The document summarizes the origins of geometry in ancient Egypt. Rope stretchers called harpenodapta would stretch ropes in triangular patterns to measure and mark farmers' fields after annual flooding from the Nile River. This was necessary because the floodwaters would wash away the boundaries each year. The triangular rope patterns were one of the earliest forms of geometry. The word "geometry" comes from the Greek words "geo," meaning earth, and "metron," meaning measurement, referring to measuring the land.

1. How Geometry Got Its Name
A story by Maria Montessori

3. Geometry
This story begins in a time of very, very long ago in the
land of Egypt (help the children to locate Egypt on the
globe.) This land was – even is today – a vast dry sandy
desert. The only place where life was possible was by
the banks of a very great river. Without this river, it
would have been impossible to live in Egypt. The river
was so important for the people who lived there that
they simply called it “The River” (Can you hear the
capital letters?).
The waters of the Nile River - this is its name – run from
south to north. The river has its source in some
mountains quite far away. Every year, at springtime, it
rains and rains in these far away mountains. All the
water from the rains cannot be absorbed by the land and
much of it flows into the river, which rises high within its
banks. By the time the waters reach Egypt, the river
overflows its banks and floods nearby fields.

4. Geometry
You might think that these floods were a disaster for the
Egyptians. No! This flooding was a real blessing for the
people in Egypt in those times of long ago. When the
river water came over the blanks, it carried debris and
mud brought along from those far away mountains. The
waters spread the rich black mud, this humus, over the
lands it flooded. This was a natural way to fertilize the
farmlands. The mud from the River Nile made the land
very fertile. This is why the river was called “The Gift of
Egypt.”
But the flooding caused some problems as well. Every
year the boundary lines that separated one farmer’s
fields from his neighbor’s fields were washed away. When
the water withdrew and it was time to cultivate the
land, the farmers argued about which land was whose.
So every year a certain group of people had to solve this
problem all over again. These people were called the
“harpenodapta.” It is a Greek word and it means “the
rope-stretchers.” This is what they did: they stretched
ropes according to a pattern. The ropes they used were

5. Geometry
knotted at regular intervals, just like this rope (showing
the rope with the knots). The harpenodapta had slaves
help them stretch the rope out in a triangular shape.
Who will be the slaves? We need three slaves to stretch
out our rope. (Have three children make a triangle with
the rope; hold a the larger knots. The triangle is placed
on the floor and held in position by the weights). Look at
what you have made with the strings! Yes, it is a right-
handed scalene triangle. Now the ancient Egyptians did
now know, or did not seem to know that the shape they
made was a right-angled scalene triangle. Maybe it had a
different name in their language.
However, the harpenodapta could make a rectangle by
reversing the original triangular shape after the vertices
of the triangle were marked on the land. To be a rope
stretcher in Egypt was a very honourable profession. This
is how geometry was begun: by measuring the earth.
Indeed geometry means in Greek: geo=earth and
metron=measurement. Well, geometry can be said to
have its beginnings with this experience of measuring
the land after the yearly flooding of the Nile River.
Geometry grew from the discoveries the people made
while working. Whatever a problem arose, they had to
find a practical solution. So whenever people needed
things, for example how to build housed and temples,
the palaces of their kings and pyramids, I am sure they
used the same critical thinking. You and I know that
there is more to geometry than a right-angled scalene
triangle (pointing to the rope triangle). But this is
another story for another day.

6. Geometry
Rope stretching was a very important profession in those
days and these people were held in high regard.
Measuring the earth thus started with the rope
stretchers.
The Greek word for measuring earth is Geometry. Today
we are going to try to measure earth like the Egyptians
used to do.
9

7. Geometry
The story brought into practice.
The story can be brought into practice in 3 different ways:
1. Doing research by asking questions
Possibilities are:
• Can you think of a way how the Egyptians can use a
rope like this to measure the land with 4 people?
• Do you have an idea what the red knots would be
meant for? Can you find a solution for this?
• What shape did you make?
• Are you able to make another shape?
2. A general lesson
We need 4 children and 4 pawns. The children are
holding the rope on the spot of the marked knots. In for
example a rope of 12 meters, after every meter there is
a knot, but knot 1, 4, 9 and 12 are marked by another
colour or size. It can be a tied rope but it is better to
use an untied rope. Three children form a triangle first
(rectangle, not equilateral triangle). Child 1 holds the
beginning, child 2 holds knot 4, child 3 holds know 9 and
child 4 holds knot 12. After knot 12 a piece of rope is
left which should be connected to knot 1. After this the
knots 1, 4 and 9 will be marked by pawns. Then child 4
takes the rope at the point of knot 12 and mirrors the
entire shape by walking to the opposite edge. If the rope
is tied, the child is supposed to let go the rope but the
pawn stays. If it is an untied, child 4 puts knot 12
exactly above knot 9 and connects the last part to knot
4. After this a pawn has to be placed on the right top
corner at knot 12. A perfect rectangle has been created,
marked with pawns or children. When you do this
exercise outside you could cover a larger surface.

8. Geometry
3. An activity
Material:
• A piece of rope (2 m or more)
• 13 beads
The pice of rope needs to be divided by knots or beads of 12
equal distances.
Possibility A
The piece of rope is divided by knots.
Possibilty B
The distances are being marked by beads:
• Start with a knot;
• Add a bead;
• Make an knot directly after the bead so that is stays
on its place;
• Choose a distance of 10 cm or more;
• Make another knot;
• Another bead;
• Another knot;
• And measure a similar distance again.

9. Geometry
4
1 12 9
4 12
1 12 9

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