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Topic: Guldinus theorem

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Solid of revolution

	Pappus's centroid theorem - Wikipedia, the free encyclopedia
		Pappus's centroid theorem consists of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.
		The theorem is attributed to Pappus of Alexandria and Paul Guldin.
		The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to product of the arc length s of C and the distance d
	www.wikipedia.org /wiki/Guldinus_theorem (204 words)

	PlanetMath: Pappus's centroid theorem
		Theorem 1 The surface of revolution generated by a smooth curve
		In English-speaking countries, these two theorems are known as Pappus's theorems, after the ancient Greek geometer Pappus of Alexandria.
		This is version 4 of Pappus's centroid theorem, born on 2005-08-15, modified 2005-08-27.
	planetmath.org /encyclopedia/PappussTheoremForSurfacesOfRevolution.html (404 words)

	theorem of pappus : Definition from the Online Dictionary at Datasegment.com
		In analysis, the term is sometimes applied to a rule, especially a rule or statement of relations expressed in a formula or by symbols; as, the binomial theorem; Taylor's theorem.
		Negative theorem, a theorem which expresses the impossibility of any assertion.
		Particular theorem (Math.), a theorem which extends only to a particular quantity.
	onlinedictionary.datasegment.com /word/Theorem+of+Pappus (216 words)

	PlanetMath:
		Gauss' mean value theorem for harmonic functions owned by pahio
		generalized mean value theorem (=extended mean-value theorem) owned by mathwizard
		Guldinus theorem (=Pappus's centroid theorem) owned by stevecheng
	planetmath.org /encyclopedia/G (990 words)

	Maybe this can forecast the market trend... best Guldinus Theorem (Site not responding. Last check: 2007-10-21)
		Swiss mathematician who rediscovered Pappus's theorem, which for this reason is sometimes known as the "Guldinus theorem...
		Centroids and Centers of Mass by the Theorems of Pappus and Guldinus.
		First Theorem - The area of the surface of revolution is equal to the product of the distance through which the centroid of the line moves and the length of the line.
	ascot.pl /th/Fourier4/Guldinus-Theorem.htm (489 words)

	Cavalieri the Person (Site not responding. Last check: 2007-10-21)
		This important work described a number of theorems based on physics and this concept that objects were composed of smaller indivisible components.
		The theorems of ratios of magnitudes and the equivalence of magnitudes all come into play once Cavalieri presented his theorems that the set of points or lines or planes was indeed a magnitude.
		Cavalieri published the theorem bearing his name and also provided a number of solutions to problems using the theorem.
	filebox.vt.edu:8080 /r/rboehrin/Cavalieri/CavalieriTheMan.htm (1727 words)

	Pappus of Alexandria
		Now, analysis is the path from what one is seeking, as if it were established, by way of its consequences, to something that is established by synthesis.
		In synthesis, by reversal we assume what was obtained last in the analysis to have been achieved already, and, setting now in natural order, as precedents, what before were following, and fitting them to each other, we attain the end of the construction of what was sought.
		A generalization of the Pythagoras Theorem (extended Theorem).
	www.mlahanas.de /Greeks/Pappus.htm (886 words)

	MATH-HISTORY-LIST Archives -- December 1997 (#23)
		Ivor Bulmer-Thomas, however, did not believe all that was written, and, perhaps, remembering that paper resists large quantities of ink randomly printed on it, made his case.
		Most people have believed that Pappus' statement (of the theorem under discussion) was not included in the FIRST edition of Pappus' "Collection" by Federico Commandino (1509-1575), and that it first appeared in the second edition (Bologna 1660).
		And, since Paul Guldin died in 1643, obviously enough Guldin could not have been acquainted with the theorem.
	www.maa.org /scripts/WA.EXE?A2=ind9712&L=math-history-list&T=0&F=&S=&P=2312 (419 words)

	Livid's Lividict - theorem of pappus (Site not responding. Last check: 2007-10-21)
		Not theories, but theorems (?), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively.
		By the theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures.
		Note: A theorem is something to be proved, and is thus distinguished from a problem, which is something to be solved.
	livid.3322.org /lookup/Theorem%20of%20Pappus.html (539 words)

	Spring'01 Teaching Assignment: Statics and Buoyancy (Site not responding. Last check: 2007-10-21)
		Center of gravity and centroid; center of gravity of sytem of particles, a body and composite bodies; theorems of Pappus and Guldinus.
		Moments of inertia; parallel-axis theorem; second moments of composite areas; product of inertia; mass moment of inertia.
		Hydrostatic pressure; hydrostatic forces on plane and curved surfaces; hydrostatic force on a body; buoyancy; Archimedes principle; metacenter; stability of floating and submerged bodies.
	www.oe.fau.edu /~ananth/eoc3105-sp01.html (210 words)

	Clearing up the market cycle... best Pappus-Guldinus Theorem (Site not responding. Last check: 2007-10-21)
		If Periodia value is 26, that means that from the vary last maximum of its passed 26 ticks of time and we have "period length"/2-26 ticks of time to reverse point.
		security concerns, de pappus teorema guldinus pappus take longer to reach pappus proof theorem in their...
		security concerns, alexandria pappus guldinus pappus take longer to reach pappus proof theorem in their Cato, Spottswood offices.
	ascot.pl /th/Fourier5/Pappus-Guldinus-Theorem.htm (506 words)

	Lecture Notes (Site not responding. Last check: 2007-10-21)
		This is similar to finding the surface area of a cylinder.
		Second Theorem - The volume of the area of revolution is equal to the product of the distance through which the centroid of the area moves and the area.
		Pappus-Guldinus Theorems can also provide an easier way to find centroids than by integration.
	web.umr.edu /~be50-5/lessons/21/p_g_theorem (118 words)

	Clearing up the market cycle... best Pappus Chain (Site not responding. Last check: 2007-10-21)
		Pappus's centroid theorem, the Pappus chain, Pappus's harmonic theorem, and...
		centroid theorem, the Pappus chain, Pappus's harmonic theorem, and...
		They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic theorem...
	ascot.pl /th/Fourier5/Pappus-Chain.htm (626 words)

	MATH-HISTORY-LIST Archives -- December 1997 (#22)
		rediscovered rediscovered independently Pappus's theorem that the volume generated by the complet e revolution of a plane closed curve that lies wholly on one side of the axis of revolution equals the area bounded by the circumference of the circle traversed by the center of gravity.
		Boyer mentions the possibility that the "Guildin theorem" might be an interpolation to the Pappus "Collection," for which Boyer cites footnote 12 of the Ver Eecke translation.
		>Some time back, when discussing solids of revolution, I became aware that >the name I used(the Pappus-Guldinus theorem) was not known to the others.
	www.maa.org /scripts/WA.EXE?A2=ind9712&L=math-history-list&T=0&F=&S=&P=2209 (190 words)

	Define Theorem of Pappus : powered by In Dictionary (InDicitonary.com) (Site not responding. Last check: 2007-10-21)
		Define Theorem of Pappus : powered by In Dictionary (InDicitonary.com)
		Use the form below to search our dictionaries by entering a word you wish to define.
		"theorem of Pappus" gcide "The Collaborative International Dictionary of English v.0.48"
	www.indictionary.com /define/Theorem_of_Pappus (396 words)

	Syllabus for ENGR 2301 (Site not responding. Last check: 2007-10-21)
		Centroids and centers of gravity; First moments of areas and lines, composite plates and wires, centroids of areas and volumes by integration, theorems of Pappus-Guldinus, et.
		Moments of inertia: Second moments of areas, polar moments of inertia, radius of gyration, parallel-axis theorem, moments of inertia of composite areas.
		Define mechanics and state the fundamental principles used in the study of mechanics.
	www.accd.edu /SAC/physics/abloom/ENGR2301/syllabus.htm (1216 words)

	Boiler and Pressure Vessel engineering - Calculation of Head Weights
		As a geometry fan, If I don´t trust on a formula, I´d use the "Pappus-Guldinus" theorem.
		I reckon, that combined with Autocad, would be the fastest and more general method to solve this.
		To get the torispherical head formula, I used the "Guldin's theorem" which is the same as the "Pappa-Guldinus":
	www.eng-tips.com /viewthread.cfm?qid=27356 (3051 words)

	esm_hibbeler_engmech_10\|Center of Gravity and Centroid\|Multiple Choice
		Using integration, compute both the area and the centroidal distance
		Then, using the second theorem of Pappus-Guldinus, compute the volume of the solid generated by revolving the shaded area about the aa axis.
		Determine the volume of concrete needed to construct the circular curb.
	wps.prenhall.com /esm_hibbeler_engmech_10/0,8157,952791-,00.utf8.html (238 words)

	Department of Computer and Information Systems Engineering (Site not responding. Last check: 2007-10-21)
		Truth Function : Binary connectives, Evaluation of truth functions, Physical realizations, Sufficient set of connectives, Truth functional calculus as Boolean algebra, Duality, Fundamental theorems of Boolean algebra, Switches and Relays, Logic circuits, Speed and delays in Logic circuits.
		Minimization of Boolean Functions: Minterm and Maxterm, Karnaugh map, Simplification of Boolean functions, POS and SOP expressions.
		Basic definitions and matrix operations, Adjoint and inverse of a 3 x 3 matrix, Rank of a matrix Cayley-Hamilton Theorem, Eigen values.
	www.neduet.edu.pk /CISE/courses/se.htm (1058 words)

	UBC PhysAstro: Course Descriptions
		Statics: distributed loads, centroids, moments of inertia; Dynamics: systems of particles, kinematics and kinetics of rigid bodies (plane motion), energy and momentum methods, rotating coordinates.
		Centre of Gravity and Centroid, Centre of Mass, Centroid, Theorem of Pappus and Guldinus, General Distributed Force System, Fluid pressure.
		Area Moment of Inertia, Parallel-Axis Theorem, Radius of Gyration, Integration method, Composite Areas, Mass Moment of Inertia.
	www.physics.ubc.ca /physoffice/course-outlines/1996-97/phtml/phys270.phtml (137 words)

	ES 235 (Site not responding. Last check: 2007-10-21)
		Determine moment of inertia of a three-dimensional body by integration.
		Use parallel axis theorem, polar moment of inertia concept, and radius of gyration concept in solving problems on moment of inertia.
		Graphical and Component methods of vector addition in two and three dimensions, equilibrium of a particle, free body diagram.
	faculty.fmcc.suny.edu /pynadath/es_235.htm (630 words)

	[No title]
		Marked all points _ISN or _CEL to indicate reference frame.
		Replaced calculation of parallelepiped volume with Pappus-Guldinus theorem for torus volume.
		Compute the volume of a sector of a toroid, using the Pappus-Guldinus Theorem.
	lena.gsfc.nasa.gov /studies/SimpsonDG/Weekly/Sep2303/density24_f90.txt (924 words)

	Curriculum
		Integral Calculus - rules and methods of integration, definite integral, applications (area, volume, centre of gravity, moments of inertia), Pappus Guldinus theorem, Simpson's rule.
		Differential Calculus - Leibnitz's, Taylor and Maclaurin's theorems, partial differentiation, homogeneous functions, transformation of variables, applications.
		Integral Calculus - double and triple integration, system of co-ordinates - applications to physical problems, Beta and Gamma functions and their applications, complex numbers - De Moivre's theorem, hyperbolic functions, separation of real and imaginary parts.
	hardiktank.4t.com /curriculum.htm (4988 words)

	MATH-HISTORY-LIST Archives -- December 1997 (#21) (Site not responding. Last check: 2007-10-21)
		Some time back, when discussing solids of revolution, I became aware that
		the name I used(the Pappus-Guldinus theorem) was not known to the others.
		Can anyone elaborate on when the hyphenated name might have been in use?
	enterprise.maa.org /scripts/WA.EXE?A2=ind9712&L=math-history-list&D=0&H=1&T=0&P=2102&D=1 (134 words)

	User:Charles Matthews/red links - Art History Online Reference and Guide
		Jacobi polynomial - Jacobi relation - Jacobs theorem - James embedding - Jensen formula - Jensen measure - Jessen-Wintner theorem - Jordan theorem (group theory) -
		Zariski surface - Zariski's main theorem - Zariski's theorem on holomorphic functions - Zariski Riemann surface - Zariski space -Zaremba theorem - Zero-cycle - Zoll surface - Zonal spherical function -
		Brauer-Siegel theorem - Higher reciprocity laws - p-adic metric
	www.arthistoryclub.com /art_history/User:Charles_Matthews/red_links (571 words)

	[No title]
		Find the moment of the force about the origin.
		State the theorems of Pappus and Guldinus to find out the surface area and the volume of a body.
		A belt embraces an angle of 200(over the surface of a pulley of 500 mm diameter.
	www.annauniv.edu /academic/GE_131.doc (1431 words)

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