Izvleček
Pascalov aritmetični trikotnik in Leibnizev harmonični trikotnik sta trikotni shemi števil, ki imata neskončno
mnogo vrstic. Oba trikotnika sta simetrična glede na navpično simetralo. Števila, ki nastopajo v obeh trikotnikih, so med seboj povezana na zanimiv način.
Pascalov aritmetični trikotnik je v našem šolskem prostoru precej znan in se z njim pogosto srečajo že osnovnošolci, ko preiskujejo zanimive lastnosti števil v njem, srednješolci pa ga uporabljajo predvsem kot pomoč pri računanju binomskih koeficientov.
Leibnizev harmonični trikotnik je morda še marsikje prezrt, čeprav se tudi v njem skrivajo mnoge zanimivosti. V prispevku bomo nakazali možnosti za preiskovalne aktivnosti v Leibnizevem harmoničnem trikotniku za učence v 3. VIO osnovne šole in v srednji šoli.
Abstract
Leibniz Harmonic Triangle
Pascal’s arithmetic triangle and the Leibniz harmonic triangle are triangular arrays of numbers with an infinite number of rows. Both triangles are symmetrical on either side of the perpendicular bisector. The numbers appearing in both triangles are linked to one another in an interesting way.
Pascal’s arithmetic triangle is rather well known in Slovenian schools and is often encountered by primary
school pupils when inquiring about the interesting properties of the numbers in it, whereas secondary school students mostly use it as an aid in calculating binomial coefficients.
The Leibniz harmonic triangle is perhaps still overlooked in many schools despite the many interesting features it contains. This paper will indicate the possibilities for carrying out inquiry activities in a Leibniz harmonic triangle for pupils in the 3rd educational triad of primary school.