Lens manual
Photo: for the application the tool is rotated 90 degrees. The median light beam is drawn. A convex lens has been drawn. The tool is positioned to create the mirror.
Draw a line with the ruler to represent the median light beam.
Align the tool on the line.
Draw the inner contour for the mirror, the convex or the concave lens.
You can add additional light beams to show light breaking and reflection effects.
Hyperbole manual
Photo: An X and Y axis are drawn. The graph is drawn in the first quadrant. The tool has been rotated 180 degrees clockwise so the second part can be created. A pushpin is at position X=0,Y=0.
Draw an X and Y axis with the ruler
Be aware, the effect of the additional material is also that the actual X and Y axis are covered by the tool.
Align the tool with the two axis by placing the flat sections at the tails with the axis.
For convenience you can place a pushpin in the crossing of the X and Y axis.
Draw along the contour of the tool.
Rotate the tool 180 degrees clockwise. Align the tool with the axis and draw the second part of the graph.
GraphGrid frame manual
Preparation
The default setup has rubber bands every two centimetre in horizontal and vertical direction, so forming a grid.
Two rubber bands go around the frame to indicate two axes.
However, before mounting the GraphGrid frame on the TactiPad make sure all rubber bands are provided according your preference.
Low and high rubber bands – Using differences in height
The framework of the GraphGrid has a thickness of four millimeters. Therefore there is a well noticable difference in height between the bands that run along the top side (outer) part or the bottom side (inner)
Part of the frame. The lower rubber bands that are attached to the hooks run alongside the inner part of the GraphGrid and can lay flat on the drawing surface.
The rubber bands can be placed horizontally and vertically with a minimum distance of 1 centimeter.
The bands can also be placed at an anglle of any number of degrees.
Note: The hooks at the inside edge are at every centimetre. Adding rubber bands to each hook will result in a (too) denced grid.
Placing the grid lines and axes
The hooks and indents are positioned every centimeter along the frame, so the minimum cell dimensions are one by one centimeter. To form a larger grid, you can place the rubber bands two or more centimeters apart by skipping one or more hooks.
Spare rubber bands
Additional rubber bands for more grid lines and axes are supplied with the GraphGrid. These are standard, thin rubber bands with a length of 12 to 15 centimetres.
To keep the rubber bands in place, the hooks have such a shape that the rubber bands will not come loose if they are positioned properly in the frame. Pplacing a rubber band is easiest if you hold the rubber band with two hands, keeping it perpendicular to the frame so you can slide it through the slot to the end of the hook. First of all, you span the rubber band in two opposing hooks, so that it forms a double line between two sides of the GraphGrid. You then take the upper of these two lines and slide it into the next desired hook in both sides of the frame to form the second grid line.
The higher rubber bands are stretched around the outside of the GraphGrid and fall naturally into the indents.
Getting started
To begin with, make sure the TactiPad has the landscape orientation with the hinge facing backwards.
To hold the GraphGrid frame,, place the knobs at aproximately five centimeters away from the corners.
To position the GraphGrid frame correct, place the flat corner in the upper right corner of the TactiPad.
It is possible that of one of the rubber bands coincides with the position of one of the knobs. Therefore, the holes in the GraphGrid around the knobs are extra-long so you can slide the knobs aside for the desired placement of the rubber band.
Photo: Stack of TactiForma tools
The TactiForma set consists of the following tools:
7 squares, 7 triangles, 1 rectangular L-shape hook, 5 polygon tools plus magnetic foot, 2 spur wheels, 4 ellipses.
The square tool, the equilateral triangle tool, the ellipse tool and the regular polygon tool come in different sizes. Knowing about the width of one, two or three of your fingers or the length of one finger, makes it easier to measure distances or finding the right tool without (extensive) counting the measurement indications.
Although the tools are recognizable by their shapes and the names of the tools clarify their purposes, it is highly recommended to read the descriptions and manuals because the tools contain many more applications than you will notice at first sight.
Especially the regular polygon deserves reading the detailed description and manual while the usage differs from the rest.
To avoid confusion while reading the texts where the name of the tool and the shape that is created is used, the words shape or tool will be added as much as possible.
We introduce some of our own terminologies that are applied throughout the pages such as finger fitters, finger entrance, small, medium and large sized indents for measuring and alignment.
For the tools see the sections:
Square
Equilateral triangle
Ellipse tool
Rectangle hook
Regular polygon tool
Spur wheel
Photo: The 8 centimetre square tool on the TactiPad
The TactiForma set contains seven squares. The length of the sides range from two to eight centimetres.
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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.
When you position the square somewhere on the TactiPad in any orientation and then draw along the inner contour, ou 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.
With the square tool you can create many more shapes such as a rectangle, triangle, parallelogram, trapezium and also 3D figures like cube or pyramid.
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.
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.
Photo: square against ruler, which is placed on two knobs, moved to the right after drawing the bottom line and left side
By drawing two connected full sides of the square and the diagonal line between the two line endings will create 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.
By drawing only parts of two connected sides from the tool and connecting the line endings, will result in a right corner triangle.
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.
Photo: connecting the two drawn sides of the 1/2/sqrt5 triangle
Calculating the surface of an isosceles triangle created with a square tool is not too complicated.
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.
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.
Photo: baseline with pushpin on halfway and opposite position, which is connected with the line endings to create the Isosceles triangle
By 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 show an irregular triangle.
Photo: all pushpins are in correct positions, the lines can be connected to complete the parallelogram
Draw the bottom line of the square. Use a smaller square tool as before. Align the bottom line with the one 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.
Photo: drawing the top line when smaller square is placed on bottom line in symmetrical position
The ‘top right view’ of the cube shows the front face, the right face and the top face of the cube.
Each corner is given a character indication. The bottom face of the cube has corners A, B, C and D. The top surface has corners E, F, G and H. Corner E is above corner A. Please note, there are also other naming conventions.
Photo: completed cube top right view
(*) Little to the right and a little up
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 out a distance of 60/70% of the side length along this line.
The hypotenuse of the 30triangle can also help here.
Photo: triangle placed on parallelogram, drawing the last line
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.
Photo: The eight centimetre equilateral triangle on the TactiPad
The TactiForma contains seven equilateral triangles. The length of the sides range from three to nine centimetres.
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The body of the triangle is about 12 millimetres wide. On all three of the outer sides a finger fitter is provided for easy lifting or extra grip. One outer corner is rounded, the other two are sharp. All three corners have a pushpin marker at the top surface. Along the outside and inside are indents located at every centimetre. They align with each other. In case the length of the side is odd numbered, there is an indent in addition at the halfway position.
The TactiForma triangle tools are designed as equilateral triangles. This shape is more difficult to draw than an irregular triangle; therefor, you can just mark three positions or place three pushpins somewhere in the drawing area and connect them with a straight line. More triangle variations with specific properties, can be created with the square tool or the rectangle hook tool.
When you place the triangle tool somewhere on the TactiPad in any orientation and then draw along the inner contour, you have created your first equilateral triangle.
Mark with a dot, or for convenience place a pushpin at the halfway position of a side.
Start to draw a line from here into a corner. Continue drawing a full side 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.
Photo: pushpin is placed in correct position; time to draw the last line of the right corner triangle.
Determine what is going to be the bottom side of the triangle. Draw the bottom 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. 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.
Photo: the triangle is rotated over 180 degrees, to draw the second part of the diamond
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.
Photo: four equal sided pyramid is finished
Photo: Rectangle hook tool
The TactiForma has one rectangle hook tool with two orthogonal rulers with a length of 10 centimetres.
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The rectangle hook tool has the shape of a capital l, where the horizontal and vertical part of the character have the same length of 10 centimetres / approx. 4 inches. The two parts enclose an angle of 90 degrees. They are equipped as a ruler with measurement indications in centimetres at the top surface and indents per half centimetre along the sides. The body of the tool is two centimetres wide. On the outer side, near to the rounded corner and to the tips you find finger fitters for easy lifting or extra grip. The corner between the sides is rounded at the outer side. At the top surface is a groove under an angle of 45 degrees for alignment. The rulers are ending with a 90 degree hook serving as a pen blocker. Pushpin markers are located near the rounded corner and near to the tips.
By drawing along the rulers into the enclosed corner, two lines under an angle of 90 degrees occur.
When connecting the two endings of the previously created lines you get a right corner triangle.
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 drawing instructions are similar as for the diamond.
Photo: creating the last line of the kite conform the instructions
Fit a diamond exactly in the eight times six centimetres ellipse. The corners of the diamond are all four exactly on the ellipse outline.
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.
Photo: The five sided regular polygon tool, holding the magnetic foot with pushpin
The TactiForma set contains regular polygon tools with five, six, seven, eight or nine corners referred to as pentagon, hexagon, heptagon, octagon and nonagon respectively. The radius of the polygons range from three to eight centimetres. The magnetic foot is an essential part of the regular polygon tool, to hold the tool in place.
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Imagine a line drawing of an isosceles triangle pointing upwards. The top is cut off and replaced by a circle (a ring). The base line does not exist. The length of the two sides that stick out from the circle (the rulers) determine the maximum radius the polygon can have.
The sides are a-symetrical connected to the ring; the right ruler goes along the outer side of the triangle, the left ruler along the inner side. Where both rulers would meet in the top corner, the top is cut off and replaced with a ring, so the rulers are only partly present. The rulers have a centimetre indication at the top surface and along the side indents at every half centimetre. The measurement indications point in the same direction. They have a pushpin marker near to the ring and at the end of the ruler.
At the outer side of the right ruler, medium sized indents are provided to indicate the type of polygon. E.g. six indents means the hexagon polygon tool. The hole in the ring leaves space to find the centre position of the polygon and is also the fit for the magnetic foot to hold the tool in place during the rotation of the tool.
The ring has an inner radius of nearly two centimetres and an outer radius of nearly three centimetres. This enables a radius for the polygons ranging from a minimum of three centimetres and a maximum of eight centimetres. Three small indents are at the outside of the ring. One of them is placed on the line formed by the bisector. Two others on an orthogonal line that crosses the centre position. The round foot has two magnets fully encapsulated in rubber, to hold the body of the tool in place. It is lacking a section so the fingertip can slide in. This open area is called finger entrance. It enables exploring the drawing near the polygons centre area. The vertical groove in the middle of the finger entrance Can hold a pushpin and indicates the precise centre position of the polygon.
Knowing about regular polygons; a shape based on triangles. A regular polygon is a shape where the individual sides are all of the same length. It can also be described as a circle filled up with isosceles triangles. The sides of two adjacent triangles co-inside. However, the sides of the triangles are not present in the drawing. Only the base sides are visible as the sides of the polygon shape. For the drawing instructions: Each triangle of the regular polygon is called a segment.
The angles for the respective top corners of the pentagon, hexagon, heptagon, octagon and nonagon are 72, 60, 51, 45, and 40 degrees.
Although the corner positions can be marked with a dot only, the use of pushpins is recommended.
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. The rectangle hook tool placed against the centre pushpin and one of the corners, enables you to draw a radius.
Photo: A seven cornered polygon with pushpins at all corner positions. One side is connected, the next is to be draw with the rectangle hook tool placed against two pushpins. The pushpin indicating the centre is also present.
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.
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.
For a sophisticated spider web use different polygon tools. Create a few – slightly shifted – concentric polygons on the TactiPad and draw lines through the
There are different types of spur wheels. This shape represents the mechanical properties with which the force can be maximised. When you interlink two wheels of this type, their teeth always have a point of contact under an angle of 90 degrees when rotating. Although it looks like an arbitrary number of teeth can be placed in a circle, this is not the case.
The wheels in the set have 12 or 15 teeth respectively. The spaces between them – their negative counterparts – are placed on the inside of the round template, so that the drawing result will have its teeth on the outside. The body of the spur wheel has finger fitters in eight positions along the outside for easy lifting or extra grip. You find pushpin markers in the top surface of the body.
The spur wheel is a relative complex tool to use / shape to create. We recommend to use one to two push pins to fixate to tool on the TactiPad. Draw the inner contour of the spur wheel and you have created the first step into the mechanical domain or flower design.
Once you have interlinked two spur wheels, you will experience a complex issue: finding the perfect position for one tooth on the one and two teeth on the other wheel to “bite each other”. This gives you an impression of how delicate spur wheel systems are in mechanics.
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