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Course: Sacred Geometry Foundation

Sacred Geometry Foundation

  • Life Time Access
  • Certificate on Completion
  • Access on Android and iOS App
  • Self-Paced
About this Course

Geometry is an exploration of truth, the kind that is self-evident and universal. Where there is universal truth, there is also great beauty and from this a feeling of sacredness naturally arises. In this class you will learn everything you need to draw and experience the sacredness of geometry.

You can draw in this class using a pencil, paper, compass, straightedge (aka ruler) and/or using a free iOS app. In this course, I use Euclidea: Sketches, a 100% free iOS app, for the practical reason that it is far clearer to observe what I'm doing viewing my recorded iPad Pro screen than filming my drawing board.

To follow along with this course, you are welcome to use this app (or use another computer-aided drafting program), or draw by hand using the time-tested instruments of pencil, paper, compass and straightedge.

The following books are mentioned in the course; they're not required reading, but these are great books. If you end up loving geometry, you'll might want to eventually read some or all of these:

  • Drawing Geometry by Jon Allen ISBN 9780863156083
  • Ruler & Compass by Andrew Sutton ISBN 9780802717764
  • Sacred Geometry by Robert Lawlor ISBN 9780500810309
  • City of Revelation by John Michell ISBN 9780345236074
  • Euclid's Elements (first published circa 300 BCE, ISBN 9781375462631)
Basic knowledge
  • You can take this course using a pencil & paper, compass and straightedge or use a free iOS app
What you will learn
  • You will learn essential geometric constructions, draw solutions to some ancient problems, construct all the regular polygons up to nine sides, construct the golden ratio in several ways, see how the golden ratio is used in art & science, encode the proportions of Earth & Moon in profoundly simple diagrams and draw some classic sacred geometries
Curriculum
Number of Lectures: 40
Total Duration: 02:10:44
Introduction
  • Traditional versus digital drawing  

    Benefits of drawing by hand are contrasted with the benefits of drawing with an app. 

  • Drawing options  

    Euclidea: Sketches is a 100% free iOS app for drawing on iPhones and iPads, with or without the Apple Pencil. I have recorded screen-captured videos in this course using this app for maximum clarity and efficiency. You can search the App Store on an iOS device to locate this app. Here is what its icon looks like:



    To follow along with this course, you are welcome to:

    • Use the above app.
    • Use any computer-aided drafting program.
    • Draw by hand using the time-tested instruments of pencil, paper, compass and straightedge.


Essentials
  • Organizing sketches with tags  

    Creating, assigning, deleting and restoring tags. Sketches can have multiple tags. Deleting a tag does not delete sketches. How to create new sketches and return to the dashboard.

  • Sketch management tips  

    Here you learn how to create, delete and rename files. The temporary buffer is also covered. You don't necessarily need names to save files in the mobile app, unlike desktop applications.

  • Bisecting line segments  

    In this video we bisect a line using the traditional technique of drawing circles at each endpoint and constructing the vesica piscis form. We also learn to use specialized tools in the app that bisect by adding a point or a perpendicular line. We also learn drawing navigation with the hand tool.

  • Controlling drawing element appearance  

    Using the artist palette mode we learn how to change the colors, line thicknesses and line patterns. We are able to affect line, circles and points.

  • Bisecting angles  

    Here we bisect an angle using the traditional method of drawing three circle and we also do it more efficiently using the bisect angle tool in the app. We also label and decorate the angles to prove that the resulting angles are equal.

  • Perpendicular through point not on line  

    In this video we construct a perpendicular line to a point not on the line using both analog and digital techniques.

  • Perpendicular through point on line  

    In this video we draw a perpendicular line through a point on the line; both traditional and digital methods explored.

  • Drawing parallel lines  

    Here we construct a parallel through a given point using the compass and straightedge and also with the digital tool.

  • Two and three-point circles  

    We draw two-point circles by bisecting the points to find the center. We draw three-point circles by bisecting two of the lines implied by the points to find the center.

  • Lines tangent to circles  

    Here we find points of tangency between a circle and a point on a line passing through the circle's center by bisecting the distance between the point and the center. This point is the center of a new circle whose points of intersection with the original circle are the sought for points of tangency.

  • Method for dividing into arbitrary number of segments  

    This video teaches how to divide any segment into an arbitrary number of equal parts by drawing a parallelogram, which allows you to transpose divisions onto the original segment.

Ancient Problems Solved Approximately
  • Trisecting an angle  

    Using the ancient Greek technique of neusis, we trisect an angle, dividing it into three equal angles.

  • Squaring the circle  

    We attempt to square the circle using an approximate construction that is 99.9% accurate in terms of lengths.

Constructing Regular Polygons
  • Equilateral triangles  

    Here we draw regular triangles with a given edge length or by inscribing it within a circle.

  • Squares  

    In this video we draw squares both inscribed and circumscribed and at 45 degree angles.

  • Pentagon and pentagram by Western technique  

    By bisecting a segment and an angle and constructing a parallel line we are able to construct a pentagon and its inscribed pentagram.

  • Pentagon and pentagram by Eastern technique  

    We construct a regular pentagon and inscribed pentagram by drawing a number of circles.

  • Pentagon by neusis  

    Here we construct a pentagon by neusis, aka marked ruler technique, or verging. 

  • Inscribed and edge length hexagons  

    We draw an inscribed hexagon from 3 circles and a hexagon by edge length from 6 circles surrounding one central circle.

  • Septagon and septagram approximation  

    In this video we draw an approximation of a septagon that has 99.9% accuracy. It works in the lower half of the vesica piscis.

  • Octagons and octagram star  

    In this video we both inscribe and circumscribe octagons and end by drawing the octagram star.

  • Enneagons and their stars  

    Here we construct an approximation with 99.6% accuracy of a regular nine sided polygon. We inscribe three different kinds of stars within.

  • Quality vs quantity in form  

    Here we draw polygons generating from the vesica piscis and explore the concept of quality versus quantity.

Golden Ratio Constructions
  • Golden ratios from the vesica piscis  

    Here we show four golden ratios that emerge or are encoded in the vesica piscis, as pairs orthogonal to one another.

  • Golden ratios from an equilateral triangle  

    In this video we identify 6 golden ratios that emerge from the relationship of an equilateral triangle and its circumcircle.

  • Golden ratios from a square  

    Here we identify 6 golden rectangle that are encoded in a square's relationship with a line connecting one of its edge midpoints with an opposite corner.

  • Pentagrams and the golden ratio  

    Here we show how pentagrams encode an infinite number of golden ratios through inner recursion.

  • Golden ratios in art  

    Exploring how the golden ratio has been used in art history in the West from Leonardo to Michelangelo, Vermeer, David, Ingres, Dali and others.

  • Golden ratios in science  

    Here we examine the golden ratio in science. Metrology, Moon and Earth, Saturn and its rings, visible light, DNA, and the grand scale of all things are examples.

Planetary Proportions
  • Tangent circles  

    We construct an approximation of the Moon to Earth proportion using tangent circles.

  • Square and pentagram  

    Here we see how objects as fundamental as square and pentagram encode the proportions of moon and earth.

  • Sacred geometry of the pentagram  

    The pentagram encodes squaring the circle, the proportions of moon and earth, and the slope of the Great Pyramid of Giza.

Classic Sacred Geometries
  • What is the flower of life?  

    Here we explore examples of the flower of life in the work of Da Vinci, the Osirion in Egypt, and the Cosmati pavement in Westminster Abbey.

  • How to draw the flower of life  

    In this video we draw the pattern and contemplate it as a metaphor for the creation of the universe.

  • Drawing projection grid for a dodecahedron  

    Here we draw a projection grid for a dodecahedron within the flower of life pattern.

  • Dodecahedron within the flower of life  

    We draw a 2D projection of the 3d dodecahedron using the projection grid in the flower of life.

  • Metatron's hypercube  

    Metatron's higher dimension cube is drawn as a 2d shadow anchored in the flower of life.

  • Bonus  

    Thanks for taking this course! If you liked it, here is coupon code 10SIMPLIV, good for 10% off my more extensive course Sacred Geometry Essentials hosted on my personal site:


    https://www.scott.training/courses/sacred-geometry

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