The document discusses communication in social insects like bees and ants. It describes how bees use a waggle dance to communicate distance and direction of food sources to other bees. The dance includes a straight run indicating direction and speed indicating distance - faster dances mean closer food. Experiments with ants in mazes found they can adapt routes using pheromones when paths are blocked, zigzagging to find alternatives. Hexagonal structures in bee hives are also mathematically efficient for enclosing space with less material.

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COMMMUNICATION SKILLS
OF SOCIALS INSECTS
Mathematical modelling on social insects such as
honeybees,ants,etc. To know how they use local information to
generate complex and functional pattern of communication.

5. INTRODUCTION
 Many
insects
exhibit
"social"
behaviors
(e.g. feeding aggregations, parental care of the
young, and communal nest sites). In a broad
sense, any insect that interacts with another
member of its own species could be called a
social insect. But as a rule, entomologists do
not regard these behaviors as sufficient
justification for classifying a species as truly
social (i.e. eusocial). In order to qualify
as eusocial, a species must exhibit the
following characteristics:

6. TOWER OF HANOI
•The tower of Hanoi commonly also known as the "towers of
Hanoi", is a puzzle invented by E. Lucas in 1883
Disks are arranged from largest on the bottom to smallest on
top placed on a rod, together with two empty rods, the towers of
Hanoi puzzle asks for the minimum number of moves required
to move the stack from one rod to another, where moves are
allowed only if they place smaller disks on top of larger disks.
The puzzle with pegs and disks is sometimes known as Reve's
puzzle.

7. STEPS INVOLVED

8. Ants perform their task into a graph of possible
moves and convert that in turn into a maze of
hexagons. Having initially allowed a colony of ants
to explore the maze and lay down pheromones
(short-lived foraging pheromone and long-lasting
exploration pheromone), the team then placed
food at the end of the maze and filmed the ants as
they tried to identify the optimal route through the
maze to the food while the team blocked off
routes and opened up alternatives.

9. MAZE OF HEXAGON
The ants had little problem coping with change. Initially, the
insects found the shortest route, scurrying along the outer edge
of the maze to the food source. However, when the team blocked
this route and opened up another through the middle of the maze,
the ants changed course, zigzagging across the maze,
perpendicular to their original route until they found the
alternative.
The team suspects that both pheromones played critical roles,
with short-lived foraging pheromone allowing the ants to respond
quickly.
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10. Bees and math
Bees have not studied tessellations theory.
However, some of their behavior patterns can be
explained mathematically. One such phenomena
which mother nature instilled in the bee is the nature
to use the least expenditure of energy and materials.
The hexagon has the smallest perimeter for a given
area. So, when bees are constructing hexagonal
prism cells in the hive, they use less wax and do less
work to enclose the same space than if tessellating
space with prisms of square or triangular bases.

11. COMPARISON
Area and Perimeter
Formulas
A = s^2 P = 4 x s
A = 1/2as P = 3 x s
A = 1/2a(6s) = 1/2ap
P=6xs
.
Area
Area is constant and
should be around 36
The area of the three
Side = 6 Area = 6 x 6 Side = 9 Area = 1/2 x Side = 3.6 Area = 1/2 polygons should be
= 36
9 x 7.79 = 35.05
x 3.5 x 21.6 = 37
approximately similar. i.e,
around 36.
.
Perimeter
If the area is equal and we
compare the perimeter of the
Side = 6 Perimeter = Side = 9 Perimeter = Side = 3.5 Perimeter
square, triangle, and
4 x 6 = 24
3 x 9 = 27
= 6 x 3.6 = 21.6
hexagon, the hexagon has
the smallest perimeter.
Area
If the perimeter is equal and
Side = 4 Area = 1/2 x we compare the area of the
Side = 3 Area = 3 x 3 Side = 4 Area = 1/2 x
1√3 x 6 x 2 = 6√3 = square, triangle, and
=9
4 x 2√3 = 4√3 = 6.9
10.4
hexagon, the hexagon has
the largest area.
.
.
Perimeter
.
.
.
Tessellations
Perimeter is constant and Side = 3 Perimeter = Side = 4 Perimeter = Side = 2 Perimeter =
is equal to 12
3 x 4 = 12
4 x 3 = 12
2 x 6 = 12

12. VECTOR DANCE
 Honeybees have a unique
 When the distance of resource
communication style called dance
location is closer to the hive,forger
language. The dance communication
bees dance rapidly.the waggle
is revealed in detail since CARLVON
dance thus have two kind of
FRISCH‘S work and the dance of
information for food direction and
honeybees is a body language to
distance to the nectar resource.
communicating the resource direction
and distance.a forager be seeks
flower for her nectar and returns to
the hive.when she arouses the other
colleagues bees for the location of
flowers.she uses her waggle dance by
walking in a straight line and wagging
her abdomen from side to side.

13. More about bee
dance.... by dance
Bees communicate
language.
Bees use dance as a form
of communication for
distance and direction of
food sources or nest sites.
1- Round dance (running in
a circle, is performed for
close sites)

14. DISTANCE
When food is within 50–75 meters of the hive, the scouts dance
the "round dance
" on the surface of the comb (left).
But when the food is farther than 75 meters from th
e hive, the scouts dance the "waggle dance" (right). The waggle
dance has two components:
•a straight run — the direction of which conveys information about
the direction of the food
•the speed at which the dance is repeated which indicates how
far away the food is.

15. CREATION :
 SHAGUN UPPAL
 SUKRITI RAMPAL
BMOUNT ABU PUBLIC SCHOOL
SECTOR-5, ROHINI
NEW DELHI-85
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