Nevertheless, an individual may prefer to have this type of calculus removed for other reasons or otherwise as part of a long-term treatment regimen. For example, Bennett and Mccrochan note that, "When the American Dental Association later approved Warner-Lambert's mouthwash, Listerine, by stating that 'Listerine Antiseptic has been shown to help prevent and reduce supragingival plaque accumulation and gingivitis. . ., ' sales rose significantly" (1993:398). It remains unclear, though, what effect, if any, that supragingival calculus has on gingival inflammation. For instance, Mandel and Gaffar report that, "Although there is no doubt that gingivitis can develop in the absence of supragingival calculus, it is not clear to what extent the presence of mineralized deposit enhances gingival inflammation" (1986:249). Although the composition of the material is the same, the location of calculus below the gumline is termed "subgingival" and this condition is discussed further below.

Subgingival. Because of its location below the gumline, researchers have increasingly focused on treatment modalities that could treat subgingival calculus. The results of clinical studies concerning the efficacy of various treatment modalities reported by Cooley and Lewkowicz include the use of Elyzol dental gel with subgingival scaling. These early studies, though, were flawed in several ways, and appeared to be biased favor of using Elyzol gel for the initial treatment or as a replacement for the subgingival scaling. According to these researchers, "As the gel is an antiobiotic, it is reasonable that the gel should be applied only if the mechanical treatment fails to solve the pocket. Moreover, the study groups in the studies seem to have been poorly defined" (Cooley & Lewkowicz 2003:63). The results of a more recent randomized clinical and microbiological slit-mouth design study (Stelzel & Flories-de-Jacoby 1996) concerning the efficacy of metronidazole 25% dental gel compared to subgingival scaling on recall subjects showed that there were no statistically significant differences between the two treatment modalities. Some of the limitations of this study concerned the relatively few subjects involved (n=30) and smokers were included in the sample which may have influenced the study's outcomes (Cooley & Lewkowicz 2003).

According to Zacharczenko (1998), many prescription drugs have also been introduced in recent years to treat periodontal disease and the inflammatory response that is associated with the condition. These products include Peridex (chlorhexidine gluconate, Zila) and Perioguard (chlorhexidine gluconate, Colgate Oral Pharmaceuticals) rinses and over-the-counter, non-prescription alternatives such as Colgate's Total and Viadent Advanced Care toothpastes that are designed to treat initial colonization of bacterial growth on teeth as wel as plaque accumulations and gingivitis (Zacharczenko 1998). One such product, PerioChip (chlorhexidine gluconate 2.5 mg, Astra), has been introduced as a treatment for adult periodontal disease (Zacharczenko 1998). The product is described by Zacharczenko as "a biodegradable, subgingival, sustained-release chip, measuring 4mm x 5mm x 350 microns" (1998:56). The product is inserted into a periodontal pocket by the treating dentist and simply degrades over the next week to 10 days, at which point the treatment is complete (Zacharczenko 1998). The active ingredient in the PerioChip, chlorhexidine, is a powerful bactericidal agent and has been shown to be highly effective in treating periodontal disease (Zacharczenko 1998). It should be noted, though, that the PerioChip treatment is intended to be part of a more comprehensive treatment regimen and is intended to supplement traditional periodontal therapeutic interventions (Zacharczenko 1998).

The focus of a study by Alaluusua, Calderara, Gerthoux, Lukinmaa, Kovero, Needham, Patterson, Tuomisto and Mocarelli (2004) was to determine the effect of dioxins on human organogenesis, including periodontal health in general and the percentage of subgingival calculus sites in particular. Although it was determined that dioxins could affect the organogenesis process in human in general, exposure did not affect the number of subgingival calculus sites (Alaluusua et al. 2004:1313).

Finally, a summary of epidemiological studies concerning supragingival calculus reviewed by Mandel and Gaffar (1986) are provided in Table 1 below.

Table 1

Summary of Supragingival Calculus Epidemiological Studies

Author/Date

Key Findings

Comments

Ainamo (1970)

Subjects were 154 U.S. Army recruits (age 19-22 yrs); author found a high positive correlation between both subgingival and supragingival calculus as well as gingivitis. Author also found that there was a higher correlation between calculus related plaque and gingivitis compared to carcinogenic plaque.

Author used retention index that distinguishes between the types of plaque that are associated with calculus and those that are associated with caries.

Alexander (1971)

This study examined the distribution pattern of supragingival and subgingival calculus, bacterial plaque and gingival inflammation in 200 dental students and 200 dental clinic patients. Author found that the papillae exhibited the highest prevalence of gingival inflammation and the buccal margins the lowest.

This pattern coincided with the highest prevalence of subgingival calculus on the interproximal surface and the lowest on the buccal.

Buckley (1980)

Also found a strong correlation between the buccal and lingual gingival indices and their respective plaque and supra- and subgingival calculus indices.

There was a higher degree of correlation for gingival indices vs. plaque than for gingival indices vs. calculus.

Lennon & Clerehough (1984)

229 children followed from ages 14-16, authors found that the presence of subgingival calculus on mesio-buccal sites was the best predictor of future attachment loss.

Screening tests based on subgingival calculus would tend to have low sensitivity, in other words it would miss some subjects who would go on to develop loss of attachment but it would have high specificity. Authors indicate this is an area that needs further research.

Cereck et al. (1983)

Monitored the healing events of seven patients with generalized chronic periodontitis during three consecutive phases of treatment (brushing and flossing; the use of a Perio-Aid subgingivally and supra- and subgingival instrumentation). Authors found limited improvements in the bleeding scores and pocket depths on probing with brushing and flossing alone. The use of the Perio-Aid to remove plaque subgingivally provided no additional improvements.

This study is especially interesting because it attempted to separate out subgingival plaque removal with the Period-Aid from removal of subgingival calculus plus plaque by instrumentation. It would appear that with subgingival calculus present, subgingival plaque cannot be adequately removed or if it is removed the mineralized deposits are themselves capable of perpetuating periodontal disease.

Implications of the Removal of Dental Calculus

There are some interesting and contrasting views concerning the implications of the removal of dental calculus reported in the literature in recent years. For instance, on the one hand, Sheiham emphasizes that the removal of calculus can actually do more harm that good when the resources required and the overall effects on periodontal health are taken into account. In this regard, Sheiham notes that, "Commitment to provide high quality oral health care should be at the heart of everyday dental practice. Numerous dental procedures are ineffective at best and harmful in many cases" (2001:53). Because the majority of gingival inflammation cases remain uneventful, Sheiham suggests that there is no clear-cut connection between gingivitis prevention efforts and improved outcomes for destructive periodontal diseases. In this regard, Sheiham adds that, "The need for periodontal treatment is relatively low. Since most gingival inflammation does not progress to periodontitis it is not clear whether prevention of all gingivitis is necessary for preventing destructive periodontal diseases" (2001:54). Moreover, calculus removal, for other than personal reasons related to appearance or otherwise notwithstanding, Sheiham concludes that the removal of calculus is not supported by the evidence to date. According to Sheiham, "Calculus (tartar) does not have a major role in the pathogenesis of periodontal diseases. Apart from social reasons, the clinical basis for calculus removal is unjustified" (emphasis added) (2001:54).

On the other hand, though, a number of researchers indicate that there is an inextricable relationship between calculus and other periodontal disease processes. For instance, Schermer reports that, "Periodontal disease, reflected by calculus deposits (mineralized dental plaque) and resorbed alveolar bone, correlates strongly with both caries and attrition" (2004:577). This observation has special significance for some Native Americans and developing regions of the world. In this regard, Schermer also notes that, "Diets high in starchy foods (such as corn) or protein (such as bison) can accelerate the development of dental plaque, while grit in ingested items and tough or fibrous foods can accelerate attrition" (2004:577).

Conclusion

The research showed that a number of factors contribute to periodontal health, including tobacco use, changes in hormonal levels, stress, medication regimens, nutritional practices, other illnesses, and clenching and grinding teeth. The research also showed that although there is a consensus among healthcare practitioners that periodontal health is important for a number of reasons, there remains less agreement concerning the need for the removal of sub- and supragingival calculus accumulations. Some authorities indicate that calculus accumulations can lead to other, more serious periodontal diseases including gingivitis while others maintain that calculus does not play a major role in the pathogenesis of periodontal diseases and its removal is clinically unjustified.

References

Alaluusua,…

Alaluusua, S., Calderara, P., Gerthoux, P.M., Lukinmaa, P.L., Kovero, O., Needham, L.,

Patterson, D.G., Tuomisto, J. & Mocarelli, P. 2004 "Developmental dental aberrations after the dioxin accident in Seveso." Environmental Health Perspectives 112(3): 1313-

Ainamo, J. 1970 "Concomitant periodontal disease and dental caries in young adult males."

Suomen Hammaslaakariseran Tomituksia 66: 301-364.

"Calculus removal." 2010 Integrated Publishing. [online] available: http://www.

"Oral health. 2010 World Health Organization. [online] available: <http://www.who.int/topics / oral_health/en/>.

Being able to "crunch the numbers" is an essential part of the manager's role. Too often managers feel uncomfortable working with numbers because of their limited mathematical background. This reduces their usefulness, however. Strong managers are not intimidated by the numbers, but rather view them as an essential component of the job. Therefore, part of the process of studying business management is to build the set of tools that

(Hilton, 26) in general, no mathematician would be willing to accept the solution to a problem without some sort of proof, and in the same way, no student of calculus would be ready to accept the resolution of a problem without the necessary proof. (Cadena; Travis; Norman, 77) It must be stated that Newton's mathematics that involved 'fluxions' was one of the first forms of the area defined as 'differential

Calculus and Definitions of Its Concepts Indefinite integration Indefinite integration is the act of reversing any process of differentiation. It is the process of obtaining a function from its derivative. It is also called anti-derivative of f. A function F. is an anti-derivative of f on an interval I, if F'(x) = f (x) for all x in I. A function of F (x) for which F'(x)=f (x), this means that for

Mamikon even takes this simple observation about curves to establish a new relationship between the tractrix and exponential curves (Apostol & Mamikon 2002). Mamikon's visual understanding and explanation of calculus is not limited to two-diemnsional curves, nor does he concern himself only with new insights into mathematical relationships. In another paper, again published with Apostol, Mamikon established new proofs for Archimedes' discoveries concerning polyhedrons and their circumscribing prisms (Apostol &

The semi-minor and semi-major axis are easily determined, and can then be subbed into the standard equation for an ellipse. Taking the square root of y will result in a plus/minus, and discarding the minus erases the lower half of the ellipse. The long axis extends horizontally, and the short axis extends vertically. The x and y axis bisects the ellipse already, so both a and B. are available:

Derivatives and Definite Integrals Word Count (excluding title and works cited page): 628 Calculus pioneers of the seventeenth century such as Leibniz, Newton, Barrow, Fermat, Pascal, Cavelieri, and Wallis sought to find solutions to puzzling mathematical problems. Specifically, they expressed the functions for derivatives and definite integrals. Their areas of interest involved discussions on tangents, velocity and acceleration, maximums and minimums, and area. This introductory paper shall briefly introduce four specific questions