Marjon Tas

Detailed description of the square tool

The sizes of the squares ranges from two to eight centimetres. The frame that forms the square is one centimetre wide. Two finger fitters are provided in opposing sides. Two opposite diagonal corners are rounded. The others are sharp. At each corner a pushpin marker is located. Along the outside and inside a small indent is provided at every centimetre. In case the length of the side is odd numbered, there is in additional indent at the halfway position.

Drawing instructions

Square
When you position the square somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first square.

Alignment for horizontal or vertical oriented shapes
Aligning the tool with the ruler that is placed on two opposing TactiPad knobs, will make sure the aligned side is horizontal or vertical, relative to the measurement indications of the TactiPad.

Other shapes
With the square template you can create many more shapes such as a rectangle, triangle, parallelogram, trapezium and also 3D figures like cube or pyramid.

Rectangle 1
Choose the square tool that has the longest side of the rectangle that you want to create.

Draw the bottom line. Determine the width (is height) of the rectangle and draw the left and right line from the same position on to the bottom line. Move the tool downwards so the top side is almost on the line endings of the two (vertical) sides.

For convenience place a pushpin in the positions along the two short sides and draw a line from here to the bottom line.
Move the tool towards you until the top side hits the two pushpins. Draw the top line and remove the tool.

Rectangle 2
For larger rectangles alignment with the ruler works well.
Place the ruler on two knobs. Place the tool against the ruler and draw the bottom line and the left side. Move the tool to the right for as long as you want the length of the bottom line of the rectangle. Draw the rest of the bottom line and also the right side of the rectangle.

Connect the two line endings of the sides with the ruler.
Pushpins in these positions can be handy.

45 triangle – 1/1/sqrt2 triangle
Drawing two connected full sides of the square and the diagonal line between the two line endings creates a rectangle triangle, also known as a 1/1/sqrt2 triangle.
Placing pushpins in two diagonal positioned corners can help to draw the diagonal line.

Right corner triangle
Drawing only parts of two connected sides from the tool and connecting the line endings, will result in a right corner triangle.

Triangle with sides 1/2/SQrt5
Draw a line from a halfway position into a corner. Continue with a line along the full side. Remove the tool. Connect the two line endings.
This is also a right corner triangle with specific proportions for the length of the sides: 1/2/SQrt5.

Isosceles triangle
Draw a line as the base line for the triangle and check the halfway position on this line. Mark or place a pushpin in exact the same position in the opposite side. Connect this top corner position with each of the two line endings of the base line.
Calculating the surface of an isosceles triangle created with a square tool is not too complicated.
The surface is the multiplication of the length of the base line and the length of the side of the tool that is used, divided by two.

Irregular triangle
Drawing – a part of – a side and then marking or placing a pushpin along one of the three other sides and providing lines from this position on to both line endings will create an irregular triangle.

Parallelogram
Draw the bottom side of the square.
Place a pushpin two or three centimetres to the right in the bottom line.
Move the tool to the right until it hits the pushpin. Make sure the tool is still aligned with the bottom line.
Place a pushpin at the desired height position at the inner left side of the tool. Mark or place a pushpin in the right side on the same height as well.
Move the tool downwards until it hits the pushpins. Draw the top side of the parallelogram.
Remove the tool and connect the lines.

Trapezium
Use two different squares, one that has the size of the bottom of the trapezium, and one the size of the top of the trapezium.

Draw the bottom line of the square with the largest square. Take the smaller square and align its bottom line with the line that was created already. Draw the top line of the smaller square. Connect the line endings between the top and bottom line.
When placing the halfway position of the smaller square at the halfway position of the larger square, the trapezium will be symmetrical. Again you can use pushpins to mark specific positions, like line endings or the halfway position.

From a square to a cube
To begin with: draw a square. This square is the front face of the cube.

Draw a second square, the rear face, a little to the right and a little upwards. Make sure the bottom lines of the square stay parallel. Connect each of the four corners with the ones closest of the second square.
As the above is a start, you have to be aware that some of the lines are (partly) invisible. They should be dashed.

So, for a more realistic drawing instruction, each corner is given a character indication.

The lower left corner of the front face square is called A, the one at the lower right B, Going up from there is C and going left is corner D. The rear face has the corner E in the lower left and going counter clockwise F, G and H.

The square of the rear face is partly covered by the front face. So parts of the sides of this square have to be dashed.

The line E-H has to be fully dashed. The line E-F until it crosses the line B-C, the right line of the front face square, has to be dashed. The rest of the line is solid.

Four lines to connect the corners of the two squares completes the cube. Only the line A-E has to be dashed, the others are solid.

About the amount for ‘a little to the right and a little upwards’ can be discussed. A rule of thumb is to imagine a line under an angle of 30 degrees starting in the A corner. Set a distance of 60/70% of the length of the side of the applied square for the E corner.
The 30triangle can also help here.

Pyramid (symmetric)
For a start take the eight centimetres square and equilateral triangle with the same side length.
The base of this pyramid is a parallelogram. The four side faces are triangles. The front face is equilateral.

Draw a parallelogram where the top side is moved upwards and to the right with the rule of thumb in mind; an angle of 30 degrees and a length of 60% of the length of the side.

Dash the left hand side and the top side of the parallelogram because they are invisible.
Place the triangle aligned with the bottom line of the parallelogram where the corners match. Draw the two remaining sides of the triangle where they meet in the top corner T.

The corners of the base (floor) of the pyramid are named A, to D, counter clock wise.
To complete the pyramid, provide a solid line from C to T and a dashed line from C to T.

Taller pyramid
The top of the pyramid can be placed in many positions and the figure will still be a pyramid, but not symmetrical.
To keep it as such, the top T has to stay on the altitude line that arises from the crossing of the diagonals; the lines A-C and B-D, the centre of the parallelogram.
To set the top T, use the ruler that goes across the TactiPad, in equal positions of the frame and also meeting the centre position of the parallelogram.

Drawing instructions

Equilateral triangle
When you place the triangle tool somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first equilateral triangle.

Right corner triangle
Mark with a dot, or for convenience place a pushpin at the halfway position.
Start to draw a line from here into a corner.
Continue drawing a full side off from the same corner.
Draw a line from the halfway position to the opposite corner.
you have created a 30/60/90 degrees triangle, also known as a 1/2/square root3 triangle.

Isosceles triangle
Determine what is going to be the bottom side of the triangle.
Draw a line from the desired corner position on to the halfway position. Continue this line until you reach the position that has the same distance to the halfway position as your starting point has. The starting point is not necessary the corner of the tool.
For convenience you may place pushpins at the corner positions first or after you have created the base line.
Just mark the top corner or place a pushpin in the top corner and provide the lines from the top corner to both base line corners.

Irregular triangle
Draw a section of one side, not necessary starting from or ending at a corner of the tool. For convenience you can place pushpins first. Mark or place a pushpin in the desired position along one of the other sides. Provide lines from the marked position to both line endings.

Diamond with 60 degrees angle
Place the triangle on the TactiPad. Draw two of the three sides fully. For convenience place a pushpin in one of the corners at the line ending. Lift the tool and rotate it 180 degrees. Place the tool back against the pushpin. Rotate until the free corner matches the line ending. Draw line from here into the corner. Draw the last line, so they connect again in the corner.
Diagonals can be provided by drawing the lines between opposing corners.

Draw a house
For the outline of a traditional house use a square and draw three-quarter of the shape. Leave the top side open. To draw the roof, use a triangle, preferably a little larger than the square size. Place this above the walls of the square and draw the inner contour as the top part of the front face.
Use the smaller square tools to add windows.

Fantasy
Draw a triangle and place a pushpin in one of the corners. Rotate the triangle in any of both directions and draw again – a part of – the triangle. Repeat this a few times and change the corner to rotate.

Four equal sided pyramid
To start, for convenience, use one of the larger sized triangle tools. Orient the bottom side horizontally. Draw the inner contour.
Look for the halfway position on the bottom line. From here, image a line under an angle of 30 degrees and a length of 60% or 70% of the tools side length on this line. Mark this position or place a pushpin there.
Draw a line from the right corner on to this position. Also one line from here to the top of the triangle.
Finally a dashed line from the left corner to the marked position.

Drawing instructions

Right corner
By drawing along the rulers into the enclosed corner, two lines under an angle of 90 degrees occur.

Right corner triangle
When connecting the two endings of the previously created lines you will get a right corner triangle.

Diamond
For the centre position, use a pushpin. For high precision you might want to use four additional pushpins for the corners.
Place a first pushpin at the centre position of the diamond.
Place the enclosed corner of the rectangle hook against the pushpin in the desired orientation. Most logical is to have one ruler pointing left, the other ruler downwards.
Mark or place a pushpin at the desired horizontal ruler position for corner A.
Mark or place the third one along the vertical ruler for the B corner. Now the centre pushpin and the marks (or all three pushpins) are positioned in a triangle.
Lift the tool and rotate 90 degrees counter clockwise.
Place the enclosed corner of the tool again against the pushpin that marks the centre position and make sure the ruler touches the B pushpin.
Place a fourth pushpin for corner C, which is opposite A.
Rotate again 90 degrees.
Place a fifth pushpin for corner D in the identical ruler position as for corner B.
Connect the four corners.

Kite
In the kite shape the distance from ONE pair of opposing corners to the centre position differs. In other words, one of the diagonal lines is cut in two sections with different lengths.
Apart from this, the drawng instructions are similar as for the diamond.

Challenge
Fit a diamond exactly in the eight times six centimetres ellipse. The corners of the diamond are all four exactly on the ellipse outline.

Drawing instructions

For the first segment, place a (pointing) finger on the desired position in the drawing area and move the foot with the finger entrance against the fingertip.
Place the ring of the tool over the foot.
Determine by rotating the tool, the orientation for the first segment.
Decide on the radius of the polygon and place a pushpin in the corresponding indent of both legs.
For the second segment: Rotate the tool slightly off from the pushpins and lift the tool and rotate further in any of both directions until the legs have passed the pushpins. Slide the tool back against the pushpin and place another pushpin in the appropriate radius position in the unmarked leg.
Repeat this till you are back at the starting point.
After creating all the segments you can remove the tool and the magnetic foot and connect the pushpins/corners with straight lines.
In addition, by leaving the pushpin in the centre one or more radii can be drawn.

More precision with alignment
Place a pushpin first to mark the centre position in case this is relevant.
Move the magnetic foot so the groove in the finger entrance embraces the pushpin.

Aligning the polygon tool with existing lines
The ring has small indents for alignment of the polygon with a line.
Placing the bisector indents on a line, the centre will be on that line. The segment is cut in half.
Placing the orthogonal indents on a line puts the centre on the line and ensures the side of the segment is parallel to the line.

Spider web
For a sophisticated spider web use different polygon tools.
Create a few – slightly shifted – concentric polygons on the TactiPad and draw lines through the corners. See what happens when the more cornered polygons are at the outside of the web.

Drawing instructions

Utilising the spur wheel tool
We recommend to use two pushpins to fixate to tool on the TactiPad, because the spur wheel is a relative time consuming shape to create.
Draw the inner contour of the spur wheel and you have created the first step into the mechanical domain.

Interlinking the 12 and 20 teeth spur wheel
Once you have interlinked two spur wheels, you will experience a complex issue: finding the perfect position for one tooth on the one and one tooth on the other wheel to “bite each other”.
The distance between the centre positions of the two spur wheels is 17 centimetres.
Draw a straight line and align the spur wheels with the finger fitters with this line. Carefully check the positions of the teeth! You may need to slightly rotate the second spur wheel.

Finding the centre position of the spur wheel
The open space at the inside of the spur wheel does not make it easy to place the centre on a pre-defined position. You have to create support lines and align the tool with the finger fitters. Let us know your experiences.

Fantasy: Spur wheel as the start for a flower

Use the 12 teeth spur wheel. Combine this with the 6*4 centimetres ellipse in the ‘horizontal’ or ‘vertical’ orientation.
Enclose three teeth within the ellipse and draw the whole or a part from the ellipse. Repeat this three times until you have got all teeth covered.
Alternatively enclose two teeth within the ellipse and draw the shape five times for a more delicate flower.

Drawing instructions

Ellipse shape
Place the ellipse tool on the TactiPad and hold it at the finger fitters positions.
Draw along the inner contour for the ellipse shape.

Finding the centre position.

As long as you create two crossing lines that are symmetrical, they will pass the centre position. Symmetrical here means each line is a diameter line, from opposing angle positions, not necessary the lines of the longest and shortest diagonals.
When connecting the pushpins at 0 and 180 and also those at 90 and 270 degrees, you obtain the longest and shortest (orthogonal) diameters.
The full lines will cross the centre position.
Be aware, when placing all four pushpins at the outside and then lifting the tool might cause the pushpins fall out. To avoid this, place two pushpins at the inner side a 0 and 90 degrees and two along the outside at 180 and 270 degrees. By moving the tool slightly upwards off from the pushpins you can safely lift the tool.

Placing the ellipse on a pre-determined centre position
The open space at the inside of the ellipse does not make it easy to place the ellipse centre on a pre-defined position. You have to create support lines.
We might need to develop an insertion tool for positioning.

Dome

Instead of drawing the full contour you can draw parts or a dashed section of the ellipse. Dashed lines are applied to indicate invisible lines of 3D figures.
For a dome, orient the longest diagonal of the ellipse horizontally on the TactiPad. Draw the lower part of the contour as a solid line and the top half as a dashed line. Now you have the bottom section of a dome. The dashed section represents the invisible part of the dome.
This 3D figure can be completed by placing the top (T) somewhere above the dashed section of the contour and providing two lines from the position T to both ends of the virtual diagonal.
While the push pins are still there, the line for the diagonal at the bottom should be dashed as well because this line is not visible.

Fantasy 1
Create an ellipse and place a pushpin somewhere along the inner side and rotate the ellipse and draw it again.
Choose a different position for the pushpin. Repeat this a few times, for an unexpected result.

Fantasy 2
Combine the ellipse with the triangle or square and fit the shapes into each other.