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#### Resources tagged with Investigations similar to Scale Invariance:

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### Scale Invariance

##### Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

### Bessel's Equation

##### Stage: 5 Challenge Level:

Get further into power series using the fascinating Bessel's equation.

### Making More Tracks

##### Stage: 5 Challenge Level:

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

### Building Approximations for Sin(x)

##### Stage: 5 Challenge Level:

Build up the concept of the Taylor series

### A Different Differential Equation

##### Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

### Stirling Work

##### Stage: 5 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Big and Small Numbers in the Physical World

##### Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

### Big and Small Numbers in the Living World

##### Stage: 3 and 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### 9 Hole Light Golf

##### Stage: 1, 2, 3, 4 and 5 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

### More Bridge Building

##### Stage: 5 Challenge Level:

Which parts of these framework bridges are in tension and which parts are in compression?

### Trig-trig

##### Stage: 4 and 5 Challenge Level:

Explore the properties of combinations of trig functions in this open investigation.

### Genetic Intrigue

##### Stage: 5

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

### Diamonds Aren't Forever

##### Stage: 5 Challenge Level:

Ever wondered what it would be like to vaporise a diamond? Find out inside...

### Powerfully Fast

##### Stage: 5 Challenge Level:

Explore the power of aeroplanes, spaceships and horses.

### Escape from Planet Earth

##### Stage: 5 Challenge Level:

How fast would you have to throw a ball upwards so that it would never land?

### Peeling the Apple or the Cone That Lost Its Head

##### Stage: 4 Challenge Level:

How much peel does an apple have?

##### Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

### The Invertible Trefoil

##### Stage: 4 Challenge Level:

When is a knot invertible ?

### Problem Solving: Opening up Problems

##### Stage: 1, 2, 3 and 4

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

### Chance of That

##### Stage: 4 and 5 Challenge Level:

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

### Two Regular Polygons

##### Stage: 4 Challenge Level:

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

### Eight Ratios

##### Stage: 4 Challenge Level:

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

### Smoke and Daggers

##### Stage: 5 Challenge Level:

We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

### Mach Attack

##### Stage: 5 Challenge Level:

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

### What Salt?

##### Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

### The Power of Dimensional Analysis

##### Stage: 4 and 5

An introduction to a useful tool to check the validity of an equation.

### Clear as Crystal

##### Stage: 5 Challenge Level:

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### Reaction Rates!

##### Stage: 5

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

##### Stage: 5

Read about the mathematics behind the measuring devices used in quantitative chemistry

### Modelling Assumptions in Mechanics

##### Stage: 5

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

### Sextet

##### Stage: 5 Challenge Level:

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

### What Do Functions Do for Tiny X?

##### Stage: 5 Challenge Level:

Looking at small values of functions. Motivating the existence of the Taylor expansion.

### Which Twin Is Older?

##### Stage: 5

A simplified account of special relativity and the twins paradox.

### Geometry and Gravity 1

##### Stage: 3, 4 and 5

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

### Few and Far Between?

##### Stage: 4 and 5 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

### CSI: Chemical Scene Investigation

##### Stage: 5 Challenge Level:

There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...

### Take Ten Sticks

##### Stage: 3 and 4 Challenge Level:

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

### Robot Camera

##### Stage: 4 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

### Perfect Eclipse

##### Stage: 4 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

### Very Old Man

##### Stage: 5 Challenge Level:

Is the age of this very old man statistically believable?

### Odd Stones

##### Stage: 4 Challenge Level:

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

### Spokes

##### Stage: 5 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.