## Spirograph Simulator

The equations underlying the popular spirograph toy can be relatively simply expressed in parametric form. Allow your students a hands-on parametric experience with this spirograph simulator. The accompanying blog post explains the derivation of the equations.

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## Related resources

Use this interactive spreadsheet to create beautiful spirograph patterns. Suitable for a trigonometry project - the students can create the spreadsheet themselves.

#### If Spirograph were 3D

Imagine a world where you could buy 3D spirograph toys. What patterns could you make? Allow your students to explore the possibilities using this Autograph Activity. The accompanying blog post explains the mathematics behind it.

By owenelton

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#### Fermi's Study in Spirograph

The Vela pulsar outlines a fascinating pattern in this movie showing 51 months of position and exposure data from Fermi's Large Area Telescope (LAT). The pattern reflects numerous motions of the spacecraft, including its orbit around Earth, the precession of its orbital plane,
the manner in which the LAT nods north and south on alternate orbits, and more. The movie renders Vela's position in a fisheye perspective, where the middle of the pattern corresponds to the central and most sensitive portion of the LAT's field of view. The edge of the pattern
is 90 degrees away from the center and well beyond what scientists regard as the effective limit of the LAT's vision. Better knowledge of how the LAT's sensitivity changes across its field of view helps Fermi scientists better understand both the instrument and the data it
returns.
Credit: NASA/DOE/Fermi LAT Collaboration

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#### NASA | Fermi Traces a Celestial Spirograph

NASA's Fermi Gamma-ray Space Telescope orbits our planet every 95 minutes, building up increasingly deeper views of the universe with every circuit. Its wide-eyed Large Area Telescope (LAT) sweeps across the entire sky every three hours, capturing the highest-energy form of light -- gamma rays -- from sources across the universe. These range from supermassive black holes billions of light-years away to intriguing objects in our own galaxy, such as X-ray binaries, supernova remnants and pulsars.
Now a Fermi scientist has transformed LAT data of a famous pulsar into a mesmerizing movie that visually encapsulates the spacecraft's complex motion.
Pulsars are neutron stars, the crushed cores of massive suns that destroyed themselves when they ran out of fuel, collapsed and exploded. The blast simultaneously shattered the star and compressed its core into a body as small as a city yet more massive than the sun. One pulsar, called Vela, shines especially bright for Fermi. It spins 11 times a second and is the brightest persistent source of gamma rays the LAT sees.
The movie renders Vela's position in a fisheye perspective, where the middle of the pattern corresponds to the central and most sensitive portion of the LAT's field of view. The edge of the pattern is 90 degrees away from the center and well beyond what scientists regard as the effective limit of the LAT's vision. The movie tracks both Vela's position relative to the center of the LAT's field of view and the instrument's exposure of the pulsar during the first 51 months of Fermi's mission, from Aug. 4, 2008, to Nov. 15, 2012.
The pattern Vela traces reflects numerous motions of the spacecraft. The first is Fermi's 95-minute orbit around Earth, but there's another, subtler motion related to it. The orbit itself also rotates, a phenomenon called precession. Similar to the wobble of an unsteady top, Fermi's orbital plane makes a slow circuit around Earth every 54 days.
In order to capture the entire sky every two orbits, scientists deliberately nod the LAT in a repeating pattern from one orbit to the next. It first looks north on one orbit, south on the next, and then north again. Every few weeks, the LAT deviates from this pattern to concentrate on particularly interesting targets, such as eruptions on the sun, brief but brilliant gamma-ray bursts associated with the birth of stellar-mass black holes, and outbursts from supermassive black holes in distant galaxies.
The Vela movie captures one other Fermi motion. The spacecraft rolls to keep the sun from shining on and warming up the LAT's radiators, which regulate its temperature by bleeding excess heat into space.

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## Popular resources by this author

#### Diamond Jubilee Arithmetic Game

Mathematics game. Based on the popular '24 Game' this file contains a set of cards where, instead, a goal of 60 is set. Each card contains four single-digit numbers which must be used exactly once to reach the target.

By owenelton

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#### Balancing Equations

Here is a worksheet I produced when introducing the idea of equations to year 7 students. The balance method is key in convincing students to visualise an equation as it should be; a mathematical statement saying that the value of the thing on the left is the same as the value of the thing on the right.

By owenelton

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#### Mathematical Christmas Tree Decorations

Here are a couple of Christmas decorations to make. The snowflake is known as a Koch Snowflake (you might want to decide whether to mention that on a class-by-class basis). The file entitled dodeckthehalls contains an easy-to-make rhombic dodecahedron, each face associated with one of the twelve days of Christmas. It is a modified version of one of the projects on the magnificent website cutoutfoldup.com

By owenelton

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#### I Believe i Can Fly

How on earth can the imaginary realm of complex numbers tell us anything about the physical world? Well, here's just one application. The Autograph Activity will demonstrate to students how a complex transformation can turn a cylinder into an aeroplane wing; the consequences are discussed in the accompanying blog post.

By owenelton

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## Popular paid resources

#### Nth Roots of a Complex Number

Use de Moivre’s theorem to find nth roots of a complex number. Graph nth roots of a complex number on the Argand diagram. Generalize the position of the nth roots in the complex plane. Display the nth roots on your calculator.

By bgm2016

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#### Conjugate root theorem, sum and product of polynomial roots

Power Point presentation, 12 slides, demonstrating that for a given polynomial that has a complex zero z, then its conjugate z* is also a zero of the polynomial, based on IB Higher level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OldENnRERSZ29PYU0/view?usp=sharing

By oralhurt

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- $3.31

#### Solving system of equations

Power Point presentation, 10 slides, Explaining how to solve system of equations with two or three unknowns, using the methods of substitutions, elimination and the Gaussian elimination Method, based on IB Higher level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlcW9QalZzSm9JX2s/view?usp=sharing

By oralhurt

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- $3.31

#### Complex numbers - PowerPoint

Complex numbers - introduction, imaginary number i, addition, subtraction, multiplication and division of complex numbers.

By NewMathWorld

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- $2.00