
	Where results make sense

Topic: Envelope (mathematics)

In the News (Sat 2 Jun 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Springer Online Reference Works
		For example, the envelope of spheres with the same radius and centres on a straight line is a cylinder.
		The line of contact of the envelope with one of the surfaces of the family is called a characteristic.
		A cuspidal edge on the envelope in turn is usually the envelope of the characteristics.
	eom.springer.de /e/e035840.htm (525 words)

	Ravi Vakil on the Mathematics of Doodling
		Ravi Vakil of Stanford University unveiled the surprisingly rich mathematics of this common pastime in a recent presentation at the MAA's Carriage House Conference Center.
		Further investigations of this particular doodle and several variants highlighted the relevance of such mathematical notions as the convexity of polygons, the nature of polyhedrons, and the role of derivatives in characterizing various aspects of the resulting figures.
		One of Vakil's goals is to attract high school and undergraduate students to the mathematical sciences, and his lectures on the mathematics behind doodling are an exciting way to expose young people to interesting and accessible mathematics.
	www.maa.org /news/121407vakil.html (556 words)

	Envelope (disambiguation) - Wikipedia, the free encyclopedia
		An envelope is a thin paper container formed by folding a sheet of paper and securing the edges, and is the major staple consumable of a letterpost service.
		envelope (mathematics) -- a curve, surface, or higher dimensional object defined as being tangent to a given family of lines or curves (or surfaces, or higher dimensional objects, respectively).
		In music theory, the envelope of a sound is its variation in amplitude over time; in Sound synthesis, envelopes are characterised by the attack, decay, sustain, and release times of the sound.
	en.wikipedia.org /wiki/Envelope_(disambiguation) (376 words)

	Ugh
		The greater the amount in the first envelope, the less likely the second envelope is to contain the larger amount.
		Nevertheless, in terms of the mathematical definitions of expectation and random variables, it may be the case that E(XY=z) > z for all z and E(X) <= E(Y).
		In the case of the amount in the envelopes being determined in a manner that results in the expectation being infinite, your intuition is wrong.
	www.upl.cs.wisc.edu /~bethenco/puzzles/twoenvelopecomments.html (686 words)

	envelope
		Young, hot stars often eject envelopes or produce them by ionizing nearby material.
		Old stars, in their red giant phase, shed their outer layers and produce cool envelopes rich in molecules and dust.
		When the core of the dying star is exposed, ultraviolet light from the core makes the envelope luminesce as a planetary nebula.
	www.daviddarling.info /encyclopedia/E/envelope.html (118 words)

	envelope. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		Mathematics A curve or surface that is tangent to every one of a family of curves or surfaces.
		French enveloppe, from envelopper, to envelop, from Old French envoloper.
		The word envelope was borrowed into English from French during the early 18th century, and the first syllable acquired the pronunciation (
	www.bartleby.com /61/74/E0167400.html (299 words)

	EXTEND: Teaching Interdisciplinary Courses
		The mathematics is not clearly visible, except as a collection of skills needed to accomplish the matter at hand.
		Mathematics teachers are used to traditional goals-- numbers, graphs, equations.
		Since teachers know so little about the role of mathematics in careers, I find quite often that students' sense of what is gong to be relevant to their future careers is way off base.
	www.stolaf.edu /other/extend/Integration/dialogue.html (1711 words)

	Illuminations: Mathematics and Football
		As teachers of mathematics, we are aware that students become better problem solvers when they are asked to take an active role in formulating some of their own problems.
		Their task is to write on the piece of paper one word problem based on the data in the news clipping, put the clipping and the piece of paper back into the envelope, and pass it on to the next team.
		The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students.
	illuminations.nctm.org /index_d.aspx?id=212 (820 words)

	The Schoyen Collection: 9. Mathematics (Site not responding. Last check: )
		MS 4523), and b) the present system with the tokens enclosed inside a hollow bulla-shaped rollsealed envelope, sometimes with marks on the outside representing the hidden contents.
		Only one nearly as old mathematical table text is known, a table of squares of length measures, with the products expressed as area measures, Berlin VAT 12593.
		The problem texts were the higher mathematics of the time, and for the better students only.
	www.nb.no /baser/schoyen/5/5.11/index.html (3687 words)

	Category Mathematics - the free encyclopedia (Site not responding. Last check: )
		Mathematics is often defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers".
		Because of its applicability in a wide variety of scientific disciplines, mathematics has been called "the language of the universe".
		See the list of mathematical topics for a far more comprehensive list of mathematical topics.
	www.free-web-encyclopedia.com /default.asp?t=Category:Mathematics (97 words)

	The Schoyen Collection: 9. Mathematics
		The sides of the 6 rectangles in the ratio 1:60 demonstrates that the mathematics taught in the scribe schools in Sumer before the middle of the third millennium BC was unexpectedly sophisticated.
		The problem texts were the higher mathematics of the time, and for the better students only.
		The text can also be expressed as: To compute a number R such that 1 shekel of silver is the total price of R units of each of 4 different commodities with the individual market rates 1, 2, 3 and 4 units per shekel of silver.
	www.schoyencollection.com /math.htm (4327 words)

	Mathematics League - High School Contest Organization
		For no other reason may the contest envelope be opened prior to the actual time of use in the contest, except that special arrangements may be made for handicapped students, and dictionaries may be made accessible to non-English-speaking students.
		No graph paper, compasses, straight edges, rulers, printed mathematical tables, or other devices shall be allowed, except where special arrangements have been made for handicapped students or when dictionaries are made accessible to non-English-speaking students.
		Answers mathematically exactly equivalent to the official answer(s) should be given credit, provided that, when a specific answer form has been asked for, that answer form has been adhered to.
	www.mathleague.com /hsrules.htm (1210 words)

	Convolution Example 2: ADSR Envelope
		In a practical ADSR envelope, the time-constants for attack, decay, and release may be set independently.
		Thus, the envelope approaches the attack level at the attack rate (where the ``rate'' may be defined as the reciprocal of the time constant), it next approaches the sustain level at the ``decay rate'', and finally, it approaches zero at the ``release rate''.
		Such an ADSR envelope is typically used to multiply the output of a waveform oscillator such as a sawtooth or pulse-train oscillator.
	www.dsprelated.com /dspbooks/mdft/Convolution_Example_2_ADSR.html (396 words)

	[No title]
		The purpose of this note is to introduce envelopes of families of lines, to study some of the geometric properties of envelopes, and finally to present a closed form expression of the envelope.
		We define the envelope of this set of lines to be a function y=g(x) such that every line in the family is tangent to the graph of y=g(x) at some point and through each point on the graph of y=g(x), there passes a line in the family that is tangent to y=g(x).
		We use the notation f(x)->g(x) to denote that the envelope of the family of lines y=a*x+f(a) is the function y=g(x).
	archives.math.utk.edu /ICTCM/EP-7/SA21/abstract.txt (275 words)

	Overview of Mesopotamian Mathematics
		The outside of the envelope was marked with the tokens, so that you would know what was inside without having to break the envelope.
		However, since most mathematics was applied, problems tended to be stated, and answers had to be given in particular units of weights and measures.
		The next great flowering we know of was the development of mathematical astronomy in the late Babylonian period of the last few centuries B.C. Go on to Tokens.
	it.stlawu.edu /~dmelvill/mesomath/overview.html (562 words)

	UM-Flint Mathematics Department (Site not responding. Last check: )
		Inside the Essay envelope you will find an unsealed envelope with only the team number, not the name of the school (to ensure unbiased grading).
		At the end of the 40 minutes collect and put all (and only) the answer pages inside the small envelope, checking that they are identified by the team number only.
		The schools and room number are indicated in the program and on the envelope you will receive at the advisors’ meeting.
	www.flint.umich.edu /departments/math/Field_Day/proctor_instructions.html (1525 words)

	Why Does Maths work so well?
		Mathematics has proved to be invaluable in helping us to understand quantum mechanics for example.
		Another strange example of the practical use of mathematics is the use of imaginary numbers to distinguish between the dimensions of space and time.
		Pythagorus discovered the mathematical relationship between the lengths of strings that produced harmonic tones, the octave, for example, corresponded to the ratio 2:1.
	www.thekeyboard.org.uk /Mathematics.htm (4067 words)

	Push the envelope
		Wolfe didn't originate the term, although it's appropriate that he used it in a technical and engineering context, as it was first used in the field of mathematics.
		The envelope here isn't the container for letters, but the mathematical envelope, which is defined as 'the locus of the ultimate intersections of consecutive curves'.
		That envelope is the description of the upper and lower limits of the various factors that it is safe to fly at, i.e.
	www.phrases.org.uk /meanings/push-the-envelope.html (430 words)

	EMSC Content Page
		Errors in Envelope Procedures: If a student inadvertently seals the answer sheet in the envelope or seals the envelope without enclosing the test booklet and/or scrap paper, the proctor should have the student open the envelope and remove the answer sheet or enclose the test booklet and scrap paper.
		Hold up an envelope and show the students where they should print their name and the name of the school.
		After each student has sealed the envelope securely, make sure that the student places the blue label across the flap in the outlined space and signs his or her name across the blue label and onto the envelope.
	www.emsc.nysed.gov /osa/hsinfogen/det397r-0106.htm (3905 words)

	Probability paradox II « Gowers’s Weblog
		This is true: if your envelope has x dollars the other has either 2x or x/2, so if you gain, you gain x; if you lose, you lose x/2.
		If the envelope you chose initially is the one with t, switching gains t dollars; if it is the one with 2t, switching loses you t dollars.
		If you open an envelope with $1000 in it, it either means n=3 and you picked the small envelope, or n=2 and you picked the big envelope.
	gowers.wordpress.com /2008/02/03/probability-paradox-ii (3232 words)

	No. 2040: The Envelope Game
		In fact, for a very large number of envelopes, the mathematical odds are exactly 36.78...
		The envelope game is more commonly known in mathematical circles as the secretary problem, deriving from a scenario in which a manager is interviewing candidates for an administrative position rather than choosing an envelope.
		The precise result for the number of envelopes one would best look at out of a very large number of envelopes, N, would be N/e, where e is the base for natural logarithms, 2.718...
	www.uh.edu /admin/engines/epi2040.htm (743 words)

	NSDL Metadata Record -- Envelopes : how can you fold a piece of paper to make an envelope?
		This activity challenges students to fold a sheet of paper to create a business-size envelope in a way that wastes as little paper as possible.
		collection of 80 challenges emphasizing real-world uses of mathematics, introduces tessellations and explains how they are used to manufacture containers efficiently.
		Students are encouraged to begin the challenge by examining the pattern of an unfolded business envelope.
	nsdl.org /mr/442234 (166 words)

	[No title]
		From 1998 to 2002, I was associated with the Summer Institute in Mathematics for Undergraduates (SIMU) at the University of Puerto Rico, Humacao in different capacities.
		The envelope is a curve such that all the curves in the family are tangent to the envelope at their points of intersection with the envelope.
		If the curves in the family are circles, for instance, the envelope describes the boundary of the region swept out by a circle moving along the path described by the centers as the parameter varies.
	math.holycross.edu /~little/SIMU.html (282 words)

	Envelopes of Zags
		The zags often, as in the Default example, form a highly visible envelope, that is a curve which they appear to be tangent to.
		The numbers a and c govern the speed with which the centre moves round the fixed circle and the rate of spin of the moving circle.
		Different envelopes of (red) zags require different a and c to make the (blue) whirligig fit.
	www.maa.org /pubs/mm_supplements/giblin/envelopes.html (647 words)

	Tractrix - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		At every moment, the thread will be tangent to the curve y=y(x) described by the object, so it gets completely determined by the movement of the puller.
		Mathematically, the movement will be described then by the differential equation
		The envelope of the normals of the tractrix, that is, the evolute of the tractrix is the catenary (or chain curve) given by
	www.godseye.com /stat/en/t/r/a/Tractrix.html (303 words)

	Tokens - the earliest mathematical artifacts
		Their significance as the precursors of both mathematics and writing was first recognized by Denise Schmandt-Besserat of the University of Texas at Austin in the early 1970's.
		Envelopes provided a solution to the problem of secure storage of tokens, but like many technological solutions, raised problems of their own.
		The outside marks could then serve as a reference and the envelope could be broken open to check the actual contents if there was any dispute about the marks.
	it.stlawu.edu /~dmelvill/mesomath/tokens.html (822 words)

	Parabola as envelope of lines from Interactive Mathematics Miscellany and Puzzles
		This is the parabola with focus F and the apex on the x-axis.
		The parabola is said to be the envelope of the family of straight lines {t}.
		If, at the outset, the parabola is not given, but only a point and a line, we may produce any number of creases by folding the paper so that the given point falls onto the given line.
	www.cut-the-knot.org /Curriculum/Geometry/ParabolaEnvelope.shtml (521 words)

	Mathematics of Volatility
		This essay is written for anyone in the Mechanical Investing community who would like to study the mathematics of investment volatility, in some depth, and for any other quantitatively-inclined investors who may stumble across it while browsing the web.
		The pale red envelope encloses the region in which the price trajectory is most likely to move; this region clearly expands much more rapidly in the direction of higher prices than it does towards lower.
		To treat this sampling varation mathematically, we consider each datum to be a random variable, and the estimator to be a transformation of those random variables.
	www.aetheling.com /MI/Volatility/math.html (2975 words)

	Envelope (mathematics) - Wikipedia, the free encyclopedia
		For other senses of this word, see envelope (disambiguation).
		The simplest formal expression for an envelope of curves in the (x,y)-plane is the pair of equations
		The logic of this form may not be obvious, but in the vulgar: solutions of (2) are places where F(x,y,t), and thus (x,y), are "constant" in t -- ie, where "adjacent" family members intersect, which is another feature of the envelope.
	en.wikipedia.org /wiki/Envelope_(mathematics) (321 words)

Try your search on: Qwika (all wikis)