Τρίτη 11 Οκτωβρίου 2011
Παρασκευή 23 Σεπτεμβρίου 2011
eTwinning Quality Label from Greek NSS
to Greek pupils and Greek School.... too.
"κάλλιο αργά παρά ποτέ..."
Κυριακή 18 Σεπτεμβρίου 2011
LABEL de qualité
La commission d’attribution du LABEL de QUALITE eTwinning national a le plaisir de vous informer que vous avez obtenu ce Label pour votre projet : Enseignement M@ths en utilisant ICT
Note : 38/50
Commentaire :
. Projet mathématique très novateur mené par 4 classes partenaires, en anglais, français et grec, visant à créer une forte motivation des élèves pour les Maths à partir de propositions de travail, élaborées par l'équipe enseignante, basées sur le lien entre les mathématiques et le réel. Les élèves des 4 pays, à partir de ces propositions communes, échangent entre eux (chat, blog, email, …) pour rechercher ensemble des solutions aux problèmes posés, réaliser et publier des documents. Le support principal de ce projet est un Blog d'une qualité remarquable.
Note : 38/50
Commentaire :
. Projet mathématique très novateur mené par 4 classes partenaires, en anglais, français et grec, visant à créer une forte motivation des élèves pour les Maths à partir de propositions de travail, élaborées par l'équipe enseignante, basées sur le lien entre les mathématiques et le réel. Les élèves des 4 pays, à partir de ces propositions communes, échangent entre eux (chat, blog, email, …) pour rechercher ensemble des solutions aux problèmes posés, réaliser et publier des documents. Le support principal de ce projet est un Blog d'une qualité remarquable.
Κυριακή 28 Αυγούστου 2011
Bonne rentrée scolaire with a kite
Il y a trop longtemps que les enfants regardaient ainsi l’arrivée à l’école...
Pour ma part, je vous souhaite à tous, collègues et élèves une bonne rentrée scolaire et surtout, une année très fructueuse!
Πέμπτη 16 Ιουνίου 2011
It's summer time! This is a short break...
Dear students, Dear colleagues,
Can you believe the end of the year is already here?
Everything has gone by so quickly...
Your hard work has paid off.
The children will graduate on to the next grade! The teachers will plan the next successful courses.
The end of the school year is an exciting time for all: We turn the page which we will start again next September (?) with improvements and fresh ideas and now we are planning and dreaming their beautiful summer vacations.
But there is no time for words!
Enjoy your moments in Greece, Romania and France as well.
Can you believe the end of the year is already here?
Everything has gone by so quickly...
Your hard work has paid off.
The children will graduate on to the next grade! The teachers will plan the next successful courses.
The end of the school year is an exciting time for all: We turn the page which we will start again next September (?) with improvements and fresh ideas and now we are planning and dreaming their beautiful summer vacations.
But there is no time for words!
Congrats to everybody for the great job during this year 2010-11!!!
Many thanks for the excellent collaboration!!!
I send my best wishes for a wonderful summer time... to all of you...Enjoy your moments in Greece, Romania and France as well.
Greece-Colorful pagess
Τετάρτη 15 Ιουνίου 2011
Delphi: Omphalos of the World
Distances among ancient temples in Greece
Delphi: the omphalos of the Earth
More PowerPoint presentations from KF
Using Google Earth / Mappi etc calculate the distances between:
a.
- Delphi oracle and Parthenon in Athens
- Delphi oracle Aphaia Temple on Aegina island
- Poseidon Temple in Sounion/Attica and Acropolis of Athens
- Poseidon Temple in Sounion/Attica and Aphaia Temple on Aegina island
- Delphi oracle and Olympia
- Delphi oracle and Acropolis of Athens
- Delphi oracle and Dodona
- Delphi oracle and Dion
- Save a map of Greece in a powerpoint file in your working area and design the lines among the above temples.
- What kind of geometrical shapes do you form?
- Which are the distances between the temples?
- Do you agree with the measurements in the above presentation file?
- What is the meaning of the phrase: "Delphi is the omphalos of the world", according your own point of view?
Hubble Space Telescope
Measurements over the Universe - Photos from Hubble
Watching the presentation you will find the distances between the Earth and some Planets or Nebulas.
Searching on the Internet, make sure that these measurements are valid (with documentation).
Afterwards
Watching the presentation you will find the distances between the Earth and some Planets or Nebulas.
Searching on the Internet, make sure that these measurements are valid (with documentation).
Afterwards
- create an excel file (well formatted) using these measurements in light years and parsec (using math formulas) as well.
- Sort this information according to the distances in ly and save the file.
Hubble telescope
More PowerPoint presentations from KF
Powers of 10
Powers of Ten takes us on an adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this famous film transports us to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only a s a speck of light among many others. Returning to Earth with breathtaking speed, we move inward- into the hand of the sleeping picnicker- with ten times more magnification every ten seconds.
The journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell. POWERS OF TEN © 1977 EAMES OFFICE LLC (www.eamesoffice.com)
Powers of 10
A voyage from St. Mark's Square in Venice/Italy to the edge of the visible universe...
Each circle is 10 times larger than the one before:
1 meter = 1,09 yards
--------------------
10^0 = 1 meter = the hula hoop
10^1 = 10 m = the crowd around the hula hoop
10^2 = 100 m = St. Mark's Square
--------------------
1 kilometer = 1000 meters = 0,62 miles
--------------------
10^3 = 1 kilometer = Venice's city center
10^4 = 10 km = all the islands of Venice
10^5 = 100 km
10^6 = 1.000 km = everything from central Germany to the southern end of Italy
10^7 = 10.000 km = almost earth's diameter
10^8 = 100.000 km = 1/4 of the distance between earth and our moon
10^9 = 1.000.000 (one million) km = 2/3 of the sun's diameter
10^10= 10.000.000 km
10^11= 100.000.000 km = 2/3 of the distance between earth and sun
10^12= 1.000.000.000 (one billion) km
10^13= 10.000.000.000 km = the diameter of our entire solar system
10^14= 100.000.000.000 km
10^15= 1.000.000.000.000 (one trillion) km
--------------------
1 lightyear = 9.460.528.000.000 kilometers = 5.878.499.562.555 miles
--------------------
10^16= 1,06 lightyears = would take modern spacecrafts 20.000 years to travel
10^17= 10,6 ly = twice the distance to our neighbor stars
10^18= 106 ly
10^19= 1.060 ly
10^20= 10.600 ly
10^21= 106.000 ly = diameter of our galaxy, including 100 billion stars
10^22= 1.060.000 (one million) ly
10^23= 10.600.000 ly
10^24= 106.000.000 ly
10^25= 1.060.000.000 (one billion) ly
10^26= 10.600.000.000 ly
--------------------
13,7 billion lightyears = size of the visible universe
78.0 billion lightyears = estimated size of the whole universe which is the same as 737.921.184.000.000.000.000.000 kilometers or 458.522.824.023.264.000.000.000 miles...
--------------------
A spaceship with todays technology would take almost two hundred billion years to reach only the "edge" of the visible (!) universe...
if it wouldn't expand with the speed of light which is 18.000 times faster than our spaceship...
Because it is, no matter what technology is used, physically impossible to travel with the speed of light (the mass of any body traveling with that speed would increase to infinite requiring infinite amounts of fuel to move) we will never be able to reach any edge or border of the universe...
Τρίτη 14 Ιουνίου 2011
Τρίτη 12 Απριλίου 2011
Fueling Hunger
From the New York Times
...with food prices rising sharply in recent months, many experts are calling on countries to scale back their headlong rush into green fuel development, arguing that the combination of ambitious biofuel targets and mediocre harvests of some crucial crops is contributing to high prices, hunger and political instability.
This year, the United Nations Food and Agriculture Organization reported that its index of food prices was the highest in its more than 20 years of existence. Prices rose 15 percent from October to January alone, potentially "throwing an additional 44 million people in low- and middle-income countries into poverty."
The development of greener fuels through maize, cassava, sugar, palm and rapeseed oil, and other crops has been a necessary and positive progression in environmental stewardship. Now though, many are justifiably calling for an urgent shift to research and development of more sustainable biofuel sources (such as switchgrass and agricultural waste products). This in an effort to end what has become a feeding of fuel demands at the cost of starving some of the world's hungriest populations.
διατυπώστε τις θέσεις σας. Νομίζετε πως υπάρχει τέτοιος κίνδυνος και στην Ελλάδα?
'--------------------------------------------------------------
This year, the United Nations Food and Agriculture Organization reported that its index of food prices was the highest in its more than 20 years of existence. Prices rose 15 percent from October to January alone, potentially "throwing an additional 44 million people in low- and middle-income countries into poverty."
The development of greener fuels through maize, cassava, sugar, palm and rapeseed oil, and other crops has been a necessary and positive progression in environmental stewardship. Now though, many are justifiably calling for an urgent shift to research and development of more sustainable biofuel sources (such as switchgrass and agricultural waste products). This in an effort to end what has become a feeding of fuel demands at the cost of starving some of the world's hungriest populations.
2 λόγια... στα ελληνικά
Αφού διαβάστε το παρακάτω άρθρο των New York Times:
"... με τις τιμές των τροφίμων ν'αυξάνονται κατακόρυφα τους τελευταίους μήνες, πολλοί ειδικοί καλούν τις χώρες να περιορίσουν τις προσπάθειες για πράσινη ανάπτυξη καυσίμων, με το επιχείρημα ότι ο συνδυασμός των φιλόδοξων στόχων για βιοκαύσιμα και η μέτρια συγκομιδή ορισμένων κρίσιμων καλλιεργειών συμβάλλει στις υψηλές τιμές της αγοράς, της πείνας και της πολιτικής αστάθειας.
Φέτος, ο Παγκόσμιος Οργανισμός Τροφίμων και Γεωργίας ανέφερε ότι ο δείκτης του των τιμών των τροφίμων ήταν o υψηλότερος των τελευταίων 20 ετών. Οι τιμές αυξήθηκαν κατά 15 τοις εκατό από τον Οκτώβριος-Ιανουάριος, "ρίχνοντας" επιπλέον 44 εκατομμύρια ανθρώπους σε χώρες χαμηλού και μεσαίου εισοδήματος στη φτώχεια».
Η ανάπτυξη των οικολογικότερων καυσίμων από καλαμπόκι, μανιόκα, ζάχαρη, φοινικέλαιο και κραμβέλαιο, καθώς και άλλες καλλιέργειες ήταν μια αναγκαία και θετική εξέλιξη στην περιβαλλοντική διαχείριση. Τώρα όμως, είναι δικαιολογημένα έκκληση πολλών για επείγουσα στροφή προς την έρευνα και την ανάπτυξη περισσότερο βιώσιμων βιοκαυσίμων από άλλες πηγές (όπως το switchgrass και τα γεωργικά απόβλητα). Αυτό για να μη στραφεί η προσπάθεια παραγωγής βιοκαυσίμων σε βάροςτων πεινασμένων του κόσμου."
Η ανάπτυξη των οικολογικότερων καυσίμων από καλαμπόκι, μανιόκα, ζάχαρη, φοινικέλαιο και κραμβέλαιο, καθώς και άλλες καλλιέργειες ήταν μια αναγκαία και θετική εξέλιξη στην περιβαλλοντική διαχείριση. Τώρα όμως, είναι δικαιολογημένα έκκληση πολλών για επείγουσα στροφή προς την έρευνα και την ανάπτυξη περισσότερο βιώσιμων βιοκαυσίμων από άλλες πηγές (όπως το switchgrass και τα γεωργικά απόβλητα). Αυτό για να μη στραφεί η προσπάθεια παραγωγής βιοκαυσίμων σε βάροςτων πεινασμένων του κόσμου."
διατυπώστε τις θέσεις σας. Νομίζετε πως υπάρχει τέτοιος κίνδυνος και στην Ελλάδα?
'--------------------------------------------------------------
Δείτε περισσότερα...
Κυριακή 20 Μαρτίου 2011
Τετάρτη 9 Μαρτίου 2011
Snow in Athens like a magic image!
We are listening to "Solitary Man" by Neil Diamond
For full screen press right click --> Zoom
Στην Εθνική οι μαργαρίτες δεν πτοήθηκαν από το χιονιά!
Τρίτη 8 Μαρτίου 2011
How many?
- Excel functions: Theory (download as doc format)
- Excel sheet: Exercise (download as xls format)
- Excel exercise (download as pdf format)
Κυριακή 6 Μαρτίου 2011
Πέμπτη 3 Μαρτίου 2011
Κυριακή 27 Φεβρουαρίου 2011
Aquarium.gr
This is the Greek version of AQUARIUM post of the french team
Μεταφράσαμε το θέμα AQUARIUM της γαλλικής ομάδας για τους Έλληνες μαθητές, προκειμένου να
- απαντήσουν στις ερωτήσεις
- χρησιμοποιήσουν το Excel για τους υπολογισμούς και
- παρουσιάσουν τα στερεά με το power point.
Click στο φυλλάδιο, για να ανοίξει...
press Play ...στη παρουσίαση...
Τετάρτη 23 Φεβρουαρίου 2011
What is Maths?
What else?
math·e·mat·ics n. (used with a sing. verb). The study of the measurement, properties, and relationships of quantities, using numbers and symbols. [From Middle English mathematik, from Old French mathematique, from Latin mathematica, from Greek mathematike (tekhne)]
math-e-mat-ics n. ... the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
Webster's New Collegiate Dictionary
Mathematics is a language.Gibbs, Josiah Willard. 1839-1903.
American mathematician and physicist.
To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.American mathematician and physicist.
Richard Feynman. 1918-1988.
American physicist.
The Character of Physical Law
American physicist.
The Character of Physical Law
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell. 1872–1970
British philosopher, mathematician.
Mysticism and Logic
All science requires Mathematics. The knowledge of mathematical things is almost innate in us... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.British philosopher, mathematician.
Mysticism and Logic
Roger Bacon. 1214-1294
English philosopher, scientist.
Opus Maius
English philosopher, scientist.
Opus Maius
What is mathematics? Most people would say it has something to do with numbers, but numbers are just one type of mathematical structure. Saying "math is the study of numbers" (or something similar) is like saying that "zoology is the study of giraffes". Math may be better thought of as the study of patterns, but this too falls short...
The more I study math, the more I wonder about what exactly math is. Actually nobody knows. It seems to be a product or our minds, and yet reflects the external universe with uncanny accuracy. A mathematician develops a mathematical theory for its aesthetic unworldly beauty and it's compelling evolution, with no thought of how it might be applied to the world. A century later a physicist finds this theory to be perfect to use as a framework to express his physics (this sort of thing happens frequently). Pretty weird how intimately connected our innermost "mind" and the outermost "universe" really are. This is a profound mystery!
Bruce Bennett, my advisor in grad school, defines mathematics as "unified consciousness theory". As you come to master a branch of mathematics, it's as though you've grown a new abstract organ of perception through which you may then view the world. You've grown a new "mind's eye" that can perceive realities literally inconceivable without this new organ of perception.
Rafael Espericueta
Professor of Mathematics
Bakersfield College
Professor of Mathematics
Bakersfield College
Τρίτη 22 Φεβρουαρίου 2011
Κυριακή 20 Φεβρουαρίου 2011
Σάββατο 29 Ιανουαρίου 2011
Πέμπτη 27 Ιανουαρίου 2011
Life is wonderful (goes full circles)
... dedicated to my dear colleagues from France, from Romania, from Greece and to my pupils too...
Δευτέρα 24 Ιανουαρίου 2011
Google Sketchup...
La modélisation 3D
Tutoriel pour l’utilisation du Google SketchUp
Have a look at Google SketchUp Toolbars in english
Click HERE
Tutoriel pour l’utilisation du Google SketchUp
Presentation1
More PowerPoint presentations from ap
____________________________________
Have a look at Google SketchUp Toolbars in english
Click HERE
Κυριακή 23 Ιανουαρίου 2011
Aires et Volumes
______________________________________________
Συμπληρώστε το γλωσσάρι με τους παραπάνω όρους!
Fill in the above terms in the Glossary!
Click HERE!
Géométriquement votre ...
(Watch the presentation...click the link below... or press play ||> )
De la géométrie dans l’espace à la géométrie dans le plan
Κυριακή 16 Ιανουαρίου 2011
Golf ball
A golf ball is dropped and a regular strobe light illustrates its motion as follows...
We observe that it is a parabola.
Problem:What is the equation of the parabola that the golf ball is tracing out?
ΓΙΑ ΤΟΥΣ ΜΑΘΗΤΕΣ: χρησιμοποιήστε το Excel για να σχεδιάσετε το γράφημα.
Use Excel for making the graph and finding out the equation!
We can model the motion from the data points obtained by observing the position (height) of the ball at various times.
This is the table of values time/height:
You can use Microsoft Excel to module a parabola. After you plot the points, right-click on one of the points and choose "Add Trendline (Γραμμή Τάσης)".
Choose Polynomial, degree 2. In "Options (Μορφοποίηση γραμμής τάσης --> Επιλογές)" you can get Excel to display the equation of the parabola on the chart.
Problem:What is the equation of the parabola that the golf ball is tracing out?
Use Excel for making the graph and finding out the equation!
We can model the motion from the data points obtained by observing the position (height) of the ball at various times.
This is the table of values time/height:
Source: http://www.intmath.com/Plane-analytic-geometry/4_Parabola.php, http://wn.com/The_Ball_and_the_Parabola
Also the tennis ball does the same motion. Watch the video:
____________
Using Excel to Model Curves
You can use Microsoft Excel to module a parabola. After you plot the points, right-click on one of the points and choose "Add Trendline (Γραμμή Τάσης)".
Choose Polynomial, degree 2. In "Options (Μορφοποίηση γραμμής τάσης --> Επιλογές)" you can get Excel to display the equation of the parabola on the chart.
Is the Gateway Arch a Parabola?
The Gateway Arch, or Gateway to the West, is part of the Jefferson National Expansion Memorial in St. Louis, Missouri.
Built as a monument to the westward expansion of the United States, the arch has become the iconic image of St. Louis. It typifies "the pioneer spirit of the men and women who won the West, and those of a latter day to strive on other frontiers". At 630 feet (192 m), it is the tallest man-made monument in the United States, and Missouri's tallest accessible building. Located on the west bank of the Mississippi River.
Why do they use the parabola shape for bridges ?
The arch helps transfer force to the outside of the bridge so that the abutments can support it.
Comparing our parabola to the photo, we can see (especially near the waterline at the bottom) the shape of the arch is not really a parabola at all. The designer of the Gateway Arch, Eero Saarinen, knew that a parabola was not the best shape for such an arch. An arch shape that is often used is the catenary. The Gateway Arch is also the largest architectural structure designed as a weighted or flattened catenary arch.
So, the Gateway Arch is not a parabola. It is a catenary arch!!!
Gateshead Millennium Bridge in Newcastle
Blinking eye bridge
The bridge takes its place at the end of a line of distinguished bridges across the River Tyne, including the Tyne Bridge and Robert Stephenson's High Level Bridge.
Linking Gateshead with Newcastle via Gateshead Quays (described as one of the best places in Europe by Tony Blair) and Newcastle's Quayside, the bridge not only serves a functional purpose as the River Tyne's only foot and cycle bridge, but its grace and engineering attract people from all over the world.
Linking Gateshead with Newcastle via Gateshead Quays (described as one of the best places in Europe by Tony Blair) and Newcastle's Quayside, the bridge not only serves a functional purpose as the River Tyne's only foot and cycle bridge, but its grace and engineering attract people from all over the world.
The 130m long deck is parabolic in elevation and of steel box section that tapers in plan towards the centre of the deck. It carries a pedestrian footway that varies from 3m to 5m in width as well as a 2.5m cantilevered cycleway.
The main arch is also parabolic in shape and tapers both in plan and elevation.
Six 450mm diameter Hydraulic rams (three on each side, each powered by a 55kW electric motor) rotate the bridge back on large bearings to allow small ships and boats (up to 25m tall) to pass underneath. The bridge takes as little as 4.5 minutes to rotate through the full 40° from closed to open, depending on wind speed. Its appearance during this manoeuvre has led to it being nicknamed the "Blinking Eye Bridge".
Τρίτη 11 Ιανουαρίου 2011
Resume: The Quadratic function
Glossary
Fill in the shells of the shared document with the words from the above text of math terminology:
Fill in the shells of the shared document with the words from the above text of math terminology:
WorkSolve the exercises on URLs:
Source: Wikipedia
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