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Topic: Semiperimeter

	Triple quad formula proof - Wikipedia, the free encyclopedia
		Three points are collinear if the triangle they enclose has zero area.
		where s = the semiperimeter of the triangle,
		Quadrance being the square of length, this is equivalent to the triple quad formula:
	en.wikipedia.org /wiki/Triple_quad_formula_proof (254 words)

	[No title]
		Then the perimeter is x + y + z, and the semiperimeter is (x + y + z)/2.
		Another consideration is that if the semiperimeter is even, then there are only 4 of the 12 values that will remain in the sequence.
		This is because the numerator must be odd for the middle 6 terms, and the denominator must be odd for the 3 terms with.5 as a multipler.
	www.kermitrose.com /math/numbers/semiperimeter (800 words)

	AMERICAN MATHEMATICAL MONTHLY -December 2004
		For example, the ratio of the area of any region bounded by a circumgon to its semiperimeter is equal to its inradius (just as the ratio of the area of a circular disk to its semiperimeter is its radius).
		Also, the area centroid of any region bounded by a circumgon and the centroid of its boundary curve are collinear with the incenter, at distances in the ratio 2:3 from the incenter, as in the case of a triangle.
		The ratio of the area to the semiperimeter of such a ring is equal to this constant width.
	www.maa.org /pubs/monthly_dec04_toc.html (685 words)

	3. Zebras, generating trees and previous constructions (Site not responding. Last check: 2007-10-11)
		A parallelogram polyomino is a translation invariant array of unit squares bounded by two lattice paths that use the steps, (0,1) and (1,0), and that intersect only initially and finally.
		The semiperimeter of a polyomino is the length of either of these paths; the width of a polyomino is the number of its columns.
		We denote the set of all zebras by Z, the semiperimeter of a zebra P by n(P), and the set {P in
	math.boisestate.edu /~sulanke/PAPER1/PergolaSulanke/node3.html (565 words)

	SparkNotes: Geometric Measurements: Area of Triangles
		The semiperemeter of a triangle is equal to half the sum of the lengths of the sides.
		Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the three sides.
		The proof of Heron's Formula is rather complex, and won't be discussed here, but his formula works like a charm, especially if all that is known about a triangle is the lengths of its sides.
	www.sparknotes.com /math/geometry2/measurements/section5.rhtml (604 words)

	incircle_triangle (Site not responding. Last check: 2007-10-11)
		We will be using the semiperimeter, commonly written as "s," which is half the normal perimeter.
		The side opposite of an angle is denoted by the lower case version of the angle name.
		I claim that when we let r be the inradius of triangle ABC, and let s be the semiperimeter of triangle ABC, then the area of triangle ABC = rs.
	www.plu.edu /~huntinal/web_project/incircle_triangle.html (449 words)

	Exercise from K. Holing
		Let I be the incenter of a triangle ABC and let D be the point of contact of the incircle and side AB.
		If ID is extended outside AB to H such that DH is equal to the semiperimeter of the triangle ABC, show that the quadrilateral AHBI is cyclic if and only if the angle C is right.
		Given s is the semiperimeter for a triangle with sides of length a, b, and c,
	jwilson.coe.uga.edu /emt725/Bob2/KH/RghtTri.html (362 words)

	MathLinks Math Forums :: View topic - radius of apollonius circle
		prove the radius of the apollonius circle (the apollonius circle that is externally tangent to the three excircles) is r^2 + s^2 / 4r (r = inradius, s= semiperimeter* as usual).
		This is a piece of triangle geometry far from being simple, hence please excuse me for the long depiction.
		Let r be the inradius and s the semiperimeter of triangle ABC.
	www.mathlinks.ro /Forum/ntopic-5681.html (1137 words)

	id:A000984 - OEIS Search Results
		Number of ordered trees with 2n+1 edges, having root of odd degree and nonroot nodes of outdegree 0 or 2.
		Also number of diagonally symmetric, directed, convex polyominos having semiperimeter 2n+2.
		The second inverse binomial transform of this sequence is this sequence with interpolated zeros.
	www.research.att.com /projects/OEIS?Anum=A000984 (1058 words)

	Previous Questions
		The area of a polygon circumscribed around a triangle is the product of the semiperimeter of the polygon and the radius of the circle.
		So if a circle is inscribed in a right triangle and the triangle has sides 3, 4, and 5,
		then the radius of the circle times the semiperimeter of the triangle equals the area of the right triangle which is 6.
	www.gomath.com /Questions/question.php?question=5881 (534 words)

	Triangles, Inscribed and Circumscribed Circles (Site not responding. Last check: 2007-10-11)
		The area of the triangle, K can be found by the following formulae:
		, where K is the area of the triangle and s is the semiperimeter.
		Similarly, given any triangle, a circle can be circumscribed around the triangle, containing all three of the vertices.
	courses.ncssm.edu /goebel/STATECON/Topics/triangl/TRIANGL.htm (210 words)

	SparkNotes: Geometric Measurements: Terms and Formulae
		, where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the three sides.
		Perimeter - The length of the simple closed curve or curves that define a region.
		A = Square root [s(s-a)(s-b)(s-c)], where s is the semiperimeter and a, b, and c are the lengths of the sides of the triangle.
	www.sparknotes.com /math/geometry2/measurements/terms.html (608 words)

	CS 157 / ECE 155 Assignment 3 (Site not responding. Last check: 2007-10-11)
		The area of a triangle can be calculated from its side lengths by Heron’s formula:
		where a, b, and c are the side lengths and s is the semiperimeter; that is,
		Write a program that will prompt the user for the three side lengths as integers, compute the semiperimeter s as a double, compute the area, also as a double, and print the answer.
	faculty.valpo.edu /jcaristi/cs157/a2.html (179 words)

	A triangular pyramid problem
		Note that the area T of the triangle is the product of the radius r of the inradius and the semiperimeter s, which is (a + b + c)/2.
		The commentary to proposition IV.4 mentioned above also gives a derivation of Heron's formula for the area T of the triangle in terms of the semiperimeter s,and the sides a, b, and c, namely, T equals the square root of s(s – a)(s – b)(s – c).
		We can now compute the lateral surface area of the minimal-area pyramid.
	aleph0.clarku.edu /~djoyce/mpst/pyramid (766 words)

	Triangles, Inscribed and Circumscribed Circles (Site not responding. Last check: 2007-10-11)
		Given a triangle with sides that have length a, b, and c.
		The semiperimeter s is half the sum of the lengths of the sides.
		This time we will start with the area formula
	courses.ncssm.edu /goebel/STATECON/Topics/Triangl/proof_2.htm (48 words)

	41st IMO shortlist 2000/N5 solution (Site not responding. Last check: 2007-10-11)
		Show that for infinitely many positive integers n, we can find a triangle with integral sides whose semiperimeter divided by its inradius is n.
		Let the sides be a, b, c the semiperimeter s = (a + b + c)/2, the inradius r, and the area A. We have A = sr, A
		So r = A/s = 2 and s = nr, as required.
	www.kalva.demon.co.uk /short/soln/sh00n5.html (539 words)

	CS210 Examples from Weiss (Site not responding. Last check: 2007-10-11)
		An interface can have only public abstract methods and public static final fields only, so we can’t implement semiperimeter here, just list it as something all Shapes can compute:
		double area() { … } // implements area, perimeter, semiperimeter
		Note a class can extend only one class, but can implement many interfaces.
	www.cs.umb.edu /cs210/handout2.html (177 words)

	Math Forum Discussions - User Profile for: ilarrosaQUITARMAYUSCULA_@_undo-r.com (Site not responding. Last check: 2007-10-11)
		Re: I don't know why I'm getting the correct answer
		Re: Semiperimeter center or hopeless center of a triangle?
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/search!execute.jspa?userID=46535&forceEmptySearch=true (67 words)

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