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Journal articles on the topic 'Calculus – History'

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Published: 4 June 2021
Last updated: 31 January 2023

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1

Katz, Victor J. "Using the history of calculus to teach calculus." Science and Education 2, no. 3 (1993): 243–49. http://dx.doi.org/10.1007/bf00490066.

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2

Cirillo, Michelle. "Humanizing Calculus." Mathematics Teacher 101, no. 1 (August 2007): 23–27. http://dx.doi.org/10.5951/mt.101.1.0023.

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The history and the mathematics used by Newton and Leibniz in their invention of calculus. The exploration of this topic is intended to show students that mathematics is a human invention. Suggestions are made to help teachers incorporate the mathematics and the history into their own lessons.
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3

Machado, J. Tenreiro, Virginia Kiryakova, and Francesco Mainardi. "Recent history of fractional calculus." Communications in Nonlinear Science and Numerical Simulation 16, no. 3 (March 2011): 1140–53. http://dx.doi.org/10.1016/j.cnsns.2010.05.027.

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4

Alexander, Amir. "The Secret Spiritual History of Calculus." Scientific American 310, no. 4 (March 18, 2014): 82–85. http://dx.doi.org/10.1038/scientificamerican0414-82.

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5

Vergadia, Ankita, Neeraj Bansal, and Nitin Gupta. "Giant vesical calculus." International Journal of Research in Medical Sciences 7, no. 7 (June 28, 2019): 2842. http://dx.doi.org/10.18203/2320-6012.ijrms20192931.

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Author presented a case report of a 42-year-old male patient who presented with dysuria, heaviness in lower abdomen since last 3 years associated with pain over bilateral lumber region since 2 years. He had history of recurrent urinary tract infection for last 6 months with blood in urine occasionally. Routine urine examination detected red and white blood cells with culture growth of E. coli. Ultrasound of abdomen confirmed the presence of vesical calculus of 10x7x5 cm.
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6

Swoyer, Chris. "C.I.Lewis’s calculus of predicates." History and Philosophy of Logic 16, no. 1 (January 1995): 19–37. http://dx.doi.org/10.1080/01445349508837238.

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7

Otero, Daniel E. "Calculus Gems." British Journal for the History of Mathematics 36, no. 3 (September 2, 2021): 219–21. http://dx.doi.org/10.1080/26375451.2021.1997199.

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8

Ehrhardt, Caroline. "CARAMALHO DOMINGUES (João), Lacroix and the Calculus." Histoire de l'éducation, no. 123 (July 1, 2009): 127–31. http://dx.doi.org/10.4000/histoire-education.2039.

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9

Arndt, Michael. "The Explosion Calculus." Studia Logica 108, no. 3 (April 12, 2019): 509–47. http://dx.doi.org/10.1007/s11225-019-09861-6.

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10

Schroeder-Heister, Peter. "Frege and the resolution calculus." History and Philosophy of Logic 18, no. 2 (January 1997): 95–108. http://dx.doi.org/10.1080/01445349708837278.

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11

Tarasov, Vasily. "On History of Mathematical Economics: Application of Fractional Calculus." Mathematics 7, no. 6 (June 4, 2019): 509. http://dx.doi.org/10.3390/math7060509.

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Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.
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12

Priestly, W. M. "Mixing Calculus, History, and Writing for Liberal Arts Students." Humanistic Mathematics Network Journal 1, no. 13 (May 1996): 39–42. http://dx.doi.org/10.5642/hmnj.199601.13.19.

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13

McCullough-Benner, Colin. "Applying unrigorous mathematics: Heaviside's operational calculus." Studies in History and Philosophy of Science 91 (February 2022): 113–24. http://dx.doi.org/10.1016/j.shpsa.2021.11.013.

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14

Fleury, Marie-Renée, and Myriam Quatrini. "A Mixed λ-calculus." Studia Logica 87, no. 2-3 (November 23, 2007): 269–94. http://dx.doi.org/10.1007/s11225-007-9089-y.

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15

Eisenhofer, Raphael, Hideaki Kanzawa-Kiriyama, Ken-ichi Shinoda, and Laura S. Weyrich. "Investigating the demographic history of Japan using ancient oral microbiota." Philosophical Transactions of the Royal Society B: Biological Sciences 375, no. 1812 (October 5, 2020): 20190578. http://dx.doi.org/10.1098/rstb.2019.0578.

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While microbial communities in the human body (microbiota) are now commonly associated with health and disease in industrialised populations, we know very little about how these communities co-evolved and changed with humans throughout history and deep prehistory. We can now examine these communities by sequencing ancient DNA preserved within calcified dental plaque (calculus), providing insights into the origins of disease and their links to human history. Here, we examine ancient DNA preserved within dental calculus samples and their associations with two major cultural periods in Japan: the Jomon period hunter–gatherers approximately 3000 years before present (BP) and the Edo period agriculturalists 400–150 BP. We investigate how human oral microbiomes have changed in Japan through time and explore the presence of microorganisms associated with oral diseases (e.g. periodontal disease, dental caries) in ancient Japanese populations. Finally, we explore oral microbial strain diversity and its potential links to ancient demography in ancient Japan by performing phylogenomic analysis of a widely conserved oral species— Anaerolineaceae oral taxon 439. This research represents, to our knowledge, the first study of ancient oral microbiomes from Japan and demonstrates that the analysis of ancient dental calculus can provide key information about the origin of non-infectious disease and its deep roots with human demography. This article is part of the theme issue ‘Insights into health and disease from ancient biomolecules’.
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16

Bussotti, Paolo. "DIFFERENTIAL CALCULUS: THE USE OF NEWTON’S METHODUS FLUXIONUM ET SERIERUM INFINITARUM IN AN EDUCATION CONTEXT." Problems of Education in the 21st Century 65, no. 1 (June 25, 2015): 39–65. http://dx.doi.org/10.33225/pec/15.65.39.

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What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton’s Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise. Key words: mathematics education, history of mathematics, Newton, fluxions, tangents, maxima and minima, problem solving approach to mathematics education.
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17

MISSIAEN, LODE R. "ECSIM: DISCRETE EVENT SIMULATION USING EVENT CALCULUS." International Journal on Artificial Intelligence Tools 04, no. 01n02 (June 1995): 135–56. http://dx.doi.org/10.1142/s0218213095000085.

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This paper presents the theory and implementation of a logic based discrete event simulation system ECSIM, Event Calculus SIMulation. ECSIM’s representation language is PROLOG extended with temporal predicates derived from the event calculus. The theory defines the truth value of a property given a history of events. ECSIM can represent actions that happen at a particular point in time, and activities that happen over a period of time; it can represent properties that change discretely and continuously over time. ECSIM’s scheduling algorithm uses activity scanning to generate event notices for all future activities. ECSIM’s major distinction with other simulation systems is its reference to the complete history of simulated time. A given event schedule can be analyzed by deriving the properties of the world at any time in the simulated history. ECSIM’s logic programming framework enables classical simulation to be extended with explanation generation, inductive learning, planning, decision support, simulation of intelligent agents, and symbolic simulation.
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18

Ali, Azfar, Ghulam Ghous, Zakariya Rashid, Nabeel Shafi, Irshad Ali, Muhammad Hassam Khalid, and Muhammad Safdar Khan. "CALCULUS RENAL FAILURE." Professional Medical Journal 25, no. 10 (October 2, 2018): 1458–63. http://dx.doi.org/10.29309/tpmj/18.4941.

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Background: Urolithiasis is a common urological disease in Pakistan. Calculusrenal failure is a urological emergency that required immediate intervention to prevent furtherdeterioration of renal function. Objectives: The purpose of this study is to present clinical profileof calculus renal failure patient and to report our experience of management of such patients.Study Design: Descriptive Cross sectional study. Setting and Period: Department of urologyServices Hospital from July 2015 to December 2016 were included. Materials and Methods:Patients of all ages of either sex who presented with calculus renal failure. The patients withobstructive uropathy due to causes other than stone disease were excluded. Demographicinformation along with detailed history recorded. Baseline investigations included Completeblood counts, serum creatinine, serum electrolytes and ultrasound for KUB. For stone positionXray KUB in every case & CT in selected cases performed. Functional status of individual kidneywas assessed by renal scan with differential GFR. After initial emergency treatment, all patientswere subjected to definite treatment depending upon stone location and functional status ofkidney. Results: A total of 68 patients were recruited for this study. The mean age of the patientswas 48.8 + 14.13 with range 23-90. 52(76.5%) of the patients were male and 16(23.5%)were females. Most common presentation was lumber pain 46 (67.6%) followed by anorexia 42(61.8%). The average presence of the symptoms was 17.70 days. At initial management of thecondition contained, 16(23.5%) of the patients managed by peritoneal dialysis /Hemodialysis,10(14.7%) by unilateral PCN, 16(23.5%) by Bilateral PCN, unilateral JJ stenting done in 8(11.8%)while bilateral JJ stenting in 07 (10.9%), 6(8.8%). 10(14.7%) patient were managed with URS/Lithoclast therapy without any prior diversion. Renal function in 08 patients (11.8%) did notimproved after initial management and they remained on maintenance dialysis. Conclusion: Intime diagnosis and early proper treatment improves the outcome.
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19

Dhombres, Jean. "The origins of Cauchy's rigorous calculus." Historia Mathematica 12, no. 1 (February 1985): 86–90. http://dx.doi.org/10.1016/0315-0860(85)90078-3.

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20

Katz, Victor J. "The calculus of the trigonometric functions." Historia Mathematica 14, no. 4 (November 1987): 311–24. http://dx.doi.org/10.1016/0315-0860(87)90064-4.

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21

Vilar, Mariano. "The Hedonistic Calculus in the Renaissance." Viator 48, no. 2 (May 2017): 305–22. http://dx.doi.org/10.1484/j.viator.5.115986.

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22

Lee, Hyejin, Jong Ha Hong, Larisa Tataurova, Sergey Slepchenko, Jieun Kim, and Dong Hoon Shin. "Dental Calculi of Siberian Natives, Russian Settlers, and Korean People of Joseon Dynasty Period in the 16th to 19th Century Eurasia Continent." BioMed Research International 2022 (May 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/5765604.

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Objective. The prevalence of calculus is known to be variable by difference in diets or subsistence strategy between human populations. However, this situation has not been confirmed so far for hunter-gatherers and farming people in terms of history. In this study, we tried to reveal the association of diets or subsistence with calculus in different historical populations: Siberian natives, Joseon period Korean people, and Russian settlers in Siberia. Design. We examined the teeth of Siberian natives (hunter-gatherers), Russian (wheat farming) settlers, and Joseon (rice farming) people in sixteenth to nineteenth century. Age and sex were estimated using the methods of Buikstra and Ubelaker (1994). We examined specimens to detect signs of calculus formation in teeth. Calculus rates in each group were statistically compared, and the proportions of calculus by age or sex were also compared across each group. We used package R for statistical analysis. Results and Discussion. The prevalence of calculus deposition decreased in the order of Joseon people, Russian settlers, and Siberian natives. Our study proposes that the rate of calculi among farming people was evidently higher than that of hunter-gatherers in sixteenth to nineteenth century Eurasia. In all three groups, calculus prevalence became higher as age increases and was noteworthy in males. Conclusion. Current study demonstrated a significant difference of calculus formation between those groups with different diets or subsistence strategies. Higher prevalence of dental calculus was observed in agriculturalist Joseon Koreans and Russian settlers, but Siberian natives exhibited relatively lower frequency of dental calculus. The results of this study enable us to reconsider the meaning of association between subsistence strategy and calculus in different historical populations.
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23

Waring, S. P. "Cold Calculus: The Cold War and Operations Research." Radical History Review 1995, no. 63 (October 1, 1995): 29–51. http://dx.doi.org/10.1215/01636545-1995-63-29.

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24

Guitard, Thierry. "On an episode in the history of the integral calculus." Historia Mathematica 14, no. 2 (May 1987): 215–19. http://dx.doi.org/10.1016/0315-0860(87)90039-5.

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25

Boer, J. de. "On the History of Quantity Calculus and the International System." Metrologia 31, no. 6 (January 1, 1995): 405–29. http://dx.doi.org/10.1088/0026-1394/31/6/001.

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26

Brockmeier, Jens. "The Calculus of Narrative." Narrative Inquiry 9, no. 2 (December 31, 1999): 457–69. http://dx.doi.org/10.1075/ni.9.2.12bro.

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27

Pigozzi, Don, and Antonino Salibra. "The abstract variable-binding calculus." Studia Logica 55, no. 1 (1995): 129–79. http://dx.doi.org/10.1007/bf01053036.

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28

Terlecki, Ryan P., and Susan M. MacDonald. "Periurethral Gland Calculus Discovered on Workup for Dyspareunia." Current Urology 10, no. 1 (2016): 55–56. http://dx.doi.org/10.1159/000447152.

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A 55-year-old woman with a history of chronic dysuria in the absence of infection was found to have an unusual lesion below the urethral meatus. This was subsequently determined to be a periurethral gland containing a sizeable calculus. Pathologic analysis found the composition to be car bonate apatite (dahllite). Only one prior report of a female periurethral calculus has been noted in the English peer-reviewed literature.
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29

Kumar Vidhyarthy, Ajit, Tariq Hameed, Rohit Lal, Awadh Kumar, Shivanand Sahni, and Nanse Mendoza. "Giant Bladder Calculus in an Adult- A Persistent Problem in the Developing World: A Case Report." Clinical Practice and Cases in Emergency Medicine 4, no. 4 (September 23, 2020): 544–47. http://dx.doi.org/10.5811/cpcem.2020.7.47653.

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Introduction: Giant urinary bladder calculus in an adult is an uncommon entity. The number of patients with giant bladder calculi has decreased over recent years owing to wider availability of healthcare and better diagnostic modalities. Case Report: We present a case of a young adult without any history of recurrent urinary tract infections or bladder outlet obstruction with giant vesical calculus who presented to the emergency department with gross hematuria, abdominal pain, and dysuria. Investigations revealed a large calculus in the urinary bladder, and suprapubic cystolithotomy was performed. A large stone of 6.5×6×5.5 centimeters, weighing 125 grams, was removed. On follow-up, the patient was free of any symptoms and cystoscopy was normal. Conclusion: Urinary outflow obstruction must be ruled out in all patients with giant vesical calculus. Patients without any predisposing condition should be treated as a separate entity and evaluated accordingly. Multiple surgical treatment modalities are available for bladder calculus patients. Treatment is personalised as per size of stone, number of stones, and associated comorbidities.
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30

De Giacomo, Giuseppe, Yves Lespérance, and Eugenia Ternovska. "ElGolog: A High-Level Programming Language with Memory of the Execution History." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (April 3, 2020): 2806–13. http://dx.doi.org/10.1609/aaai.v34i03.5669.

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Most programming languages only support tests that refer exclusively to the current state. This applies even to high-level programming languages based on the situation calculus such as Golog. The result is that additional variables/fluents/data structures must be introduced to track conditions that the program uses in tests to make decisions. In this paper, drawing inspiration from McCarthy's Elephant 2000, we propose an extended version of Golog, called ElGolog, that supports rich tests about the execution history, where tests are expressed in a first-order variant of two-way linear dynamic logic that uses ElGolog programs with converse. We show that in spite of rich tests, ElGolog shares key features with Golog, including a sematics based on macroexpansion into situation calculus formulas, upon which regression can still be applied. We also show that like Golog, our extended language can easily be implemented in ElGolog.
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31

Irish, Stephen T. "Brodie's Calculus and Chemical Classification." Ambix 60, no. 3 (August 2013): 234–54. http://dx.doi.org/10.1179/0002698013z.00000000031.

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32

Loeb, Peter A. "A lost theorem of calculus." Mathematical Intelligencer 24, no. 2 (March 2002): 15–18. http://dx.doi.org/10.1007/bf03024611.

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33

Hildebrandt, Stefan. "The calculus of variations today." Mathematical Intelligencer 11, no. 4 (September 1989): 50–60. http://dx.doi.org/10.1007/bf03025887.

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34

Adams, Colin. "The Dog Who Knew Calculus." Mathematical Intelligencer 34, no. 1 (July 21, 2011): 16–17. http://dx.doi.org/10.1007/s00283-011-9243-2.

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35

Middleton, William D., and Irwin Rovner. "Extraction of Opal Phytoliths from Herbivore Dental Calculus." Journal of Archaeological Science 21, no. 4 (July 1994): 469–73. http://dx.doi.org/10.1006/jasc.1994.1046.

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36

Klement, Kevin. "Russell's 1903 - 1905 Anticipation of the Lambda Calculus." History and Philosophy of Logic 24, no. 1 (January 2003): 15–37. http://dx.doi.org/10.1080/0144534031000076237.

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37

Tarasov, Vasily E. "Generalized Memory: Fractional Calculus Approach." Fractal and Fractional 2, no. 4 (September 24, 2018): 23. http://dx.doi.org/10.3390/fractalfract2040023.

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The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by the function that is called the memory function, which is a kernel of the integro-differential operator. The main purpose of the paper is to answer the question of the possibility of using the fractional calculus, when the memory function does not have a power-law form. Using the generalized Taylor series in the Trujillo-Rivero-Bonilla (TRB) form for the memory function, we represent the integro-differential equations with memory functions by fractional integral and differential equations with derivatives and integrals of non-integer orders. This allows us to describe general economic dynamics with memory by the methods of fractional calculus. We prove that equation of the generalized accelerator with the TRB memory function can be represented by as a composition of actions of the accelerator with simplest power-law memory and the multi-parametric power-law multiplier. As an example of application of the suggested approach, we consider a generalization of the Harrod-Domar growth model with continuous time.
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38

Schüssler, Rudolf. "Equi-Probability Prior to 1650." Early Science and Medicine 21, no. 1 (February 22, 2016): 54–74. http://dx.doi.org/10.1163/15733823-00211p03.

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The assumption that two probabilities can be equal is a conceptual prerequisite for the development of a numerical probability calculus. Such a calculus first emerged in the seventeenth century. Several accounts have been proposed to explain the delayed development of numerical probability, yet it has thus far not been noted that the concept of equi-probability was virtually absent from medieval thought. This article argues that its rise began in the early sixteenth century, a fact that contributes to a better understanding of the preconditions which facilitated the modern mathematization of probability.
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39

Rider, Robin E., and I. Grattan-Guinness. "From the Calculus to Set Theory, 1630-1910: An Introductory History." American Mathematical Monthly 92, no. 3 (March 1985): 225. http://dx.doi.org/10.2307/2322890.

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40

Hilgert, Joachim. "David M. Bressoud: Calculus Reordered – A History of the Big Ideas." Mathematische Semesterberichte 67, no. 2 (May 29, 2020): 297–99. http://dx.doi.org/10.1007/s00591-020-00280-6.

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41

ARnerud, AR, H. Loe, and H. Boysen. "The natural history and clinical course of calculus formation in man." Journal of Clinical Periodontology 18, no. 3 (March 1991): 160–70. http://dx.doi.org/10.1111/j.1600-051x.1991.tb01128.x.

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42

Marzouk, Ines, Makram Moussa, Lotfi Saadallah, Sami Bouchoucha, and Lotfi Hendaoui. "Spontaneous uretero-sigmoid fistula secondary to calculus." Canadian Urological Association Journal 10, no. 11-12 (November 10, 2016): 401. http://dx.doi.org/10.5489/cuaj.3402.

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A 25-year-old man was referred to the urology department after a subacute history of left back pain, burning micturition associated with pneumaturia and fecaluria. Ultrasonography was performed showing hydronephrosis, and plain film radiography demonstrated a long vertical left pelvic calculi. Uro-computed tomography (CT) combined with a water enema CT showed a 10 cm long calculus with the cranial extremity fistulating the sigmoidal wall. Surgical treatment included left nephroureterectomy and sigmoidectomy with a colorectal anastomosis. Postoperative course was uneventful.
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43

Fried, Michael N., and Hans Niels Jahnke. "Otto Toeplitz's 1927 Paper on the Genetic Method in the Teaching of Mathematics." Science in Context 28, no. 2 (May 21, 2015): 285–95. http://dx.doi.org/10.1017/s0269889715000034.

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Argument“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” (1927) is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and assumptions about mathematics, history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research.
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Ali, Imtiaz, Javeria Anees, Faiza Hassan, Rabiya Siraj, Muhammad Ayub Mansoor, and Aiza Sohail Khan. "Unusual Giant Calculus of Left Submandibular Duct." Journal of Medical Research and Surgery 3, no. 2 (May 10, 2022): 41–43. http://dx.doi.org/10.52916/jmrs224075.

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Sialolithiasis account for the most common disease of salivary glands. The majority of salivary gland calculi involve the submandibular duct and rarely in its parenchyma. This is common benign disease may cause the acute or chronic sialadenitis. Sialolith can be single, multiple, unilateral or bilateral. Patient can presents with history of swelling and pain. Giant sialolithiasis is not a common condition mainly occur in submandibular duct. Here we discuss the unusual giant submandibular duct calculus in adult male patient, its Computed Tomography (CT) scan appearance and post-surgical findings.
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45

Caldwell, Bruce. "F. A. Hayek and the Economic Calculus." History of Political Economy 48, no. 1 (February 23, 2016): 151–80. http://dx.doi.org/10.1215/00182702-3452327.

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46

Moser, Georg, and Richard Zach. "The Epsilon Calculus and Herbrand Complexity." Studia Logica 82, no. 1 (February 2006): 133–55. http://dx.doi.org/10.1007/s11225-006-6610-7.

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47

Jacinto, Cesar Karunungan, Michael Geoffrey Lee Lim, Marc Paul Jose Lopez, and Dennis Pestano Serrano. "Nephrocolocutaneous fistula from a staghorn calculus." BMJ Case Reports 16, no. 1 (January 2023): e249351. http://dx.doi.org/10.1136/bcr-2022-249351.

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Fistula formation between the kidney, colon and the skin is an extremely rare complication arising from renal infections secondary to renal stone formation. During the 1980s, reports of nephrocolic fistulas, with or without involvement of the skin, were commonly caused by genitourinary tuberculosis. Due to improvements in diagnosis and specifically the development of anti-Koch’s therapy, the incidence of nephrocolic or nephrocolocutaneous fistulas has become uncommon especially in developed countries.We report a case of a patient residing in a developing country, presenting with a 20-year history of a left flank lesion extruding minimal purulent output daily. He was seen at the emergency department due to weakness and was managed as a case of urosepsis. Contrast-enhanced CT scan and fistulogram showed a staghorn calculus in the left kidney with connections to the descending colon and skin. The patient eventually underwent a left hemicolectomy with en bloc excision of the kidney and fistula tract.
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48

Fraser, Craig G. "Joseph Louis Lagrange's algebraic vision of the calculus." Historia Mathematica 14, no. 1 (February 1987): 38–53. http://dx.doi.org/10.1016/0315-0860(87)90002-4.

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49

Fraser, Craig G. "Sufficient conditions, fields and the calculus of variations." Historia Mathematica 36, no. 4 (November 2009): 420–27. http://dx.doi.org/10.1016/j.hm.2009.02.001.

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50

Wesolowski, Verônica, Sheila Maria Ferraz Mendonça de Souza, Karl J. Reinhard, and Gregório Ceccantini. "Evaluating microfossil content of dental calculus from Brazilian sambaquis." Journal of Archaeological Science 37, no. 6 (June 2010): 1326–38. http://dx.doi.org/10.1016/j.jas.2009.12.037.

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