Learn how to create tags, and how to tag and untag sketches.

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.

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.

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.

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.

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

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

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

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.

This video shows how to inscribe and circumscribe circles with triangles. We also see how to locate key points with specialized tools for triangles.

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.

Using the hand tool we see how lines connecting the ends of a circle's diameter to a point on the circle always meet at a right angle.

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

Approximating the cube root of two using a "neusis" technique by Isaac Newton

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

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.

Using the Seed of Life pattern we learn how to divide a segment into 3, 5, 7, and 9 equal parts.

Using the "starcut" diagram we divide a segment from 2 to 12 equal parts.

Download and print out a visual mnemonic "cheat sheet." Two versions are provided, US Letter (8.5" x 11") and A4 (210mm x 297mm).

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

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

The Starcut diagram is drawn by connecting the midpoints of a square to each opposite corner.

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

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

We construct a pentagon from the vesica piscis width. This is done by drawing a series of 4 equally sized circles and connecting significant intersections.

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

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

Here we draw a diagram by Albrecht Durer which joins the hexagon to the pentagon, growing out of circles.

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.

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

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

Here we construct an enneagon by neusis and make it as accurate as our hand-eye coordination allows.

Using the automatic polygon tool we generate triangles, squares, hexagons, and many more shapes rapidly and easily. We explore various 2D tiling patterns.

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

Using the automatic polygon tool we explore shapes that internally subdivide into the same forms at smaller scales, called recursion of form.

Here we draw an approximation of triangulating the circle using a 25-sided automatic polygon with astonishing accuracy.

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

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

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.

In this video we discover the golden ratios that are encoded in the geometric relationship between an equilateral triangle and a square.

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

By comparing adjacent circles and squares we see how these encode golden ratios.

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

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.

In this video we look at designed objects exhibiting golden ratio proportions, which include a Stradivarius violin, piano keyboards, vinyl records, credit cards and popular car logos.

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

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

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

In this video we derive the moon and earth proportions from the starcut diagram.

Starting by constructing a golden rectangle, we proceed to derive squaring the circle, the moon earth proportion and the slope of the great pyramid.

Simple sacred geometries encoding planetary mean orbits.

Here we see how to construct an infinite number of 3-4-5 triangles within any square.

We construct Euclid's proposition 47 without measuring by using starcut diagrams to divide squares into grids of 3, 4 and 5 squared.

In this video we see how the 3-4-5 triangle and Euclid's proposition 47 encodes the earth's tilt angle with respect to the ecliptic.

We explore how the 3-4-5 triangle is connected with squaring the circle, the proportions of moon and earth and the great pyramid.