Geometry
https://www.maa.org/taxonomy/term/42302/all
enDeterminantal Loci
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/determinantal-loci
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>This article characterizes the points \((x, y)\) in the plane for which the determinant of a matrix of a particular form involving \((x, y)\) is \(0\). The matrices of interest have the form \(A+xL+uM\), where \(A\), \(L\), and \(M\) are square matrices, \(L\) and \(M\) are of rank one, and \(L + M\) is of rank two.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com94792 at https://www.maa.orgA Geometrical Approach to Cramer's Rule
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometrical-approach-to-cramers-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Motivated by the interpretation of a determinant of a \(2 \times 2\) matrix as the area of a parallelogram, the author derives Cramer's rule geometrically.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95056 at https://www.maa.orgA Picture is Worth a Thousand Words
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-picture-is-worth-a-thousand-words
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author provides geometric illustrations of four subspaces associated with a matrix. Thinking of a matrix as a map between real vector spaces, the illustrations motivate the decomposition of the domain and range into orthogonal subspaces and the decomposition of vectors into orthogonal components. The author also indicates how the illustrations can be related to the solvability of certain matrix equations.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95111 at https://www.maa.orgA Geometric Approach to Linear Functions
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometric-approach-to-linear-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>There are three somewhat distinct topics in this article: the condition for linear functions to commute, a linear function as a transformation of the number line, and linear difference equations. A linear function \(y=f(x)=ax+b\) can be characterized in terms of slope and the “center of reflection,” both of which reflect the geometric property of the function. </em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95221 at https://www.maa.orgThe Axis of a Rotation: Analysis, Algebra, Geometry
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-axis-of-a-rotation-analysis-algebra-geometry
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Given any 3 by 3 rotation matrix \(A\) (i.e. orthogonal with determinant \(1\) and an arbitrary vector \(x\), the vector \( Ax +A^{T}x+[1−\)tr\((A)]x\) lies on the axis of rotation. The article provides three different approaches, requiring various levels of background knowledge, to prove and/or explain the given result.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95339 at https://www.maa.orgProof without Words: A 2 x 2 Determinant Is the Area of a Parallelogram
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-a-2-x-2-determinant-is-the-area-of-a-parallelogram
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author presents a visual proof that the determinant of a 2 by 2 matrix equals the area of the corresponding parallelogram.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95382 at https://www.maa.orgFinding the Volume of an Ellipsoid Using Cross-Sectional Slices
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finding-the-volume-of-an-ellipsoid-using-cross-sectional-slices
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author shows that the volume of an ellipsoid can be determined by three parallel slices.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95423 at https://www.maa.orgA Surprise from Geometry
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-surprise-from-geometry
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Consider \(n\) vectors issuing from the origin in \(n\)-dimensional space. The author shows that the statement “any set of \(n\) vectors in \(n\)-space, no two of which meet at greater than right angles, can be rotated into the non-negative orthant” is true for \(n \leq 4\), but false for \(n>4\).</p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95490 at https://www.maa.orgAn Infinite Series for \(\pi\) with Determinants
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-infinite-series-for-pi-with-determinants
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author gives an expression for \(\pi\) involving an infinite sequence of determinants, each representing the area of a triangle.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95601 at https://www.maa.orgDefinitely \(\sim\) Positively the Pits
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/definitely-sim-positively-the-pits
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author classifies the quadratic forms defined by simple 2 by 2 matrices and illustrates them with corresponding quadratic surfaces.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95657 at https://www.maa.orgOn the Measure of Solid Angles
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-measure-of-solid-angles
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author revisits formulas of measuring solid angles that he could find only in centuries-old literature, and provides modern versions of the proofs.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95666 at https://www.maa.orgLinear transformation applet
https://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformation-applet-0
Thu, 24 Apr 2014 15:39:10 +0000
lang388254 at https://www.maa.orgEigen demo with sound
https://www.maa.org/programs/faculty-and-departments/course-communities/eigen-demo-with-sound
Thu, 24 Apr 2014 16:24:51 +0000
lang388333 at https://www.maa.orgComputer Graphics Project
https://www.maa.org/programs/faculty-and-departments/course-communities/computer-graphics-project
Fri, 25 Apr 2014 01:49:05 +0000
lang388773 at https://www.maa.orgGeometry of Linear Transformations of the Plane
https://www.maa.org/programs/faculty-and-departments/course-communities/geometry-of-linear-transformations-of-the-plane
Fri, 16 May 2014 16:17:34 +0000
lang403837 at https://www.maa.org