Exercise 3: Manually Graphing the Projection of the Trefoil Knot onto the xy-Plane https://youtu.be/2_Zp2N35lYQ

In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I also plot the trefoil knot in 3D using the amazing GeoGebra graphing calculator as well as the new Desmos' graphing calculator. 

#math #trefoilknot #geogebra #desmos #calculus

Charged Particles Moving in Electromagnetic Fields https://youtu.be/48quQVxKZQ8

In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed and position of a charged particle, the motion is either a cycloid or a trochoid (a more general version of a cycloid). I then take a detour into the mainstream physics of charged particle motion in electromagnetic fields in general, and read up on magnetic mirrors, null lines, Earth's magnetic field lines, Van Allen Belts, and the Northern Lights. Buckle up!

#math #nuclear #electromagnetism #GeoGebra #physics

Example 7: Using Computers (GeoGebra) to Draw Space Curves https://youtu.be/aBuDScugCXA

In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic.

#math #3D #spacecurves #GeoGebra #calculator

Example 5: Vector and Parametric Equations of a Line Segment https://youtu.be/dSIfPYi3q4U

In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first recap on the vector equation of a line segment, which involves a parameter t between 0 and 1.

#math #vectorfunctions #geogebra  #science #calculus

Overview of the Hutchison Effect by George Hathaway in 1993 https://youtu.be/tppQ1i8gkZo

In this video I have uploaded a rare May 14, 1993 presentation of the Hutchison Effect and its history by Professional Engineer George Hathaway, a business partner and direct witness to the effect in the early 1980s. 

#HutchisonEffect #technology #AntiGravity #FreeEnergy #science

Plane Curves as Vector Functions and the Structure of a DNA Helix https://youtu.be/S94nUYS8Imc

In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix.

#math #vectorfunctions #planecurves #biology #calculus