<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Tue, 14 Apr 2026 17:50:29 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/vectors/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[The Spread Vector]]></title><description><![CDATA[Hi fellow Hiveians, Today I wanted to complain a little bit about more and more services. The Spread Vector Sadly, one of the things that we have not a lot of control over these days is the spread. What]]></description><link>http://direct.ecency.com/hive-147625/@cmplxty/the-spread-vector</link><guid isPermaLink="true">http://direct.ecency.com/hive-147625/@cmplxty/the-spread-vector</guid><category><![CDATA[hive-147625]]></category><dc:creator><![CDATA[cmplxty]]></dc:creator><pubDate>Sat, 14 Feb 2026 01:31:00 GMT</pubDate><enclosure url="https://images.ecency.com/p/FUkUE5bzkAZT3HzV5tJDiU2ik81PCd4JCyhWnRcDN8XJsVFY3UNB8DCS9HcoBdSfCpUoew2odE8FKyGZrZSeZN35UNbh4omkDvqEGKvj5mvJD2ARuZHYhyTvKkxxMQhensNhq9NFmLQGUprsKa9r1hWorMv3TzV21MDG?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas]]></title><description><![CDATA[In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the]]></description><link>http://direct.ecency.com/hive-111030/@mes/osculating-circle-of-a-parabola-summary-of-tnb-vectors-and-curvature-formulas</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/osculating-circle-of-a-parabola-summary-of-tnb-vectors-and-curvature-formulas</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 15 Jan 2026 21:36:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/8th8uW8KLF3eHoH9cP9Etf4AqMgNKtKoyu4fqZraWgFsdvwTnXiBR7fHJEcqanALKN3Y87hrGfQ7utK8XQCXyS1fdu99PTT2nkcAzkwvPbzYDSXGrNqyzmPc6CXYiAr2p4SM3tQsFidR27m46v6qGK2q4AZnKvNoeEfQZqUwud2CM1bjpbWeXrqqH1?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas]]></title><description><![CDATA[In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the]]></description><link>http://direct.ecency.com/hive-128780/@mes/c0554d3b</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/c0554d3b</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 15 Jan 2026 21:15:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/PB8ro82ZpZP35nu5CJ2bLWtWovSWCek72zkxirh28oqXP6byR2Eqv7FmdZxQjxdzFnpZsZrErzBkzEb4B1Fo8Jv2wGs4AyP8MpNJy1WWQSTdW96e?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix ]]></title><description><![CDATA[In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. YouTube - Summary - Notes - Playlist - Vector]]></description><link>http://direct.ecency.com/hive-111030/@mes/the-tnb-frame-normal-and-osculating-planes-example-on-a-circular-helix</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/the-tnb-frame-normal-and-osculating-planes-example-on-a-circular-helix</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 13 Jan 2026 22:26:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/2N61tyyncFaFVtpM8q6r7eyQFvUiqNpQu6o2Yd65xmPkkdqXi9SFbNdjYpJd8ke1gdFmtCe5mfFNvHx8qAUS2qtHTCambQ6dEeeTBr4QgS9q9kJwf4LCH68q26vDHCztkhqHsRYPPwMZ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. The TNB Frame is named after the Tangent,]]></description><link>http://direct.ecency.com/hive-128780/@mes/msfarvob</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/msfarvob</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 13 Jan 2026 22:05:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVdTJeZeR9mpZgJwQ4CSCx3drLVVDsK6aqan538K6ZgEQ2mYBEypXpEcuZiFeF5t7bb548582A?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Normal and Binormal Vectors + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. YouTube - Summary - Notes - Playlist - Vector Functions playlist]]></description><link>http://direct.ecency.com/hive-111030/@mes/normal-and-binormal-vectors-example-on-a-circular-helix</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/normal-and-binormal-vectors-example-on-a-circular-helix</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 11 Jan 2026 22:43:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/3ejZQFLqXedKXKhURdjx14Sr8NSYZmTdw2HQuQXkeUsn4X1LM6CBB673MURi3E19AyAMBuu9sLH3sbJZXcJhajNGM3FqgbcgyFL5KJoMybiwwwvsQWf99dF8APvGjVcSjee5paYSYpddt8Vq5ZAf5oux6CTdBtrTTTLN2p7fTQQwjHxtsue6WYxi5LA1M?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Normal and Binormal Vectors + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. Since the unit tangent vector is a constant-length one, its]]></description><link>http://direct.ecency.com/hive-128780/@mes/klkebgpa</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/klkebgpa</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 11 Jan 2026 06:45:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVgY8ex6gcB6PigrZDwCwAQFy8ciubZx4hdqBq78QVJjwW9e4ZvkEBEna6fUd9wPsrqhLdmjnN?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature of a Plane Curve y = f(x) + Example on a Parabola]]></title><description><![CDATA[In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. YouTube - Summary]]></description><link>http://direct.ecency.com/hive-111030/@mes/curvature-of-a-plane-curve-y-f-x-example-on-a-parabola</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/curvature-of-a-plane-curve-y-f-x-example-on-a-parabola</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 07 Jan 2026 22:51:39 GMT</pubDate><enclosure url="https://images.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv81WQjvRBmt26bsiU1YXx6cxDxCSZTQyePdKGnSd47YRGLFaWgWGrWzXdaFQdmQR1crVQPzaXBoAiDp23pwv66DEgbpN6VMFvyWU4VP4vFREFCtDpK7FBeP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature of a Plane Curve y = f(x) + Example on a Parabola]]></title><description><![CDATA[In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. The magnitude]]></description><link>http://direct.ecency.com/hive-128780/@mes/dblwgcxw</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/dblwgcxw</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 07 Jan 2026 22:35:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVbKFz9sZfgDd6HuLgJGk99K3iAZPeqqh3HNfrBdihk9Ty5w7iXs6FaBcKdRiCcxG8ADe56Ft2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature Cross Product Formula: Proof and Example on Twisted Cubic]]></title><description><![CDATA[In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two derivatives of the vector function. I derive this using the fact]]></description><link>http://direct.ecency.com/hive-111030/@mes/curvature-cross-product-formula-proof-and-example-on-twisted-cubic</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/curvature-cross-product-formula-proof-and-example-on-twisted-cubic</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 06 Jan 2026 05:44:45 GMT</pubDate><enclosure url="https://images.ecency.com/p/4bEjbgCbFMvA8T33kGvF6kHce4BTcm88Pv5WXm8EBoMz3u29V4LrZvMDXSFP2Y8y2jqDzRWJe7k1YYiaPLg3uS6HGWgP29B1QUVmx9T2TGCi9LyUTaxYVnibcc8UNc9W87pPuwLz4GgBQKCwHx6pxcKBKAuGG2Yfp6XVfHCHwvs1eEkvQX?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature Cross Product Formula: Proof and Example on Twisted Cubic]]></title><description><![CDATA[In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two derivatives of the vector function. I derive this using the fact]]></description><link>http://direct.ecency.com/hive-128780/@mes/rbhcjajw</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/rbhcjajw</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 06 Jan 2026 05:25:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVbFu4pKvsFcKD4v25HESWjZCrWXZ35JUmBtMWiHxti7m6MEvJ3fiH8ixcHy5uUzJcWvTmk9Rg?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature: Definition and Curvature of a Circle is 1/Radius]]></title><description><![CDATA[In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a given point. It is defined as the magnitude of the derivative of the unit tangent vector]]></description><link>http://direct.ecency.com/hive-111030/@mes/curvature-definition-and-curvature-of-a-circle-is-1-radius</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/curvature-definition-and-curvature-of-a-circle-is-1-radius</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 01 Jan 2026 22:45:36 GMT</pubDate><enclosure url="https://images.ecency.com/p/3DLAmCsuTe3bV13dhpqdWvcxWLWLiLiErP5TM3QSxWS71hfDuw1VaB3XHQzeSTkGRWXQBg69JUgwU8cA1kYoVV5RB8Z9vFh2NYDudGvmN8nmY9PVCvAVU4w1amC8J6TwSwC7thNRSZ9Y1bjMQNJSRrhEbDWtKou?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature: Definition and Curvature of a Circle is 1/Radius]]></title><description><![CDATA[In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a given point. It is defined as the magnitude of the derivative of the unit tangent vector]]></description><link>http://direct.ecency.com/hive-128780/@mes/ntqciskf</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/ntqciskf</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 01 Jan 2026 22:25:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVeXHigANY75N8W9DPkbEmw1SZqhF9re3z7UfDE4K8QRQDPqAkmEY8FKU7YEWGpxeSGibog1FC?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Parameterizations and Arc Length Function]]></title><description><![CDATA[In this video, I show that a curve can be represented by multiple different vector functions, called parameterizations of the curve, and that it is often beneficial to reparameterize a curve as a function]]></description><link>http://direct.ecency.com/hive-128780/@mes/eraloeiq</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/eraloeiq</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 29 Dec 2025 06:15:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVeXH4nfMpzPRmFz6tGDFNYUdVkgWLkXJ8VH2iutAPbxcBsA1uCPbC4aKoZXYX8bSPKPfQ8oNn?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Parameterizations and Arc Length Function]]></title><description><![CDATA[In this video, I show that a curve can be represented by multiple different vector functions, called parameterizations of the curve, and that it is often beneficial to reparameterize a curve as a function]]></description><link>http://direct.ecency.com/hive-111030/@mes/parameterizations-and-arc-length-function</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/parameterizations-and-arc-length-function</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 29 Dec 2025 06:09:21 GMT</pubDate><enclosure url="https://images.ecency.com/p/V9N4wevejZUbdQxawfdFtcb6UnCVe92CzSNEhVDTcYUCvfNio3G2cYzcCXfDquCnJSRhaBKwmkGgYtfpvSn3JrAb3Zusbw14vp6fKQs6ViAfNk8r5Xg5FmXGEaaEE4eAP862pNHCFyRcsKSZ7VjcQtQeHXu6teEjVfzZohsNZ8q2NxNvx7yCJvXy9eHaWqB6RskmoMNXAqCZksUcbaN7y?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Arc Length of a Space Curve + Example on Circular Helix]]></title><description><![CDATA[In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative]]></description><link>http://direct.ecency.com/hive-111030/@mes/arc-length-of-a-space-curve-example-on-circular-helix</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/arc-length-of-a-space-curve-example-on-circular-helix</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Dec 2025 22:45:54 GMT</pubDate><enclosure url="https://images.ecency.com/p/TZjG7hXReeVoAvXt29bbVGMEE7sQ8cjDLQHKvyubK83Fr7fwxWWPZg8BiNdk3BGaferNXoAZ2Q1NciBcLsyN4sf6KqQrN3t3gRx7SYb7Gnbmbvwbof9VD9DwrMhaCkwgsjbzrFSo8EsPBM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Arc Length of a Space Curve + Example on Circular Helix]]></title><description><![CDATA[In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative]]></description><link>http://direct.ecency.com/hive-128780/@mes/nizhfvfl</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/nizhfvfl</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Dec 2025 22:05:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVeDx4VBSZLpZVzA9Vk3cg3Vr3zjfr2EQd3VBBPFZZYsDDcGTyjYEDRtsH7GwGPybn78D82dZ8?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Vector Functions: Arc Length and Curvature]]></title><description><![CDATA[In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. I also go over normal, binormal vectors, as well as the TNB frame,]]></description><link>http://direct.ecency.com/hive-111030/@mes/vector-functions-arc-length-and-curvature</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/vector-functions-arc-length-and-curvature</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 24 Dec 2025 05:43:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/FUkUE5bzkAZSUQtscfU67XyuspKfVPvhJ6PgMwaumQRFSqc8YzUHX1Q1a8BCmr2exgDZdpMWAyRxkbi8Rne4dqVdD1ae6nnyeazeHA4CgJpww9Kwizt2CBMCS9xZ1wHc2iNdVQ62eRK8h8TUph8zbeEsFxyDXPuS359q?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Vector Functions: Arc Length and Curvature]]></title><description><![CDATA[In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. The arc length for a space curve is calculated in much the same way]]></description><link>http://direct.ecency.com/hive-128780/@mes/koxharrd</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/koxharrd</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 23 Dec 2025 06:30:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/S5Eokt4BcQdk7EHeT1aYjzebg2hC7hkthT45eJK5tKNu6VKP6DmSGWe5KB35i9Ypd2R26JJ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 4: Proof of Formula 5: Derivative of Cross Product of Vector Functions by Components]]></title><description><![CDATA[In this video I prove Formula 5 of the differentiation rules for vector functions, and this time derive the derivative of the cross product of two vector functions. I solve this by taking the derivative]]></description><link>http://direct.ecency.com/hive-128780/@mes/jkzwljpi</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/jkzwljpi</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 20 Oct 2025 21:05:12 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVzS9BVc5sJvENSBhV2xzbUuRSmJ8dhgUtJ411zPuEcKGrcYh3HeqwaKL4YNf4VAo78mrQBNzr?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>