# The Mathematics of Satellite Design - Origami

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Origami with squares

Solar panels are an important part of satellite design. There are design constraints on the distance a panel can be from the core of the satellite. In order to increase the area of the panels, satellites of the future may well deploy panels other than rectangular ones. This challenge looks at some of the alternatives and compares the gains to be made in terms of areas. This is for age range: 11 to 13.

Mathematical topics used in this challenge:

• Area of a square

Area of a trapezium

• Working out an nth term rule from a pattern

Origami - Solar panels with angles

This challenge looks at four designs for solar panels and considers the angles in those designs. A carefully structured framework is provided for students to guide them through the challenge. This is for the age range: 11 to 13

Mathematical topics used in this challenge:

• Interior and exterior angles in a polygon

• Angles on a straight line

• Angles in a triangle

Origami - Areas of solar panels

Increasing the surface area of solar panels gives the opportunity to feed more power to equipment inside of the satellite. This challenge looks at two potential designs for the panels: the first design is a pentagonal satellite; the second design is a hexagonal satellite. The designs are compared in terms of area. This is for age range: 14 to 16.

Mathematical topics used in this challenge:

• Trigonometry

• Area of a triangle

• Area of compound shapes

Origami - Comparing areas of solar panels

In this challenge, the areas of complex origami solar panels are calculated. In order to make the calculations, students must also work out some angles using both trigonometry and angles in a regular polygon.

This is for age range: 14 to 16

Mathematical topics used in this challenge:

• Trigonometry

• Area of a triangle

• Area of a square

• Area of a compound shape

• Percentage increase

• Interior and exterior angles of a regular polygon

Origami - Fitting a triangular satellite in a square launcher

Whilst traditionally satellites have had either square or rectangular cross-sections, having different designs for solar panels opens up the possibility of different designs for the craft themselves. This challenge looks at maximising the size of a satellite with a triangular cross-section that is to be launched using a square launcher. This for age range: 14 to 16.

Mathematical topics used in this challenge:

• Pythagoras’ theorem

• Solving equations

• Surds

• Substitution

• Origami using folding

Origami - Fitting a hexagonal satellite in a square launcher

The idea of having satellites with different cross-sections is explored further in this challenge. This challenge looks at maximising the size of a satellite with a hexagonal cross-section that is to be launched using a square launcher. This is for age range: 14 to 16.

Mathematical topics used in this challenge:

• Pythagoras’ theorem

• Solving equations

• Rationalising the denominator of a surd

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