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Resources tagged with Formulae similar to Archimedes Numerical Roots:

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Broad Topics > Algebra > Formulae

Triangles Within Pentagons

Stage: 4 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

On the Importance of Pedantry

Stage: 3, 4 and 5

A introduction to how patterns can be deceiving, and what is and is not a proof.

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Triangles Within Squares

Stage: 4 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

Ordered Sums

Stage: 4 Challenge Level:

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .

Sums of Squares

Stage: 5 Challenge Level:

Prove that 3 times the sum of 3 squares is the sum of 4 squares. Rather easier, can you prove that twice the sum of two squares always gives the sum of two squares?

For What?

Stage: 4 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Stage: 5 Challenge Level:

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

First Forward Into Logo 12: Puzzling Sums

Stage: 3, 4 and 5 Challenge Level:

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Double Time

Stage: 5 Challenge Level:

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Stage: 4 Challenge Level:

Explore the two quadratic functions and find out how their graphs are related.

In Particular

Stage: 4 Challenge Level:

Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11. Then find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers.

Screen Shot

Stage: 4 Challenge Level:

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

Stage: 5 Challenge Level:

Find a quadratic formula which generalises Pick's Theorem.

What's That Graph?

Stage: 4 Challenge Level:

Can you work out which processes are represented by the graphs?

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?