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03 Zigzag triangle

Photo: Zigzag triangle in the circle frame

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Global description

The size of the zigzag triangle is such so that it fits exactly inside the 20 centimetres diameter of the circle.The three sides of the body of the triangle all have a different pattern. The middle section of the triangle is open. The inner sides have the same patterns at a smaller scale as along the outside. The zigzag triangle is also called a ‘Christmas tree’.

Detailed description

The corners of the triangle are rounded. One corner has an alignment indentation to align the triangle with the degree markings along the edge of the circle. The side opposite the indented corner is straight.
Another one provides a smooth wave pattern, the final one has a zigzag pattern. Along the inner and outer side of the straight side two small indents indicate the length of a line segment to construct an hexagon. In the straight side oval holes can be found to hold a pen while rotating the triangle. The holes are placed to obtain curves at four, five, six, seven, eight or nine centimetres relative to the centre of the circle. Pushpin markers are placed near the corners.

Zigzag triangle manual

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Preparing the TactiPad

Place all eight knobs of the TactiPad approximately five centimetres away from the corners. Place the circle frame on top of the TactiPad.

Using the zigzag triangle

The zigzag triangle fits exactly inside the circle with the rounded corners nearly touching the circle edge. It can rotate freely. Place your pointing finger on the alignment indent and align the triangle at 12 o’clock. Now you can create an equilateral triangle inside the circle. Start with the indented corner at 12o’clock and draw along the straight outside of the triangle. Rotate the tool over 120 degrees clockwise (which is at 4 o’clock) and draw the line. Rotate once more over 120 degrees (which is at 8 o’clock).

 

Photo: Two sided of the equilateral triangle are drawn with the zigzag triangle

Hexagon in the circle

Align the indented corner at any degree indication and draw a line only between the two indents along the inner or outer straight side. Rotate the triangle over 60 degrees and repeat the draw. In total four more rotations are required to finish the shape.

 

Photo: Hexagon is finished in the CircleFrame

Repetitive patterns; Mandala type of figures

By tracing segments of the sides and/or combining patterns intriguing drawings will emerge. Whatever you do, the result is fascinating.

 

Photo: With wave-side of the zigzag triangle a repetitive pattern is made

Oval holes to create arches

The holes in the straight side of the triangle can hold a pen. Rotate the triangle holding the pen. Arches with a length depending on the amount of rotation and the selected radius will occur.

 

Photo: arches created by moving the zigzag triangle holding the pen in different holes

 

02 CircleFrame frame

Circle frame on the TactiPad

Photo: Circle frame positioned on the knobs of the TactiPad.

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Global description of the circle frame

The actual frame of the CircleFrame has similar dimensions as the TactiPad (28 cm by 37 cm). The thickness of the frame is four millimetres.
Near the outer edge of the frame oval holes can be found to place the frame in one of three positions on the TactiPad. For an a-centric position, two additional holes are present at both sides near the circle.

Detailed description

In the middle of the CircleFrame is a large circle cut out with a diameter of 20 centimetres. This is the actual drawing area. Along the edge of this circle medium sized indents every five degrees are provided, which form a large protractor. Around the outside of the circle there are extra markings: a teardrop shape for every 30 degrees, a line for every 45 degrees, or a combination of both where they coincide at 0, 90, 180 and 270 degrees. Indentations are placed around the outside of the circle frame in which rubber bands can be attached. These indentations are positioned at every 10 degrees seen from the centre of the circle. Slightly wider indents make the positions for 0, 30, 45, 60, 90 degrees, etc. easily recognizable

Circle frame manual

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Storage of the CircleFrame

The frame of the CircleFrame will sit or can sit already on top of the drawing board for storage. The additional tools for the CircleFrame have their place in the paper pocket.

Preparing the drawing board

Place the knobs of the TactiPad five centimetres away from the corners. The CircleFrame can be placed n three different positions: in the middle of the drawing board with the edges coinciding with those of the TactiPad, or in two positions left and right of the drawing board’s centre when in landscape orientation. Make sure the eight oval holes near the outer edge of the CircleFrame fit all over a knob.

 

Photo: Indications run along the edge of the circle: indents for every 5 degrees, drop shaped ones every 30 degrees and straight ones every 45 degrees.

Because the circle is exactly in the middle of the circle frame, the frame is horizontally and vertically symmetrical. Mounting the CircleFrame on the TactiPad therefore needs no consideration.

Inserting the tools in the circle

The wedge tool, the 468triangle or the zigzag triangle can rotate freely over 360 degrees within the circle. The drawing tools preferably are aligned with the degree markings along the circle.

For detailed descriptions and manuals of related tools see:

Zigzag triangle

468Triangle

Wedge tool

More ideas

01 Getting started

 

Photo: CircleFrame with 3 tools on the TactiPad

The CircleFrame includes the zigzag triangle, the 468triangle and the wedge tool. They are only applied in conjunction with the CircleFrame frame.

For the CircleFrame see the section:
CircleFrame frame

To apply the tools inside the frame see the sections:
Zigzag triangle

468Triangle

Wedge tool

For even more applications see the section:

More ideas

0.5 GraphGrid frame

The GraphGrid frame

Detailed description
The GraphGrid frame is yellow with a thickness of four milimetres. It is placed on the TactiPad like a picture frame. Eight oval holes in the frame fit around the knobs of the TactiPad to hold it in place. Three of the four corners are rounded.
Along the inner edge, small curved hooks are placed at a regular interval of 1 centimeter. Along the outer edge of the GraphGrid, indentations are made with a spacing of 1 centimeter as well. Slightly wider indications mark 5 centimeter intervals. The indentations hold rubber bands.
The locations of the hooks and indentations both exactly match with the centimetre scale along the edges of the TactiPad.
The ‘graphing paper’
The measurements of the drawing board become tangible on the entire drawing surface.
The frame overlaps the drawing surface along the edges by one centimeter.
Because of the A4 dimensions of the drawing surface (29.7 cm by 21.0 cm), the centimeter scale is not symmetrical along the TactiPad. Therefore the starting point for horizontal and vertical distances is at the upper left corner of the drawing board and GraphGrid frame when in landscape orientation.

0.4 Hyperbole tool

Hyperbole; tool to draw y=1/X

Global description
The global shape of the tool is a rectangle hook with the curved contour at the inner side.
Pushpin markers are provided at the top surface.
A small square for alignment is left out at the lower left corner of the tool.
By nature of the formula, the tails of the tool become very thin. To maintain the sturdiness of the tool, additional material has been added.
the graph contour endings contain a pen blocker.

Detailed description
The formula represented in this tool is a smooth curve only going down, seen from
X equals 0 to X equals 8.
Along the curve small indents are provided to indicate Y values corresponding with X values equal 0,25, 0,50, 1, 2, 3, 4, 5, 6, 7 and 8 respectively.

0.3 Lens tool

Lens; tool for convex and concave lens or mirror

Global description
The symmetrical tool could be described as a traditional house where the top part is curved. The first floor is one big window where to top side is curved. The second floor has a window where the top and bottom sides are curved in opposite directions.
The shape of all curves represent the curves of the lenses.
In the top and bottom sides of the tool small indents are provided to align the tool on the median light beam.
Pushpin markers are provided at the top surface.

0.2 Parabola tool

Parabola; X to the power of 2

Detailed description
The inner space of this U-shaped tool has the contour of the formula X to the power of two.
The two poles of the U have indented centimetre indications along the outside.
Three medium size alignment indents are provided near the bottom; one in the middle and one in each of the two poles.
Pushpin markers are provided in the top surface of the tool.
The contour of the graph goes down and up again. At the two ends of the contour pen blockers are provided.
Indented positions along the curve reflect Y values for X equals -2, -1, -0,5, 0, 0,5, 1 and 2.

0.1 SinTang tool

SinTang; combination tool for the sine, cosine and tangent graph

Global description
The SinTang tool combines graphs for two formulas; the sin(X) and the tan(X). More precise, a half period of the sine graph and a quarter of the tangent graph.
The sine graph, is the ‘hill’ contour which is the first half period of the sine graph. The cosine is a to the left shifted sine graph.
When placing the tool looking at the hill, the top side of the tool is a left to right downhill slope. After rotating 90 degrees clockwise it represents a quarter of the tangent graph.
The vertical left and right hand sides have an indented centimetre indication.
Pushpin markers are provided at the top surface.
For sine and tangent values of 1, the distance along the Y-axis is 4 centimeters. These dimensions provide sufficient ‘tactile space’.

Detailed description of the sine tool
The range from 0 to 180 degrees X values is distributed over a length of eight centimetres (aprox. 3 inches).
At 90 degrees is the top of the graph (maximum amplitude) at an height of four centimetres.
Small indents are provided in the curve at 30, 45, 60, 90, 120, 135, 150 degrees positions.
Pen blockers are provided at 0 and 180 degrees positions.

Detailed description of the tangent tool
To use the tangent part of the tool it has to be rotated for 90 degrees clockwise.
The contour of the tangent has small indents indicating the 30, 45 and 60 degrees positions on the X axis. The tan(45) is 1. The value of the graph is 4 cntimetres.
Pen blockers are provided at the 0 degrees and towards the 90 degrees position.
A length of four centimetres along the X axis covers a range of 90 degrees.

0.1 SinTang tool

Sine graph
Photo: The first half of the sine graph has been drawn, the tool is rotated 180 degrees so the second half can be created.

Draw an X axis with the ruler. Mark the X=0 and X=180 degrees position. The distance between the two marks is eight centimetres.
Align the two two centimetre indications of the tool with the X axis.
Draw the contour line for the sine from the X value of 0. Start at the pen blocker to avoid glitches. Draw along the contour until the pen blocker at the X value of 180 degrees which is on the X axis. Hold the pen on this position and rotate the tool around this pen position so the tool is upside down. Continue drawing the second half of the tool until reaching the pen blocker again on the X axis.
For convenience place a pushpin at the 180 X position and rotate the tool around the pushpin.
You can also place pushpin(s) in the pushpin marker positions to hold the tool in place.

Cosine graph
Photo: The first quarter of the cosine graph is drawn. The tool is rotated 180 degrees clockwise, so the ‘hill’ is upside down for the negative part of the graph.

Basically the shape of the cosine has the similar shape as the sine. However the graph is shifted to the left for 90 degrees.
Draw an X axis with the ruler. Mark the 0, 90 and 180 degrees positions. A section of 90 degrees has a length of four centimetres.
Align the tool with the X axis where the right pen blocker is positioned at the 90 degrees position. Draw along the contour starting at the top (X=0) downwards to the X axis.
Rotate the tool 180 degrees clockwise. Align the tool with the X axis and draw the negative part of the graph from 90 to 270 degrees.
Rotate the tool once again. Align the tool with the X axis and draw the last quarter of the graph up from the X axis on to the top of the graph.

Tangent graph
Photo: The X and Y axis are drawn as well as the first quarter of the tangent graph. The tool is positioned so the second quarter can be created. The pen blocker is hooked with a pushpin.
Draw an X axis with the ruler. Mark the 0, 90, 180, 270 and 360 degrees positions. The distance between each position is four centimetres, which covers 90 degrees.
Draw two asymptote lines : One at 90 degrees and one at 270 degrees.
The distance for the first asymptote line is four centimetres from the 0 degrees position on the X axis, the next one is at a 12 centimetres distance.
For the first section of the graph align the short (four centimetres) side with the X axis. Start at the pen blocker (0 degrees) and draw along the tangent contour upwards until you approach the first Y axis.
For the second section of the graph find the 180 degrees position (preferably provided with a pushpin).
Hook the pen blocker with the pushpin while the tangent curve is pointing down. Align the tool with X axis and draw the lower part of the graph.
For the third section rotate the tool around the pushpin 180 degrees counter clockwise. The tool has the same position as for the first section.
The fourth section is similar to the second section. Find the 360 degrees position, hook the pen blocker to the pushpin and align the tool with the X axis and draw the curve going down unstill you approach the Y axis.

0.2 Parabola tool

Parabola manual
Photo: A parabola has been drawn at X=0 and Y=0. The tool is positioned to create a second one at X-3 and Y=2.

Draw an X and Y axis.
Align the bottom indent with the Y axis and the ones in the poles with the X axis.
Draw along the contour of the tool.
You may choose any other coordinate as the minimum for the y value. The centimetre indications help to align the tool with the axes.