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Tools
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Measure distance
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To measure the distance between two points, select Distance
from the Measure menu, fill in the labels of the points and press
the Measure button. The numerical value of the distance will be
displayed against the Result label.
To copy the result to the Notepad,
type in a name for a new variable and press the Write Down button.
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Alternatively, select either the two points or the line that joins them,
if any, click right and select Measure Distance from the popup menu.
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Draw line
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To join two points with a line, select Line from the Draw
menu and fill in the labels of the points.
Alternatively, select the two points, click right and select
Draw Line from the popup menu.
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Join solids
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The feature is available in Geometria Composer alone.
To join two solids facet-to-facet, select
Join from the Combine menu, then select the solids and
facets to join. A solid may join to itself, wherein it is thought there
be a copy of it. To have the right facets automatically highlighted,
you must have them selected in the solids' windows before addressing
the menu.
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The joining is possible whenever the two facets are congruent or just
similar and have matching orientations such as to make the operation
physically imaginable. For example, two squares
or other same dimension regular polygons,
as well as two similar isosceles triangles
will always do. If needed, one of the solids will be re-sized to make the
facets match entirely. However, the resulting solid has to be convex.
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Revolve solid
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Use Ctrl + arrow keys to turn a solid left or right or bend
it back or forth. As you revolve the solid, it may turn so that its image
grows larger than its window.
At any time, you can make the solid fit into its window
or return to its initial attitude. See the View menu for
the corresponding commands.
You do not need to hold down the Ctrl key if the solid's window is
highlighted.
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Measure angle
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To measure an angle, select Angle from the Measure menu,
fill in the labels of the angle's vertex and sides and press the
Measure button. The numerical value of the angle (in degrees) will be displayed
against the Result label.
To copy the result to the Notepad,
type in a name for a new variable and press the Write Down button.
Alternatively, select the sides of the angle, click right
then select Measure Angle as it shows up in the popup menu.
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Draw perpendicular
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To draw the perpendicular to a line through a point, select
Perpendicular from the Draw menu and fill in the labels as
prompted. The point may or may not belong to the line.
If the line
and the point belong to an edge you will be prompted
to choose between two facets in which to draw. Thus, in the attached view,
two perpendiculars can be drawn to AC through F.
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Alternatively, select the point, the line and, as the case may be,
the facet, click right and select Draw Perpendicular from the
popup menu.
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Add vertex to solid
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This feature is available in Geometria Composer alone.
To add a new vertex to an existing solid or just from scratch, select
Add Vertex from the Combine menu, then fill in the
the vertex's coordinates referenced by either
variables or numerical values, and provide a label for the new vertex.
The Get One button will do the latter job for you.
Upon the new vertex's addition, the solid is rounded up to a
convex one.
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Alternatively, get the XY grid displayed, select a base XY-point
in it, click right, select Add Vertex from the popup menu,
and select a point on the Z-line displayed. You may then adjust the
coordinates of the vertex to be added.
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View modes
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You may switch between three view modes in the View menu.
Default is the the Transparent mode. Vertices and drawn points
are highlighted while edges and drawn lines are all outlined, whether they
are visible or not. This provide a comfortable interface for selecting
points and lines.
In Monochrome mode, facets are painted in same color, its hue
varying according to the view angle so creating a realistic 3d image.
In Geometria Composer, you may choose between several
basic colors for your solid.
In Polychrome mode, facets are painted in different colors and
there is no 3d effect. The Geometria Composer
allows you to select each facet's color individually.
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Measure area, volume
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These features are available in Geometria Composer alone.
To measure the area of a facet, select Facet Area
from the Measure menu, then select an item from the list and press
the Measure button. The numerical of the area will be displayed
against the Result label.
The volume of a solid is measured in a similar way.
To copy the result to the
Notepad, type in a name for a new
variable and press the Write Down button.
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Draw midpoint
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To draw the midpoint of a previously drawn line, select Midpoint
from the Draw menu, fill in the labels of the end points and provide a
label for the midpoint. The Get One button will do the latter
job for you.
Alternatively, select the line, click right and select
Draw Midpoint from the popup menu.
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Draw bisector
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To draw the bisector of a previously drawn angle, select Bisector
from the Draw menu and fill in the labels of the angle's vertex and
sides.
Alternatively, select the sides of
the angle, click right and select Draw Bisector as it shows up
in the popup menu.
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Draw intersection
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To intersect two previously drawn lines, select Intersect from the
Draw menu and fill in the labels of the end points.
Alternatively, select the lines, click right and select
Draw Intersection from the popup menu.
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Lay distance
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To lay a distance off a point to a previously drawn line,
select Lay Distance from the Draw menu, fill in the
variable or numerical value of the distance to be laid and refer the
point and the line. The point may or may not belong to the line. You will
be prompted if the distance is too short to reach the line or, on the
contrary, too long.
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Lay angle
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To lay an angle off a previously drawn line,
select Lay Angle from the Draw menu, fill in the
variable or numerical value (in degrees) of the angle and the labels of
the line's end points.
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If the line is part of an edge
you will be prompted to choose between two facets in which to
draw. Otherwise, there still may exist two different angles
laid off the same line. Geometria will draw them both. You will
be prompted if the angle is too large to fit into the facet.
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Cut solid
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To cut a solid through three points, select Cut
from the Draw menu and fill in the labels of the points. If checked,
the Preserve drawings option will keep on the traces of all
'maternal' drawings on the 'child' facets.
The cut results will be displayed in new windows and given relevant
names. For example, Solid 2 may yield into
Solid 2:1 and Solid 2:2. This allows an easy tracking of
results for multiple cuttings.
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Notepad
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A Notepad record originates in either a
calculation or a measure operation.
A new record begins with the name of a
variable followed by the variable's definition. Examples:
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- Angle AFC has been measured and variable
q assigned to it
- Distance GH has been measured and denoted by variable
side.
- Area of facet EFBA has been measured and denoted by variable
a1
- Volume of solid ABCDEFGH has been measured and denoted
by variable vol.
- The last record in the attached view may have appeared as result
of a calculation.
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Calculator
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To compute an expression, type it in against the Calculator
label and press the Write Down button. You will be prompted to
assign a variable to the result thereafter a new
notepad record
will appear. You may refer to the new variable in your further calculations
and also in operations like Lay angle,
Lay distance,
Answer problem, and others.
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The expression must have a valid algebraic form. It may include:
- Previously defined variables and the constant pi;
- Round brackets, wherever necessary;
- The signs of common operations +, -, *, /, and
the 'power' operation ^. For example,
a^(1/3) means 'a at power 1/3'.
- Function names: sin, cos, tan, asin,
acos, atan, sqrt (square root). Brackets around function
arguments are mandatory. All trigonometric and reverse trigonometric
functions operate in degrees.
If you want just to find the numerical value of an expression, type it in
and press the Get Value button.
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