exciting time--a time that not only stimulates our imagination but also pin points our aims in our quest to obtain zero fatalities by the year 2000, the goal expressed by William J. Tattersall, Assistant Secretary of Labor, Mine Safety and Health Administration. In the past, coal mine ventilation has often been unfortunately synonymous with explosions and resulting fires. Those not familiar with us do not recognize the painful evolution of the coal mining industry and particularly the evolution of mine ventilation. To put my presentation into perspective, I recently reviewed a U.S. Bureau of Mines Bulletin No. 586 - "Historical Summary of Coal-Mine Explosions in the United States 1810 - 1958 prepared by H. B. Humphrey Mining Health and Safety Engineer. This bulletin was published in 1960. Mr. Humphrey stated "In 1946, factors contributing to the explosions occurring from 1941 to 1945 were: (1) The rapid increase in the use of electrical equipment at face regions where gas and dust are most likely to be found; (2) the increased demand for coal with the desire to obtain maximum tonnage per machine at minimum cost, which in many mines has resulted in neglect of even rudimentary precautionary measures; (3) multiple-shift operation without provision of time for adequate maintenance of equipment, effective rock dusting, and testing for gas; (4) decrease in supervision owing to demands on supervisors for maximum tonnage and loss of competent supervisors to other employment; (5) lack of effective supervision, owing to numerous new conditions, some of them war-connected; (6) inability to obtain adequate equipment repair and replacement parts; (7) shortage of labor and inadequate training of coal-mine workers; and (8) failure of both miners and mining officials to show regard for safety in changing from hand-loading to mechanized methods". Most of the eight factors listed by Mr. Humphrey continue to affect our work lives as mining engineers. The increased demand for coal with the desire to obtain maximum tonnage per machine at minimum cost has never changed. The local and regionalized coal industry of the 40's is today competing against the world coal market. Our mines work or shut down based on cost. This has always been the case. During the five year time-frame Mr. Humphrey was documenting, 345 miners were killed in major explosions. A major explosion was one in which five or more miners were killed in a single accident. In addition, 105 more miners were killed in minor explosions for a total of 450. What a wanton waste of life. What fears, anxieties, miseries, and sufferings were created by these accidents. However, we must remember and keep in mind that the coal mining company officials, engineers, and foremen, the governmental agencies- federal, state, and local - were using the technical tools and knowledge available to operate the mines as safely as they could. Obviously mine ventilation engineering technology was woefully inadequate.

Jan 1, 1991

In this paper, the logic and the capabilities of a long term production planning method for open pit mining are presented. The method is the first attempt in obtaining simultaneous solutions to the four interrelated parameters of open pit mining; 1) the mine life, 2) the specific blocks to be mined each year, 3) the amount of ore and waste to be mined each year, and 4) the ultimate pit limits. An efficient cutoff grade can also be obtained through a sensitivity analysis. None of the existing methods can bring such a comprehensive solution to the problem. A production plan for a real life gold deposit is given to illustrate the logic and the capabilities of the method.

Jan 1, 1993

By J. S. Gardner

Fortunately, few mining professionals have dealt with what all mining professionals fear---a mine disaster. Unfortunately, many have dealt with ?accidents? which may or may not claim lives but nevertheless rise to the level of a ?disaster? given the fallout of liability and litigation in today?s society.1 The undersigned authors published an article some ten years ago regarding crisis management2 based upon their collective first-hand experiences in actual disasters to that point in history. Unfortunately, disasters have occurred since that time, prompting legislation, and a fresh analysis and expansion of those basic principles is certainly in order. Without question, no two disasters are ever alike, yet general guidelines for forming an effective plan of action can be formulated?and if a mining operation is to have any chance of survival after a disaster, such a plan is vital. The primary concern as any disaster evolves remains as stated a 2003 SME article3--the protection of human life. From that point, the focus moves to any assistance that may be needed given the magnitude of the situation. Permeating throughout this process is "damage control." The first step in dealing with a disaster, however, begins long before any threat of danger arises?formulation and implementation of an Emergency Response Plan.

Feb 23, 2014

By Paul L. Russell

Numbers, arithmetic, mathematics. Where did it all come from? Who needs it? We all do, but many school children would not agree. Engineers, physicists, accountants, tax collectors, and most of the general public are well aware that modern society in large part is founded on mathematics and could not exist without it. Mathematics developed over thousands of years as part of the everyday life of man. No one area, tribe, or race can claim discovery. In fact, from the records that do exist, it is evident that many facets of mathematics were discovered independently of others who made similar discoveries. While proof may be lacking, the earliest concepts of mathematics may be some 250,000 to 300,000 years old. The first use of numbers as written records is unknown. However, a bone of a young wolf deeply cut with 55 notches-arranged in two rows, one of 25 notches, the other of 30-was found in Czechoslovakia. Dated to be about 30,000 years old, it is perhaps an early record of some kind of counting system. It is assumed that mathematics was developed as an answer to man's practical needs, but anthropological studies suggest that the art of counting may have developed in connection with the needs of primitive religious ceremonial rites. Fingers probably were first used to designate sets of from one to five objects. Using both hands, up to 10 items could be indicated. As civilization developed, so did the need for more flexible systems to record items of trade, measure land, and figure taxes. Aristotle noted that the development of the decimal system comes from the fact that most people are born with 10 fingers and 10 toes. In spite of this obvious fact many early civilizations used binary, ternary, and quinary systems while vigesimal systems (with 20 as a base) and even sexagesimal systems (with 60 as a base) were used by others. A form of writing was in use in both the Mesopotamian and Nile valleys as early as 3000 to 4500 B.C. In Mesopotamia, wedge-shaped marks were impressed upon soft clay tablets that were hardened in ovens or by the sun. Many thousands of such tablets have survived. When the tablets were finally deciphered, some were found to be records of items shipped in trade, inventories, tax accounts, and mathematics exercises for teaching. Mesopotamia is also the source of an interesting board game dating back to about 2500 B.C. Its buttonlike men and triangular dice were apparently used with squares of shell, inlaid with lapis lazuli and red sandstone. Unfortunately, rules of play were not found. In Egypt, record preservation was somewhat better. Discovery of the Rosetta Stone in 1799 eventually led to deciphering the Egyptian hieroglyphics that included a numbering system at least 5,000 years old. These records show a competence in counting and numbering. A calendar of good accuracy may have been in existence as early as 4,200 years ago. Mathematics, as practiced today, developed when the Greeks added logic and proof to arithme-

Jan 12, 1982