Search results for "GEOMETRIA"

Introducing Golden Section in the Mathematics Class to Develop Critical Thinking from the STEAM Perspective

2021

The Golden Section is a mathematical concept that is one of the most famous examples of connections between mathematics and the arts. Despite its widespread references in various areas of nature, art, architecture, literature, music, or aesthetics, discussions of the golden ratio often turn out to be false or misleading. Most of the incorrect statements are based on approximations or stem from the lack of checking the facts, making scientific mistakes in verifying the original scientific, historical, cultural context, or performing arbitrary operations in the measurements. This article offers geometric data and measurements, which allow the students to explore the golden ratio in various co…

Autonomous hyperspectral UAS photogrammetry for environmental monitoring applications

2014

Abstract. The unmanned airborne system (UAS) remote sensing using lightweight multi- and hyperspectral imaging sensors offer new possibilities for the environmental monitoring applications. Based on the accurate measurements of the way in which the object reflect and emit energy, wide range of affecting variables can be monitored. Condition for reliable applications is reliable and accurate input data. In many applications, installation of geometric and radiometric reference targets in the object area is challenging, for instance, in forest or water areas. On the other hand, UASs are often operated in very poor conditions, under clouds or under variable cloud cover. Our objective is to deve…

Spectral imaging from UAVs under varying illumination conditions

2013

Abstract. Rapidly developing unmanned aerial vehicles (UAV) have provided the remote sensing community with a new rapidly deployable tool for small area monitoring. The progress of small payload UAVs has introduced greater demand for light weight aerial payloads. For applications requiring aerial images, a simple consumer camera provides acceptable data. For applications requiring more detailed spectral information about the surface, a new Fabry-Perot interferometer based spectral imaging technology has been developed. This new technology produces tens of successive images of the scene at different wavelength bands in very short time. These images can be assembled in spectral data cubes wit…

Maths in Motion : Exploring Rotational Symmetries and Triangles through Dance and Body Movement

2019

In this workshop, we share the main results of the “Maths in Motion” (MiM) Erasmus+ educational project (2017-2019), concerning how dance and body movement can be used as tools to teach mathematics. The MiM-approach is based on embodied cognition and opens up new horizons for students, teachers, and even parents by offering simultaneous experiences with the structural, spatial, rhythmic and symbolic dimensions of mathematics through body movement. We will introduce two teaching modules developed during the project. These modules follow in the footsteps of the writing, workshops, and performances of Schaffer and Stern in the field of mathematics and dance over the past few decades. The modul…

A remark on two notions of flatness for sets in the Euclidean space

2021

In this note we compare two ways of measuring the $n$-dimensional "flatness" of a set $S\subset \mathbb{R}^d$, where $n\in \mathbb{N}$ and $d>n$. The first one is to consider the classical Reifenberg-flat numbers $\alpha(x,r)$ ($x \in S$, $r>0$), which measure the minimal scaling-invariant Hausdorff distances in $B_r(x)$ between $S$ and $n$-dimensional affine subspaces of $\mathbb{R}^d$. The second is an `intrinsic' approach in which we view the same set $S$ as a metric space (endowed with the induced Euclidean distance). Then we consider numbers ${\sf a}(x,r)$'s, that are the scaling-invariant Gromov-Hausdorff distances between balls centered at $x$ of radius $r$ in $S$ and the $n$-dimensi…

Aritmeettis-geometris-harmoninen keskiarvoepäyhtälö

2008

Universalist and Particularist Discourses on the Intersection of Reality, Truth and Beauty

2016

The history of the Western civilisation can be seen as a continuum of epistemological battles and alliances between two modes of grasping and describing the world. According to these conflicting views, the world has been grasped either through particular or universal explanations. These two views have formed a dualistic scholarly context which has directed philosophers, artists, and scientists to discuss whether the world and its diverse phenomena can be perceived and explained through the universal laws of mathematics and science or rather as culture-bound narrations and symbols; whether the world is best represented using the language of mathematical formulas and equations or that of the …

Toiminnallista geometriaa : opetuskokeilu 6-luokkalaisille

2010

Tämän tutkimuksen tarkoituksena oli selvittää toiminnallisuuden merkitystä matematiikan oppimisessa. Tutkimuksessa haluttiin selvittää onko toiminnallisuudella niin suuri merkitys matematiikan oppimisessa kuin usein alaan liittyvässä tutkimuskirjallisuudessa esitetään. Tutkimus on toimintatutkimus. Toiminnallisuuden tutkimiseksi toteutettiin geometrian opetuspaketti, jonka vaikutuksia selvitettiin oppilaille tehdyillä testeillä ja kysymyksillä. Työ on laadullinen tutkimus. Tutkimustuloksista voidaan päätellä, että oppilaat pitävät toiminnallisuutta tärkeänä osana matematiikan oppimista. Oppilaan innostus kasvaa, kun hän pääsee itse erilaisia toimintavälineitä käyttäen tutustumaan matematiik…

Visuaalinen tangentti lukion pitkässä matematiikassa

2017

Opinnäytetyössä selvitellään lukion pitkän matematiikan opiskelijoiden käsityksiä visuaalisesta tangenttisuorasta (lyh. tangentista). Työ sisältää tietokoosteen tutkielman aihepiirin visuaalisesta tangentista. Lukio-opiskelijoiden käsityksiä tangentista esitellään Tallin 1980-luvun tietokoneavusteisesta opetuskokeilusta ja Bizan 2000-luvun tutkimuksesta. Empiirisessä tutkimuksessa tutkittiin lukion pitkän matematiikan oppikirjasarjan visuaalista tangenttia. Ihmiset ymmärtävät aistein havainnoitavat kohteet pääosin intuition avulla, kun taasen matemaattiset käsitteet voidaan ymmärtää aksioomien, määritelmien ja lauseiden pohjalta. Kuitenkin Bizan laaja tutkimus osoittaa, että lukio-opiskelij…

"Mirrors"

2021

[no abstract]