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.
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: Spur wheel with 12 teeth (prototype 3D-print)
Detailed description of the spur wheel template
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.
Utilising the spur wheel template
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.
Detailed description of the regular polygon template
The set contains templates for regular polygons with five, six, seven, eight and nine corners referred to as pentagon, hexagon, heptagon, octagon and nonagon respectively. The radius of the polygons ranges from two to eight centimetres.
In a regular polygon all corners have the same angle. The corners are interconnected with lines that have all the same length. Another way to describe a polygon: A polygon consists of a number of equal leg triangles where the top corners of all equal legged triangles are at the same position. So they are arranged in a circle like slices of a pie. The distance from all corners to the centre point is the same.
The body of the tool is two centimetres wide. It is shaped as a triangle where one side is not present. It could be described as a jaw hook. The angle between the two sides is less than 90 degrees. Near to the rounded outside corner and near to the tips you find pushpin markers. One side of the polygon tool contains a number of wholes, indicating the number of corners of the particular polygon.
The side with the wholes is referred to as ‘radius side’. This radius side has a centimetre indication in the top surface and indents every half centimetre. The inner side of the side with the finger fitter to the far right is referred to as ‘drawing side’. The drawing side has the same number of indents as found on the radius side.
To construct the polygon, the pen position in the radius side has to correspond with the one in the drawing side, measured starting at the inner corner. As an example, a groove as a visual tactile clue ending at the four centimetre radius indication shows the direction to look for the corresponding indent in the drawing side and/or the respective bisectrix position. The value for the radius is measured starting at the inner sharp corner and increases towards the tip. The once selected position at the radius side is going to be the centre of the polygon.
At the outer side of the drawing side you find indents as well. They indicate the position for the bisectrix of the equal leg triangle. The outside corner in between the radius side and the drawing side is rounded to allow for alignment with the ruler; the distance from the sharp hook to the ruler remains the same when you move/rotate the polygon tool.
Utilising the regular polygon template
The regular polygon tools are mainly used to create these shapes. You can also create mandalas. You have to use at least one pushpin to mark the centre of the polygon. A second pushpin is handy to mark the position to draw to along the drawing side.
Detailed description of the rectangular hook template
The two sides of the rectangular hook are under an angle of 90 degrees and are 10 centimetres long. The body of the tool is two centimetres wide. The corner between the sides is rounded at the outer side. The sides are ending with a 90 degree hook. Near the rounded corner and near to the tips, you find push pin markers.
You find indents for 30, 45 and 90 degrees at the rounded corner for alignment with the ruler. There are centimetre indicators along the inner side on the top surface. The inner sides have indents every half centimetre. At the outer side you find indents to perform a 30 or 45 degree rotation in reference to the inside angle. On the outer sides, near to the tips you find a finger fitter for easy lifting or extra grip.
Utilising the rectangular hook template
When you drawing along the two sides towards the inner corner you create two lines with a 90 degree angle. When you connect the two endings of the previously created lines you will get an irregular triangle on the TactiPad. By rotating and/or mirroring a triangle, you can create shapes such as diamond or kite.
Photo: The six centimetre equal sided triangle of the set (prototype 3D-print)
Detailed description of the triangle template
The templates for the triangles are of the type equal sided triangle. The length of the sides ranges from three to eight centimetres respectively. One outer corner is rounded, the other two are sharp. Along the outside you find indents at every centimetre. They correspond with the corners at the beginning/ending of the inner sides. The body of the triangle is about 12 millimetres wide. On the top surface, you find pushpin markers.
The inner sides have an indent at their halfway position.
On one of the outer sides you find a finger fitter for easy lifting or extra grip.
Utilising the triangle template
When you place the triangle template somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first triangle.
With the equal sided triangle you can create other shapes: a rectangular triangle of 30, 60 or 90 degrees, a diamond and star.
Photo: The four centimetre square of the set (prototype 3D-print)
Detailed description of the square template
The sizes of the squares ranges from two to ten centimetres. The frame that forms the square is one centimetre wide. So a four centimetre squared template has the inner dimension of four centimetres. The outside is six centimetres in square.
Two diagonal opposite outside corners are sharp, there you can find the pushpin. The other two corners are rounded. Along the outside a small indent is provided at every centimetre. The inner side has an indent at the halfway position of each of the four sides. In two of the opposing outer sides you find finger fitters for easy lifting or extra grip.
Utilising the square template
When you position the square somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first square. With the square template you can create many more shapes such as diamond, parallelogram, trapezium, and also 3D shapes such as pyramid or cube.
Photo: GraphGrid frame with rubber bands per two centimetres and two crossing axes placed on the TactiPad.
The easiest way to draw a graph is to draw the x- and y-axis first using the ruler and measurement indications on the TactiPad and then place the GraphGrid on the drawing board. The axes, the higher rubber bands, can now coincide with the axes drawn on the paper. You can then easily count and draw the x and y values of the graph along the flexible grid lines.
Because the grid lines are flexible, the graph values can be drawn exactly at the intersections by pulling the bands aside with the pen. Once you have marked all the coordinates of the graph, you can remove the frame and create the graph by connecting the points. If you want to create multiple graphs in the same coordinate system, it is recommended to finish one graph before starting with the next to avoid confusion between the two sets of coordinates.
Photo: two hands on the TactiPad, one referring to the coordinates, the other drawing the graph
The columns of the GraphGrid frame can be considered as bars of a bar chart. The value in each bar is indicated by the number of marked cells, starting from the lower edge of the frame or from an additional rubber band. The lower edge or the rubber band is the X axis. A cell can stand for one or multiple units or for a percentage.
Photo: GraphGrid on TactiPad with two hands drawing crosses and circle in a tic-tac-toe field in the coordinate system.
Bar chart for birthday data
This bar chart example presents an overview of when people in a group have their birthday spread over the year. Setup: Each column stands for a month. Each cell stands for one person.
Procedure: Ask who has his/her birthday in January and mark the number of cells accordingly. Do the same for all respective months. Take the GraphGrid away. You can now interpret the data by counting the number of markings in the column.
More complex data
One bar can present multiple data by applying different tactile markings in the same cell. For a male count you can apply a line in the cell from lower left to upper right and for female a line from upper left to lower right. Data that are presented with two colours could follow the same routine. Additional graphical markings can present even more complex data types.
Providing maximum value/top of the bar
To present numeric values you can find the position in the column/bar by counting upwards from the X axis. Assume the maximum value can go as high as 1000, than you might take five cells as the longest bar. A value of 700 can be indicated as a straight line horizontally in the middle of the forth cell up. Only the top of the bar needs to be indicated in order to interprete the data.
A crossing of two rubber bands can be considered as a coordinate in a grid system. Starting in the upper left corner of the GraphGrid to the right we call the X direction. Going down is the Y direction. Each crossing is identified by two numbers. With this method, the coordinate 1,1 is the lower right hand corner of the top left cell. The GraphGrid frame does not need axes. The cell size is two centimetres.
Steps
Place the frame on the drawing board.
Mark the coordinates as given in the below examples.
Take the frame away and connect the dots with straight lines as instructed with the word ‘to’.
Front face of a traditional house A2,8 to B6,8 to C6,2 to D4,1 to E2,2 to 2,8 (which is A again).
You can add a door or windows by free hand drawing separately or place the GraphGrid once again and mark the respective coordinates.
Photo: Tactile marks have been placed on the drawing board at gridbox crossing made up by the rubber bands. After connecting them a traditional house shows itself.
A cube
The eight corners of a cube are named A To H. The 12 ribs complete the cube. Some of them are marked as ‘dashed’ because they are invisible lines. In coordinates and lines they can be listed as follows:
Bottom face A2,8 to B6,8 to C10,7 dashed to D4,7 and dashed to A.
Top face E2,4 to F6,4 to G10,3 to H4,3 to E.
A to E , B to F, C to G, D dashed H.
Pyramid
Place the GraphGrid on the drawing board.
The floor of a pyramid is similar as of a cube. From the four corners sides go up to the top ‘T”.
The top can be right above the centre of the floor or somewhere else. Create the coordinates and lines A to B to C dashed to D dashed to A.
The top T has coordinate 5,3.
Draw the lines A to T , B to T , C to T, D dashed to T.
Share and surprise; connect the dots
You can create a list of coordinates for someone else or you might receive a list of coordinates from someone else. Provide instructions to mark the coordinates and how they should be connected. In the list is an ‘hidden’ image that will appear only when you follow the instructions carefully.
More details
For more detail in the image you can work with halves like 3.5, 6 etc. The level of detail of the image can be increased by working not only with straight lines. Curved lines could be indicated as ‘cu’’ or ‘cl’. The ‘u’ refers to upper half of a circle. The ‘l’ to the lower half of the circle.
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