ARIT

HM

OGO

NS

BENGT ÅHLANDER

ARITHM

OGONS

ARITHMOGONS

ARIT

HM

OGO

NS

A WAY TO VARIATE THE EDUCATION AND PERHAPS SHOW THE STUDENTS THE BENEFITS OF CAS

ARITHM

OGONS

ARITHMOGONS

Arithmogons addition

•4+8=?•8+3=?•3+4=?

3

8

4

12 11

7

Arithmogons addition

•8+10 =?•10+6 =?•6+8 =?

6

10

8

18 16

14

Arithmogons addition

• Try to find the numbers!• Is there a pattern?

10

4

7

11 14

17

?

?

Arithmogons addition

• Sum of the squares =

• • Sum of the circles =

11

9

2

11 20

13

44

22

Arithmogons addition

16

-2

11

9 14

27 24

-5

19

14 19

43

Arithmogons addition

• (a+b)+(b+c)+(a+c)=2*(a+b+c)

a c

b

a +b b + c

a + c

Arithmogons addition and algebra

6a a

3a

9a 4a

7a

?

?

2b + 2 b

b + 6

3b+8 2b+6

3b+2

?

?

?

Arithmogons addition and algebra

2b + 2 b

b + 6

3b+8 2b+6

3b+2

Arithmogons addition andpartial fractions

1

1x 1

2x

1

x

2𝑥+3¿¿

2𝑥+1¿¿¿¿

Arithmogons addition andpartial fractions

1

x

12𝑥+1

21−2𝑥

3𝑥+1¿¿

−1¿¿

¿¿

Arithmogons addition andpartial fractions

4 𝑥 ^ 2−𝑥−1¿¿ ¿¿

11𝑥−1¿¿

12𝑥−1

43𝑥+3

2𝑥𝑥−1

Arithmogons addition andpartial fractions

1𝑥

1𝑥+1

2𝑥−1

2𝑥2+𝑥+1¿¿2𝑥2−3 𝑥−1

¿¿

¿¿

Arithmogons addition fractions

TI Nspire CAS

• Make a straight line beetwen the dots and decide the equation of the lines.

• Chainrule at derivation of two factors

• Chainrule at derivation of two factors