Geometry in my country

school teacher 1 Jean Monnet High School, Romania Mihaela Git 2 Gaudeamus High School, Moldova Ludmila Cojocari 3 Tehnička škola Virovitica, Croatia Vlatka HižmanTržić

4 Cité Scolaire Brocéliande, France Bénédicte Leduc 5 Ωθηση Stamata, Greece Maria Roussak

6 Baruthane Ortaokulu, Turkey Tuğba Tekay Varol

7 Osnovna škola Nikole Andrića, Croatia Ljubica Baćić Đuračković

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean

Monnet High School

Carpet, model from Sinaia

Traditional Romanian carpets are made by hand using the weaving loom.

Traditional Romanian carpets are immortal and convey, through the design motifs, many of the Romanian values and beliefs.

https://gen90.net/copilaria-cu-miros-de-lana/

In the attached figure, the triangle EFG is equilateral with side 1u.

Calculate the area of the orange colored surface.

Clubul eTwinning „Jean Monnet”

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

Denisa Ciulei - 6 Grade

The Air Monument

In Quito Square there is the Air Monument dedicated to Mircea Zorileanu (October 14, 1883 – February 10, 1919), one of the pioneers of aviation in Romania, the second certified aviator in Romania. During the First World War, he performed numerous missions for the Romanian 2nd Army. Through his actions, he contributed to the popularization of aviation in Romania.

In 1937, the Royal Aeroclub ofRomaniadedicated a monument to him in the Quito square in Bucharest, at the intersection of Paris, Prague and Warsaw streets, a monument on the foundation of which is built the urn with the ashes of aviator major Mircea Zorileanu. The iron, bronze and stone monument was executed by Emil Ludovic Gové.

Mathematical remarks:

In reality, the sizes are about 100 times larger than those in the photo.

Some of the observed shapes or solids are the rectangle, the circle, the sphere

Useful formulas:

Perimeter and area of the rectangle:

P=2(L+l),A=L∙l

The circumference of the circle: L=2πR

The volume of the sphere:

4����3

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

Ana Rusu

The "Heroes of the Air" Monument

The "Heroes of the Air" monument is dedicated to the memory of Romanian military and civilian aviators who contributed to the development of aviation. It is located in the center of Aviatorilor Square and was made between 1928-1935.

The construction, with a total height of 20 m, is composed of bronze sculptures. Above the obelisk is placed the 5 m high statue, weighing 5 tons, depicting the flying man with outstretched wings. At the base of the obelisk, around it, three fallen airmen are depicted. On the plinth are present the badges, the helmet, the equipment of the aviators, but also the names of the fallen aviators between 1930-1935, carved in 13 bronze plates.

Calculations:

1. If the height of the flying aviator is 5 meters in reality and 8 units in the picture (=4 cm in Geogebra file), find the scale of the picture.

2. Calculate the area of the isosceles trapezoid CDEF, in which CD=2u, EF=4u, Ed=15.

3. Calculate the perimeter of the quadrilateral GHIJ, having sides GH= 9u

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

Vincent Callebaut

A Gothic and Biomimetic Forest for the Cathedral

PALINGENESIS, TRIBUTE TO NOTRE-DAME

On April 15, 2019, the Notre-Dame cathedral in Paris, built eight centuries ago, almost saw its end in the historic fire that devoured its roofs.

„Our project Palingenesis - meaning "rebirth", "regeneration" - aims to assimilate the venerable stone nave, to merge naturally like a vegetable graft harmonizing in one gesture - in one curved movement of pencil - the roof and spire.”

https://www.vincent.callebaut.org/zoom/projects/190503_ tributetonotredame/tributetonotredame_pl007

https://www.vincent.callebaut.org/object/190503_tributet onotredame/tributetonotredame/projects

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School Sofia Tănase

The Palace of Parliament

The Palace of Parliament in Bucharest,Romania(knownbeforethe 1989 revolution as House of the People), measures 270 m by 240 m, 84 m high, and 92 m below ground made in the spirit of socialist realist architecture. It has 9 levels on the surface and another 9 underground. According to the World Records Academy, the Palace of Parliament is the third largest administrative building for civil use by area in the world, the most expensive administrative building in the world, and the heaviest building in the world. The hill on which the Palace of Parliament stands today is generally a creation of nature, having an original height of 18 m, but the side facing Libertății Boulevard is artificially raised.

Geometrical remarks

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

Miruna Iscu

The Calendar Castle

The castle in Zau de Câmpie, Mureș was built according to the principles of a calendar. It has 365 windows, the number of days in a year, 4 towers, the same as the number of seasons, 52 rooms, the number of weeks, 7 terraces, the number of days in a week, and 12 halls, the number of months ofthe year.Thecastlestands underthe sign of an unfulfilled love story between the owner and a Russian princess. In 1911, the construction of the holiday residence of Baron István Ugron⁠(hu) began, an architecture faithful to French medieval castles.

The castle was, in turn, a sanatorium for TB patients, a school and a grain warehouse, and in recent years a children's home.

Geometrical remarks on the windows above the entrance

Let the center circle be O and the radius R. If the 4 circles are congruent and tangent two by two and the fifth circle has a radius equal to the distance from the center of the large circle to the point of contact, let's find out what r is.

According

OBS: If a stained glass window can in reality be 1.5m high, we can find out, approximately,thescaleatwhichthepictureistaken.

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

CARLOS-ANDRES SANZ-ENE (student)

NATIONAL LIBRARY OF ROMANIA

Polygon CDEF

Polygon GHIJ

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Jean Monnet High School

Mara Negrescu

Romanian Atheneum

In 1865, cultural and scientific personalities such as Constantin Esarcu, V. A. Urechia, and Nicolae Creţulescu founded the Romanian Atheneum Cultural Society. To serve its purposes, the Romanian Athenaeum, a building dedicated to art and science, would be erected in Bucharest

ThebuildingwasdesignedbytheFrencharchitect Albert Galleron, built on a property that had belongedtotheVăcărescufamily andinaugurated in 1888, although work continued until 1897. A portion of the construction funds was raised by public subscription in a 28-year-long effort, of which the slogan is still remembered today: "Donate one leu for the Ateneu!"

https://ro.wikipedia.org/wiki/Ateneul_Rom%C3%A2n

Mathematical remarks

In the triangle CDE, CD=DE=3cm, the angle CDE measures 145°.

1) Calculate the EC.

2) Find the scale of the attached image, if the facade has a length of 23.19 m (according to Google maps) and in the picture it is 3 cm.

3) Find the real area of CDE triangle.

Solution:

Geometry in real life

Find a function that models this skyscraper Ternary Tower in Shanghai, China

Solution:

f(x)=0.63sinx with a rotation by 90 degrees around the point O, ��:(��; ∞)

Clubul eTwinning „Jean Monnet”

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

,,Gaudeamus” high-school, Moldova

Duca Zlata

The Cathedral of Christ's Nativity

https://www.geogebra.org/m/zbw7ge7d

The Cathedral of Christ's Nativity (Romanian: Catedrala Mitropolitană Nașterea Domnului, Russian: Собор Рождества Христова) is the main cathedral of the Moldovan Orthodox Church in Sectorul Centru, Moldova. It was commissioned by the governor of New Russia, Prince Mikhail Semyonovich Vorontsov, and Metropolitan Gavril Bănulescu-Bodoni in 1830.

The cathedral was built in the 1830s to a Neoclassical design by Abram Melnikov (who had designed a similar church in Bolhrad). The cathedral was bombed during World War II, and its bell tower was destroyed by the local Communists in 1962. The new bell tower was constructed in 1997. During the Soviet period, worship was prohibited and the cathedral was transformed into an exhibition center.

The Cathedral has three levels which need to be painted. The first level’s face has 2,74 units the length and 2,69 units the width. The second has 2,16 units and 2 units. The third has 2,15 units and 1,52 units. How much paint would they need to paint it, if they spend 1 kg of paint per 0,4 units?

A1=(L1*l1)*4=2,74*2,69*4=29,4824 (units)

A2=(L2*l2)*4=2,16*2*4=17,28 (units)

A3=(L3*l3)*4=2,15*1,52*4=13,072 (units)

Atotal=A1+A2+A3=29,4824+17,28+13,072=59.8344 (units)

0,4 units … 1kg 59,8 units … x kg

Answer: approximately 149,5 kg

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Gaudeamus High School, Moldova

Petrachi Daniel

The Candle of Gratitude Informations

The Candle of Gratitude Monument is one of the best monuments in Moldova. The monument was initiated by Ion Druta and it is built on the rocks between the Nistru River and the Bechir ravine. It is also considered as a very special work of art for another reason. It is actually built in the memory of the cultural monuments in Moldova that were destroyed in the past. Time stands still when it passes through this monument. It is a silent witness of many hopes and agonies, dreams and hard works of many past generations.

Calculations

AF- 30m (Height)

BC- 8m (Width)

Perimeter-?

Area -? Solving:

Area Formula: ���� ��

Area=������ �� =����������

Perimeter Formula : AB+BC+AC

Triangle ABC-Isosceles →[����]≡[����],

According to the Pythagorean Theorem: ������ =������ +������

AC=√������ +������ =√������ +���� ≈����.����, AB=AC=30.3m

Perimeter= 30.3+30.3+8=68.6 m

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Gaudeamus High School, Moldova

Kureacih Eugen

The Soroca Fortress

The Soroca Fortress is the only monument of the medieval era in the space between the Prut and Dniester, which has been preserved almost entirely. The fortress was built of wood in the 15th century, by order of Stephen the Great, in front of the ford over the Dniester, and rebuilt of stone under the leadership of Petru Rareș, in the middle of the 16th century.

diameter of building- 37.5 m

The height of the fortress - 20-25 meters

thickness of the walls - 3.5 meters

volume-area*height=78,5*30=2355m3

Aria-3,14*5m2=78.5m 2

Diameter of cylinder-10m

Radius-D:2=10:2=5m

Calculations

……

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

____I.P.L.T„Gaudeamus”, Moldova

_____Gușanu Mădălina ___(student)

Arc de Triomphe in Chișinău Information

TheTriumphalArch(foratimecalledthe HolyGates,andundertheSovietregime theArchofVictoryandtheArchof Victory)isanarchitecturalmonumentof nationalsignificance,enteredinthe Registerofhistoricalandcultural monumentsofChisinaumunicipality.It wasbuiltin1840–1841tocommemorate thevictoryoftheRussianarmyinthe Russo-TurkishWarof1828–1829.

https://www.geogebra.org/m/wcqtpku4

In the rectangle CDEF we have CD-8 m, DE-6 m, find:

a) Perimeter of the rectangle,

b) Area of the rectangle,

c) length of diagonal CE

a) P=2CD+2DE=16+12=28(m)

b) A=8*6=48(����)

Calculations

c) AccordingtothePythagoreanformula:

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

IPLT Gaudeamus, Moldova

Țurcan Eugeniu

"The Candle of Gratitude"

This monument erected on the rock, above the old Dniester, on the outskirts of Sorocia, is one of the most important buildings in the modern history of Moldova. Here lie, poured into the foundations, bound stone to stone, the sufferings, hopes and toils of many generations of our compatriots. This extraordinary epic is dedicated to all the destroyed monuments of Moldavian culture. "The Candle of Gratitude", growing from the depths of our past, represents a tribute to all the anonymous heroes, who preserved the culture, language and history of Moldova in the polychrome palette of human civilization, at the same time perpetuating the memory of the great anonymous poet, the author of the ballad "Miorita".

The monument has the form of a cylinder

The Height 29,5 m

Lenght(diameter) 5 m

What is the volume ?

For painting the whole monument you need ..... kg of painting if you use 1 kg for every meter?

Calculations Area of the Cylinder Total surface area of a closed cylinder is:

Volume=2316.92m3

Geometryinmycountry

GaudeamusHighSchool,Moldova

DutcaArtiom(student)

"Eternity"MemorialComplex About

The "Eternitate" Memorial Complex is a historical monument located in the capital of the Republic of Moldova - Chisinau. It was built in memory of the Soviet soldiers who fell in the battles against the German-Romanian troops in the Second World War

The memorial was built by the sculptors A. Maiko and I. Poniatowki and the architect A. Minaev. Its inauguration took place on May 9, 1975, on the day of the 30th anniversary of the Soviet victory in World War II.

CD-25m(height)

FE-10m(width)

Perimeter-?

Area-?

T.Pithagora:

Calculations

Solving:

Area=(10×25):2=125m

Perimeter:FC+CE+FE

TriangleABC-isosceles

CE²=DE²+CD² CE²=625+25 CE=25,50m Perimeter=60,50m

Calculations……

Height: 29.5m

Diameter: 7m

Inner radius:2.75m

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Gaudeamus High-school, Moldova

Buga Mădălina

This monument is called "Lumânarea recunoștinței", which translated word by word would mean "The candle of gratitude". It is situated in the north of Moldova, close to the Soroca Citadel. It is one of the most important constructions from the Moldovan history being a place of hope.

If the monument was to be painted, how many liters of paint would there be needed?

V=3.14*(3.5*3.5)*29.5 V=1135l

paint V= 3.14*(3.5*3.5-2.75*2.75)*29.5 paint V=

434.2l

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Gaudeamus High School, Moldova

Vlad Vicol

Memorial Complex "Eternity" Informations

Memorial Complex "Eternity" – Also known as the “Eternal Flame”, the memorial was created by sculptors A. Maiko and I. Poniatowski and architect A. Minaev. It was inaugurated on 9 May 1975, the 30th anniversary of the Soviet victory in World War II. During the Soviet period the complex was known as the Victory Memorial.

Calculations

CF - 25m (Height)

ED - 20m (Width)

Perimeter-?

Area -? Solving:

Area Formula: ���� �� ,

Area=�������� �� =����������

Perimeter Formula : CD+CE+DE

Triangle ECD-Isosceles →[����]≡[����],

According to the Pythagorean Theorem: ������ =������ +������

EF=√������ +������ =√������ +������ ≈���� ��, CE=CD27.3m

Perimeter= (27.3 ×��) + 20 = 74,6 m ������������:������������������ ����,����,��������–

GrowingwithAppliedMathematicsExperiences(G.A.M.E.)

Geometryinmycountry

GaudeamusHighSchool,Moldova

DumitrascuCristian-Patriciu

TheTriumphalArch

The Triumphal Arch is a monument situated in Central Chișinău directly opposite Government House.

The Triumphal Arch was built in 1840 to commemorate the victory of the Russian Empire over the Ottoman Empire during the Russo-Turkish War. From its construction until 2011 the monument sheltered at its second level a huge bell that was smelted with the copper of the cannons captured from the Ottoman Empire.

The triumphal arch is a cuboid with the length and width of 10m and the total height of 13m. The pillars of support are 3x3m with a height of 7m. The upper part is 10x10m with a height of roughly 6m. Its weight is 6,4 tonnes.

With these measurements we can find out: The occupied area of it: 10 x 10 = 100 ��

The total volume occupied by the arch and it’s free space: 10 x 10 x 13 = 1300 ��

The arch’s volume: 6 x 10 x 10 = 600 (top part) �� 3

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Gaudeamus High School, Moldova

Turcan Vlad

Cetatea Soroca(Fortress Soroca)

Fortress Soroca-info

Soroca Fortress is a Moldavian fortress from the XV-th century, built of wood by Stephen the Great, in front of the ford over the Dniester, and rebuilt in stone by Petru Rares, in the middle of the XVI century.Now it's a touristic destination found in Soroca.

Calculations:

Diameter of the cylinder=10m

Radius=D:2=10:2=5m

Area=πr²=3.14•5m²=78.5m²

Height=30m(aprox)

Volume=area•height=78.5•30m=2355m³

Answer: ��������=����,������ ������������=������������

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

OŠ Nikole Andrića (school)

Borna Šimić (student)

image

About...

The Pula Arena is the largest and most preserved monument of ancient architecture in Croatia. In size, it ranks 6th among the Roman amphitheaters in the world. It is a geometrically regular structure and has an elliptical appearance.

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Nikola Andrić elementary school

Gabrijela Orešković

Cibona Tower

The Cibona Tower is a high-rise building located in the center of Zagreb, Croatia on Dražen Petrović Square 3 It was built in 1987.

It is 92 meters tall, and it has 25 levels above ground. There is a radio mast on the roof, which increases the height of the tower to 105 meters. As of 2007, Cibona Tower is ranked 3rd by height (2nd when you include the antenna) in Croatia.

The tower is a part of the complex that comprises lower business objects, a 5,400seat basketball hall, and an art installation. The skyscraper is a cylinder, 25 meters in diameter, which reduces its diameter in four stages, and ends up with a radio mast.

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Technical school Virovitica

Gabrijel Bakić

Pejačević Castle

Pejačević Castle is located in the center of Virovitica. It is one of a series of Slavonian castles of the famous Pejačević noble family, who received the noble title "Pejačevići Virovički" precisely because of this estate.

The castle was built between 1800 and 1804 according to the plans of the Viennese architect N. Roth. Anton I.dies during the construction, in 1802, and the inhabitants of the time said that he who undertook such a great job must die before the completion of construction. The castle was built for his son, Anthony II . Pejačević, and in the middle of the 19th century, Antun III. Pejačević sold it to the German princely family of Schaumburg-Lippe, who owned it until 1911, when it was bought by Count Ivan Drašković, who sold it together with the park to the city of Virovitica in 1930, and since then it has been in the service of the city. The Pejačević and Schaumburg-Lippe families left a special mark in the history of the manor and castle in Virovitica. The original purpose of the castle as the seat of the lords ended after the departure of the Schaumburg-Lippe princes, although Count Drašković used the castle for some time, the life of the lord family never took place in it again.

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Cite scolaire Broceliande, France image

About….

The Louvre Pyramid is a cultural monument made of glass and metal, located in the middle of the Napoleon courtyard of the Louvre Museum in Paris. It houses the main entrance to the museum.

It was commissioned by François Mitterrand in 1983. It was designed by the Chinese-American architect Leoh Ming Pei.

The Louvre Pyramid has a square base. One side of the square measure 35,42m. And the height of the monument is 21.64m. The 4 ridges that start from the summit measure 33.14 metres.

1- Calculate the volume of the pyramid.

Calculations

The volume of a square-based pyramid is equal to one third of the area of its base multiplied by the height of the pyramid.

We start by calculating the aera of the bases :

A = 35,42*35,42 = 1254.5764 m²

Then, we calculate :

1/3 x 1254.5764 = 418,1921 m

Finally, we calculate the volume of the pyramid :+ = height of the pyramid x square-based pyramid is equal to one third of the area of its base

21,64 x 418,1921 = 9049,677 m3

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Baruthane Secondary School

Galata Tower was converted into an even taller structure between 1445-1446. Tower; 16. it was used as a home for Christian prisoners serving in the Kasimpasa shipyards in the XVII century. after 1717, the tower was put into operation for fire observation purposes. Drums were played from the tower to announce the fire in the city to the public. in 1965, the tower was repaired for the last time. No repairs have been made since then. The Tower; III. It was used as an observatory during the Murat period. IV. Hezarfen Ahmet Çelebi, who lived during the Murat period, has written his name in history with the flight he made from this tower. He flew from this tower to Üsküdar. During the last repair of the tower, it was extended by two more floors. 40 more steps have been added. At the same time, it was built in a hall covered with 14 large masonry arches. The tower was opened to tourist visits in 1967.

The height of the Galata tower from the ground is 69,90 meters.

The outer diameter of the tower is 16,45 meters.

Area of the Tower : 2.π.8,225 (69,90)= 3 612,37 m2

The Volume of theTower: π.(8,225.8,225). 69,90= 14 855,89 m3

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Brocéliande High School (school)

Oscar M (student)

image About….

The eiffel tower is a French monument built by Gustave Eiffel in 1889 for the world exhibition in Paris and was originally to be dismantled after it

Since its opening to the public, it has welcomed over 300 million visitors

Calculations

A person who is 175 cm tall stands in front of the Eiffel Tower so that his shadow and that of the Eiffel Tower are at the same point in O

Calculate the Eiffel tower’s height to the nearest meters

We use the Thales theorem that is A/B is equal to C/D because the person and the Eiffel tower are parallel

497/2,7 is equal to C/1,75

184,0741 is equal to C/1,75

so, 184,0741=C/1,75

I multiply each side by 1,75

322,1296=C

so the Eiffel tower’s height is 322 meters

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Brocéliande

Meiko PROVOOST(student)

image

About….

The Eiffel tower was build on January 28 1887 by Gustav Eiffel .

Here , we wanna found the mesur of the tower so we have :

NC= 217m AN= 1m MN= 1,50m

Calculations……

To find its length we will use thales theorem :

We see that the dots B,M,A are aligned just like the dots A,N,C

Therefore, ���� ���� = ���� ���� 218

1 = ���� 150

We we will use then the cross products : BC = 150×218=327

Finally the length of the eiffel tower is 327m

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Brocéliande High School

Cylindrical and made of metal, white in color, with a total height of 45 meters, it offers visitors a panoramic view of the Futuroscope park while turning clockwise thanks to electric motors weighing nearly 17 tons.

Mary places herself as shown in the figure below, so that her shadow coincides with that of the towerof Futuroscope. After making several measurements, Adrien makes the diagram below (the diagram is not to scale), on which points A, E and B and points A, D and C are aligned.

Calculate the height BC of the tower.

Calculations

Property of Thales :

AC / AD = BC / DE.

BC = AC x DE / AD = 56.25 x 1.6 / 2 =45 m.

So, the height BC of the tower is 45m.

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Othisi

High School

Electra K.

These birdhouses are found in the Aegean Island of Tinos and were a symbol of social standing and wealth. They are decorated with geometric shapes as triangles, squares, circles etc. and are characteristic of the local architecture and popular art. The birdhouses were used to breed pigeons, so they were built in open spaces, near sources of water and directed to the East or the West to be protected from strong wind

Growing with Applied Mathematics Experiences (G.A.M.E.)

Geometry in my country

Othisi High School

Giannis

P.

Geometricartisaphase ofGreekart,characterized largelyby geometricmotifsinvase painting,thatflourished about900–700BC,atime ofdramaticsocialand cultural transformation.

Thevaseshadvarioususes orpurposeswithinGreek society.Duringthisperiod, theyweremostlydecorated insymmetric,strictly geometricpatternssuchas meanders,homocentric circles,semicirclesetc.

Library has been a library serving the people of Ephesus, just like today's public libraries. The sarcophagus of Celsus, the founder of the library, is also in the library.