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Topic: Herons formula

Related Topics

Scalene triangle

Triangle

Area (geometry)

Determinant

Numerical stability

Square root

Geometry

Algebraic geometry

Euclidean geometry

Heron of Alexandria

Hero of Alexandria

Linear algebra

Simple polygon

Brahmagupta

Niccolo Fontana Tartaglia

	Heron's Formula
		You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that has been know for nearly 2000 years.
		The formula is credited to Hero (or Heron) of Alexandria, who was a Greek Engineer and Mathematician in 10 – 70 AD.
		In the calculator above I have also used a special formula to calculate the angles (to provide a complete solution).
	www.mathsisfun.com /geometry/herons-formula.html (145 words)

	Heron's formula: Encyclopedia topic (Site not responding. Last check: 2007-10-10)
		Heron's formula as given above is numerically unstable (numerically unstable: in the mathematical subfield of numerical analysis, numerical stability is a property...
		The formula is in fact a special case of Brahmagupta's formula (Brahmagupta's formula: in its basic and easiest-to-remember form, brahmaguptas formula gives the area of a cyclic...
		Expressing Heron's formula with a determinant (determinant: A determining or causal element or factor) in terms of the squares of the distances (distances: The property created by the space between two objects or points) between the three given vertices,
	www.absoluteastronomy.com /reference/herons_formula (561 words)

	Brahmagupta's formula: Encyclopedia topic (Site not responding. Last check: 2007-10-10)
		In its most common form, it yields the area of quadrilaterals that can be inscribed in a circle (circle: Ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point).
		In its basic and easiest-to-remember form, Brahmagupta's formula gives the area of a cyclic quadrilateral (cyclic quadrilateral: in geometry, a cyclic quadrilateral is a quadrilateral whose vertices are all lie...
		The relationship between the general and extended form of Brahmagupta's formula is similar to how the law of cosines (law of cosines: in trigonometry, the law of cosines is a statement about arbitrary triangles which...
	www.absoluteastronomy.com /reference/brahmaguptas_formula (334 words)

	Heron's Formula and Brahmagupta's Generalization
		The actual origin of this formula is somewhat obscure historically, and it may well have been known for centuries prior to Heron.
		Furthermore, it implies that the cosine is given by the well-known formula / a^2 + b^2 - c^2 \ cos(q) = (-----------------) \ 2ab / [By the way, permutations of {a,b,c} = {3,5,7} in equation (2) give the three factorizations 675 = (15)(45) = (9)(75) = (5)(135), which leaves out (1)(675), (3)(225), and (25)(27).
		Incidentally, the formula for the area of an arbitrary quadrilateral is 1 ________________________________________________________ --- /(a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d) - 16 abcd cos(q)^2 4 where q is half the sum of two opposite angles.
	www.mathpages.com /home/kmath196.htm (512 words)

	Heron (Site not responding. Last check: 2007-10-10)
		The mechanicians of Heron's school say that mechanics can be divided into a theoretical and a manual part; the theoretical part is composed of geometry, arithmetic, astronomy and physics, the manual of work in metals, architecture, carpentering and painting and anything involving skill with the hands.
		Heron's aeolipile, which has much in common with a jet engine, is described in [Encyclopaedia Britannica.
		Works by Heron which are referred to, but no trace survives, include Camarica or On vaultings which is mentioned by Eutocius and Zygia or On balancing mentioned by Pappus.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Heron.html (2133 words)

	heron -- Britannica Student Encyclopedia
		Many of the long-legged wading birds living in the marshes of saltwater lagoons, freshwater lakes, and rivers are herons.
		Herons are widely distributed over the world but are most common in the tropics.
		Biography of this Greek geometer and inventor who is best remembered for his formula (known as Hero's formula) of the area of a triangle, and for the invention of aeolipile: the first steam-powered engine.
	www.britannica.com /ebi/article-9274860 (707 words)

	Heron's Mathematics
		Heron of Alexandria contributed to mathematics but he had not the mathematical “quality” of Euclid.
		Heron provided a solution in Metrica for the geometric problem to divide a triangle in two pieces of the same area given a point D on a side of the triangle.
		Heron described a method to calculate the square root of a number using some initial approximation.
	www.mlahanas.de /Greeks/HeronsMath.htm (1030 words)

	fUSION Anomaly. Heron
		water-driven and steam-driven machines and devised a formula for determining the area of a triangle.
		Heron, the great inventor of Alexandria, described in detail what is thought to be the first working steam engine.
		Heron did not consider this invention being useful for everyday applications: he considered his aeolipile invention as a novelty, a remarkable toy.
	fusionanomaly.net /heron.html (511 words)

	Pond Kits
		Formula to calculate the approximate quantity of "Pond" rock
		Formula to calculate the approximate quantity of "Stream" rock
		Formula to calculate the approximate quantity of stones or gravel needed:
	www.pondkits.com /technical.html (977 words)

	The Polarised Herons
		When heron’s flew in straight lines from place to place it was said that their average speed was the distance they had travelled over the time it took to get there.
		This was no surprise to them and with their great heron minds worked out that the velocity was proportional to the radius of the circle and the angular velocity of the heron.
		To this heron the laws of circular motion were obeyed precisely and the young heron’s intelligence increased in direct proportion to the time spent on the toy.
	www.spidercox.co.uk /JPedley.htm (2604 words)

	MEASURING ANIMALS THROUGH A TELESCOPE (Site not responding. Last check: 2007-10-10)
		Nevertheless, the percent error can be estimated using the formula (1 -cos a) 100% where a is the number of degrees off the perpendicular.
		For example, we were able to sex a large number of feeding herons by comparing culmen lengths, and then determining how many fell above (male) or below (female) a single gradicule scale reading of the 130 mm boundary read off a ruler placed where the herons fed.
		We estimated that of all Great Blue Herons (Ardea herodias) encountered in the field within 25 m, about 65% of the females and 73% of the males could be sexed with 95% confidence by measuring culmen lengths using this method.
	elibrary.unm.edu /sora/JFO/v061n01/p0111-p0114.html (2399 words)

	Bird Predation and Its Control (Site not responding. Last check: 2007-10-10)
		The great blue heron, one of the most common and most numerous species at northeastern aquaculture facilities, is considered to inflict the most damage to the industry.
		These herons have a chunky body and a short neck; they are about 2 feet long, with fl back and head and white stomach.
		Observations of herons feeding at catfish ponds and other warm-water aquaculture situations suggest that predation increases when fish are attracted to the surface with floating feed.
	www.aphis.usda.gov /ws/birdpred.html (4478 words)

	IS THE GREAT WHITE HERON A GOOD SPECIES?
		During this isolation genetic changes occurred which now find their visible expression in an enlargement of the bill, a reduc- tion of the occipital plumes, and (as we shall presently see) in the acquisition of genes modifying the blue plumage from the Great Blue type in the direction of the Wfirdemann type.
		Examples from the North American herons are the Reddish Egret (Dichromanassa rufescens), with a normal and a white plumage, and the Little Blue Heron (Florida caerulea), with an immature white and an adult blue plumage.
		Holt (1928) presented the evidence in favor of the specific distinction of the Great White Heron so convincingly that his thesis was adopted in the Check-List of the American Ornithologists' Union and by the great majority of subsequent writers.
	elibrary.unm.edu /sora/Auk/v073n01/p0071-p0077.html (4496 words)

	Santa Barbara Wildlife Care Network >> Baby Birds
		Volunteers act as surrogate parents to hundreds of hatchlings each year, from swallows and sparrows, to night herons and crows.
		These wild birds are without their parents care because their nests were disturbed, they were attacked by cats, or became victims of other mishaps.
		Using eye droppers and homemade formula, babies are fed up to eight times a day.
	www.sbwcn.org /babybirds.shtml (255 words)

	SAT question - don't know how to solve it (Site not responding. Last check: 2007-10-10)
		Use Herons formula with x=2 and x=12 to get a rough estimate of the min and max values of the area.
		If you want the formula for this problem, here it is. Area=1/2ab*sinC, where a and b are two sides and C is the angle between them.
		The 1/2ab in the formula is a constant.
	www.collegeconfidential.com /discus/messages/69/41110.html (1082 words)

	Chapter 5 Study Tips
		You will understand the derivations of, and be able to apply, the formulas for the cosine, sine, and tangent of a difference or sum.
		You will know Heron's formula and be able to use it to find areas of triangles and to solve appropriate application problems.
		You ought to be able to follow the proof of the Law of Cosines, although the proof of Herons' formula might be a little heavy for some.
	occawlonline.pearsoned.com /bookbind/pubbooks/demana_awl/chapter1/medialib/studytips/chapter5.html (1218 words)

	GEOMETRY, Vocational Math 2 (Math 804-380) Textbook, Madison Area Technical College
		As is shown in Chapter 6 of the Vocational Math I text, the formula for the area of a planar figure is determined by "rearranging" the figure into an equivalent rectangle having exactly the same area.
		In Herons formula, S is the "semi-perimeter" of the triangle.
		The formulas for the volumes and surface areas of solids, which are not prisms, require more elaborate geometric reasoning.
	matcmadison.edu /is/as/math/kmirus/Textbooks/804380Text/Geometry.html (1920 words)

	The Herons of America (from heron) -- Britannica Student Encyclopedia
		The great blue heron (Ardea herodias) ranges throughout the continental United States.
		The green heron (Butorides virescens) is common in the eastern United States.
		More results on "The Herons of America (from heron)" when you join.
	www.britannica.com /ebi/article-202013 (777 words)

	Electron Blue
		I've been spending the last couple of days going over proofs for "Heron's Formula," which is a way to find the area of any triangle if you know or can figure out the lengths of all three sides.
		Heron of Alexandria was a mathematician, physicist, and engineer back in the late Hellenistic world of the first century CE.
		I could just memorize the formula, which I have indeed done, but the proof of this formula carefully followed is a lesson in proof technique which I will find valuable in my later mathematical work.
	www.pyracantha.com /cgi-bin/blosxom.cgi/2004/04/28 (515 words)

	Untitled
		And, if one of the sons of the "Nature Island" soil were to be believed, these forests also carry another major secret which has the potential to rock the medical fraternity.
		Sabroache, who was reluctant to discuss the subject, is among those who will not give details of the herbal formula or disclose the name of the inmate.
		In the meantime, the man who believes he has the remedy for one of the world's most complicated medical challenges, is jealously guarding his formula to ensure that no one but him gets credit and reaps financial rewards for his discovery, in the event it proves successful.
	www.da-academy.org /johnson40.html (1017 words)

	Investigation of Open Ended Tubes.
		I can also sense the outline of a possiblity to do it algebraeically, I tried to expand the formulae for calculating the area of various shapes in order to apply them to each other, creating a 'formulae of everything'.
		It was a hard lesson in how concentrated some of these formulae are.
		Herons formula, in the terms of a, b and c, is a whole page of numbers.
	www.coursework.info /i/36006.html (386 words)

	(GC5602) Renton Riparian by BuffyAndFamily (Site not responding. Last check: 2007-10-10)
		Count them; this number will be the variable "A" in the cache formula later on.
		This number will be the variable "B" in the cache formula later on.
		During this time of the year (spring), many Herons are in the tree tops tending to the nests.
	www.geocaching.com /seek/cache_details.aspx?ID=22018 (430 words)

	Local and area news (Site not responding. Last check: 2007-10-10)
		The Brantley County Herons got a strong dose of reality Friday when, coming off a lopsided 57-20 victory over winless Long County, they suffered much the same humiliation in a 47-7 defeat in their first home game of the regular season to 2-AA behemoth Charlton County.
		The Brantley County Herons utterly defeated the Long County Blue Tide tonight in Ludowici with a score of 56-14 at last count, and Long only scored in the second half after Brantley coach Sean Pender sent in junior varsity team players.
		The Brantley County Herons will take an impressive set of stats on the road when they face off against Long County Friday in Ludowici and may very well bring home the first win of the season when all is said and done.
	www.brantleyenterprise.com /localnews/archives/2003_09.html (2810 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		This formula can be put into more symmetric form: see http://www.math.niu.edu/~rusin/known-math/97/herons.tetrahed So we see that we really do get a tetrahedron, if we can build one face, and the square of the putative volume is positive.
		Naturally, any formula which purports to give the square of a volume must be nonnegative for a realizable tetrahedron, but that argument is insufficient for me: it's not clear that positivity of the volume-squared formula is conversely enough to guarantee the realizability of the tetrahedron.
		So this formula represents the two possible tetrahedron volumes (and shapes) for a given pairing of the edges.
	www.math.niu.edu /~rusin/papers/known-math/98/tetrahedral_ineq (2424 words)

	Herons Formula
		Heron's formula states that A^2 = s(s-a)(s-b)(s-c), where s = (a+b+c)/2.
		Consider the general triangle with edge lengths a,b,c shown below:
		which is the area formula as given by Heron.
	jwilson.coe.uga.edu /EMAT6680/Brown/6690/herform.htm (160 words)

	Math Tricks (Site not responding. Last check: 2007-10-10)
		Now I know it's not a formula or theorem but I mean have you ever seen a Greek letter get used more.
		Yet another one that is not a formula or theorem but once you get to calculus, this guy will become your best friend (or worst one.)
		And this one is another one of my formulas but only between me and Jimmer.
	www.angelfire.com /mn/lysen/math.html (254 words)

	FREE Mathematics How-to Library - math homework help – math tutor software
		Uses two worked examples and the principle of inverse operations to explain how to change the subject of a formula.
		How to use the midpoint formula to find the midpoint of a line between two (x,y) points.
		The formula is explained pictorially, and the download document allows you to experiment with the formula, while displaying working steps and a labelled diagram.
	www.teacherschoice.com.au /mathematics_how-to_library.htm (1990 words)

	A Proof of the Pythagorean Theorem From Heron's Formula
		A Proof of the Pythagorean Theorem From Heron's Formula
		For a quadrilateral with sides a, b, c and d inscribed in a circle there exists a generalization of Heron's formula discovered by Brahmagupta.
		Since any triangle is inscribable in a circle, we may let one side, say d, shrink to 0.
	www.cut-the-knot.org /pythagoras/herons.shtml (230 words)

	Upcoming TI-83 Plus Math Programs - ticalc.org
		I am trying to write a program in 83/83+ BASIC that includes formulas for all useful subjects.
		The program will set some special (and currently secret) formulas into the equation editor to determine these points of concurrency.
		I also wrote some other math formulas but it doesnt pay to upload those since there are already so many distance, midpoint, slope, etc programs there
	www.ticalc.org /programming/upcoming/math/83p.html (1444 words)

	Conference 2003
		There will be basic sessions for beginners on formulas, formula preparation, and fluid therapy.
		There are sessions planned on several species that we haven't covered before: snakes, woodchucks, flying squirrels and herons.
		There are both bird and mammal sessions on anatomy, a session on avian triage and a session on the fawn rehab program.
	www.ncwildliferehab.org /conference/conf2005/conf2005.html (242 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		Our immediate problem involves our need to purchase personal items such as baby formula, diapers, toilet paper, and sanitary napkins along with cleaning products.
		These products are not available through the Distribution Center nor are they available to those in need using Food Stamps.
		Herons Glen is a great place to live
	carlsplace1.com /!!news/news.htm (2674 words)

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