While in college, why did Euler work through advanced math books on his own?

Answers

Answer 1
His teacher didnt have time so advised him to tutor privately
Answer 2

Answer:

The famous mathematician Johann Bernoulli (1667-1748) encouraged Euler, then a student at the University of Basel, to read advanced books in Mathematics after becoming aware of the Euler's talent on this subject.

Explanation:

Leonhard Euler (1707-1783) enrolled the University of Basel in 1720, at the age of thirteen (a fact not unusual at that time), where Johann Bernoulli was a math professor.

After giving some classes in elementary mathematics to young Euler, Bernoulli promptly understood that Euler had talent and determination to math, and then suggested him advanced mathematical readings and offered him private classes freely every Saturday afternoon on topics that Euler found unable to understand.

By the way, Euler's father, Paulus, a Protestant clergyman, was a friend of the Bernoulli family, and also received some math classes from another famous mathematician Jakob Bernoulli, the elder brother of Johann.


Related Questions

Which statement best describes the impact of farming on the rise of the Adena and Hopewell cultures?

Answers

Final answer:

Farming significantly impacted the rise of the Adena and Hopewell cultures by providing a stable food source, promoting population growth, allowing settlement, and facilitating the development of complex social structures.

Explanation:

The impact of farming on the rise of the Adena and Hopewell cultures was significant.

Agriculture played a central role for these societies as it provided a stable food source, which allowed for population growth, establishment of settled communities, and development of complex hierarchical social structures.

The ability to grow and store food may have reduced the need for constant migration, giving the Adena and Hopewell people time to develop their culture, creating elaborate ceremonial mounds and artifacts.

Learn more about Adena and Hopewell cultures here:

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The faces symbol,a bundle of elm or birch rods are bound together by straps with the blade of an axe protruding from the bundle, symbolizes

Answers

It symbolizes power, strength, authority, and similar things regarding power and its usage in political purposes. The name fascism comes from it because it's ruling through strength and authority. It was commonly used in ancient Rome but when it was used in the city of Rome the axe was removed, unless the ruler was a dictator who wanted to show it publicly.

The right of one consul to veto the decision of another is an example of what principle?

Plz help

Answers

the answer to your question is representative democracy

Answer:

Checks and balances

Explanation:

Grocery stores, bakeries, and pharmacies were all businesses a. that only utilized slave labor. b. that faced economic hardships during the colonial period. c. in which women were likely to be employed or run. d. that were less likely to exist in the middle colonies.

Answers

I think the correct answer would be c

Opportunities for working women in the United States in the mid-1800s

Answers

Women of all ages not only worked in the fields during harvest time, but handled household chores such as cooking, sewing, spinning, weaving, and tending children and livestock.

In the mid-1800s, women in the U.S. experienced increased work opportunities due largely to industrialization and educational reforms, filling roles in factories and new white-collar jobs. Despite this progress, they faced pay inequities and societal limitations, with work often being a necessity rather than a choice for empowerment.

In the mid-1800s, the opportunities for working women in the United States expanded due to industrial and societal changes. Although legal restrictions and societal expectations still limited women's economic independence, the rise of industrialization created a demand for factory workers, leading to an increase in employment opportunities for women, particularly in the textile industry. Additionally, education reforms enhanced girls' education, resulting in a growing number of middle-class women entering white-collar occupations such as clerking, teaching, and journalism.

The Civil War also affected women's work, with some taking on roles in managing plantations and working in manufacturing. Post-war, women increased their presence in the workforce as clerks, switchboard operators, secretaries, and nurses, which gradually shifted perceptions of the working woman. Yet, challenges remained as women were often paid less than men and mainly engaged in low-status or physically demanding jobs. Their entry into the workforce was not generally seen as a step towards empowerment, but rather a necessity for financial survival.

By the end of the 19th century, with further industrial growth, the number of women working outside the home tripled, and new job roles became available to them. Reform movements, spearheaded by women, also began to challenge traditional roles, laying the groundwork for future advances in women's rights.

How were conscientious objectors treated in the United States during World War I?

Answers

The military were determined to get everyone they could." Bernard Lawson was one of some 16,000 conscientious objectors who refused to fight as conscription laws enlisted two-and-a-half million extra British troops from 1916 onwards.

During WWI, conscientious objectors were allowed to serve in non-combatant military tasks, including farm labour in France under the American Friends Service Committee when there was a workforce shortage. However, there were conscientious objectors who refused any cooperation with the military because it would be contributing to the war effort.  These absolute objectors were imprisoned in centres like Alcatraz Island or Fort Lewis and suffered from short rations or solitary confinement.

•How did the Mexican American War disrupt Native American tribes such as the Comanche?

Answers

A captain of Doniphan's men in the name of Captain John Reid discovered that Parras in the Mexican state of Coahuila was attacked by the Comanche Indians. The captain felt sorry for the townspeople's suffering so he and his men pursued the raiders, killing almost all of them and retrieving horses and captives.
The Comanche were involved in the war before the war even began. There had been a lot of conflicts between the Comanche and Mexicans because the Comanche invaded Texas territory which disrupted the Mexican military. The Comanche were so good at pillaging the area that when the US arrived during the war the region was already devastated. Comanche were not in an alliance with the US, but they were later forced out by the US and into the reservations.

what are some ways that the South African government discriminated against nonwhite citizens?

Answers

Racism in Africa is multi-faceted and dates back several centuries. It is a phenomenon that may have been strengthened by European colonialism, under which boundaries were drawn that did not take into consideration the different peoples dwelling within the newly formed provinces.

Mandela’s speech shows that the South African government discriminated against nonwhites in many ways. For example, the government did not allow nonwhites to vote. It also limited their job opportunities. Nonwhites could not own homes or land. Also, nonwhites had to live in areas approved by the government, and they had to follow government curfews.

Which statement best describes what happened when Constantine tried to establish "New Rome"?

A)He brought the Western Empire under his control and established an empire in Italy that prospered.

B)He was not able to establish "New Rome" because Western Rome's armies were too strong and maintained control.

C)He was overthrown by a foreign prince, and his new empire crumbled under the prince's poor leadership.

D)He was successful in building a new political center in the East, unified by the Christian religion.

Answers

Correct answer choice is :


D) He was successful in building a new political center in the East, unified by the Christian religion.Explanation:

New Rome was a name granted by the Roman Emperor Constantine to his new imperial city on the European coast of the Bosphorus Strait. The city had been most generally recognized as Byzantium prior to his rededication, and as Constantinople following, until the 20th century, when it was renamed Istanbul.

Answer:

The correct answer is D) He was successful in building a new political center in the East, unified by the Christian religion.

Explanation:

This new political center was named "Constantinople" after him. Later, due to the separation of the Roman Empire, it would be part of the East Roman Empire and later on Byzantium. Also, during the reign of Constantine, Christianism started to become the dominant religion in the Roamn Empire.

Which of the following goods did the early New England colonies import from England?

Answers

The goods that New England imported was tea

Answer:

hi your question lacks the required here is the complete question and options

Which of the following goods did the early New England colonies import from England?

A. timber, tea, and household goods

B. salted fish, timber, and tea

C. glassware, tea, and household goods

D. household goods, glassware, and salted fish

Answer : glassware, tea and household goods ( C )

Explanation:

The early England colonies that were established in America had a need for various goods which were not readily available/produced in the new England colonies that were established and some of those goods were glassware, tea and household goods.

before the establishment of the colonies the  Native American populace were practicing Agriculture mainly and were not a producing economy, fish and other farm produce could be gotten from the colonial settlements but produced goods like glassware were imported from England by the colonists.

which of the following best describes a belief held by president Truman that led to the establishment of the Truman doctrine

Answers

The one that best describes a belief held by President Truman that led to the establishment of the Truman Doctrine is that the United States should help free nations resist the spread of communism. Truman Doctrine President Truman's approach of giving financial and military guide to any nation undermined by socialism or totalitarian belief system
The United States should help free nations resist the spread of Communism.!!!!

"And pile them high at Gettysburg
And pile them high at Ypres and Verdun..."
"Grass." Carl Sandburg, 1918.

To what does Sandburg allude in this passage?

a) industrial landmarks
b) famous battlefields
c) American cities
d) Midwest farm areas

Answers

Sandburg alludes to B. famous battlefields in this passage.
The battle of Gettysburg happened during the American Civil War, the battle of Ypres occurred during WWI, as well as the battle of Verdun. He is referring to these famous battles and the fields where they happened because he wants to make a powerful impact on the reader/listener.

What is metallurgy? the study of how to domesticate animals the science that studies how metals work a Hindu sacred ritual for cleansing the body the belief that natural objects have supernatural beings in them

Answers

science that studies how metals work

It is in fact B. I am 100% sure. Hope this helps!

This means to "let the decision stand". a. per curiam brief c. stare decisis b. amicus curiae brief d. de facto brief

Answers

the answer is b i think

Why did axum Marketplace develop a blended culture

Answers

People from different lands went to Axum and settled there. A lot of people wanted to settle in Axum because it was good place.

Who was Phillis Wheatley
A) an African American slave
B) one of the first women to own slaves
C) one of the first female puritans preachers
D) a leader of the Massachusetts bay colony

Answers

The answer is A. Phillis Wheatly learned to read and write in English, which was highly discouraged by most slave owners. Her owners, however, encouraged her to continue her studies of the English language.

During the 1950s and the 1960s which civil rights leader advocated black sepratism

Answers

MalcolmX advocated black separatism

Explain how the series of wars with France affected Britain's American subjects and helped pave way for their later rebellion against the mother country.

Answers

The American colonies had decent relationships with the French from the north. When Britain would wage war they would have to fight the French. They didn't want this and believed that Britain makes them fight wars that are against their well being and that they didn't cause in any way. They didn't want to fight wars against the French so they had another reason to rebel.

How did the Revolutionary War affect slaves?

Answers

About 5,000 Slaves served in the continental army, and by 1778 many states slaves who served in the American Revolution were granted their freedom.

As a result of the Revolutionary War, Slavery was eliminated in the North.

The American Revolutionary War lasted from 1775 to 1783. It was an 18th-century war waged between Great Britain and its Thirteen Colonies in alliance with France, which declared independence as the United States of America.

The war occurred after more than a decade of increasing estrangement between the British crown and a large and influential portion of its North American colonies.

(MC)What was one result of the migration from farms to cities during the late 19th century and early 20th century? steadily-rising wages for skilled and unskilled workers the inclusion of labor unions in the Democratic Party the rise of reform movements aimed at improving urban life increasing political pressure to provide subsidies to farmers

Answers

the rise of reform movements aimed at improving urban life

Imagine you are an Olympic speed skater. Explain which kinds of clothes you should wear to increase your speed. Other than air resistance on clothing, what other forces are working against your speed? What are some ideas reducing these other forces?

Answers

you should wear nylon clothes because it's sweat resistant, reducing the weight of the fabric.
wind, friction, height of the skater and the orientation of the knees and arms( inward/outward) work against your speed.
To reduce these forces, the skater's knees should be held inwards and the arms should contract towards the body, swinging hands alternatively.

There are many elements that can work against your speed, for example, your clothing. In order to improve this, you should wear light clothes that offer little to no resistance and that are tight on your body to allow for freedom of movement.

If you are skating outside, then the wind could affect your speed. This is one of the reasons why competitions are often held indoors. Moving to an indoor arena could help you improve your speed. Another force that could work against your speed is your personal strength and weight. If you get fitter, lighter or stronger, it is likely you will also be able to skate faster.

What region became the industrial center of the United States during the Industrial Revolution?
A. New England
B. The Mid-Atlantic
C. The South
D. The Midwest

Answers

D the Midwest became the industrial center of the united states during the industrial revolution

The industrial center of the United States during the Industrial Revolution was New England and the broader northeastern United States, especially in areas around the Great Lakes, also known as the Manufacturing Belt. The option (A) is correct.

The industrial center of the United States was concentrated in New England and the broader northeastern region, particularly around the Great Lakes, known as the Manufacturing Belt.

This area became a hub for manufacturing due to several factors: abundant waterways for transportation and power, proximity to raw materials like coal and iron ore, a skilled labor force, and a network of railroads connecting the region.

1). The $70 selling price of a bicycle is the cost increased by 4 times the cost. Find the cost?
2). Three pounds less than twice mikes weight is 215 pounds. What is his weight?
3). If mr Washingtons saving were increased by 5 times his savings. He would then save $36,000. How much has he saved ?

PLEASE SHOW YOUR WORK !!!!

Answers

1 ) The $70 selling price is the cost increased by 4 times:
Cost - x
4 x = 70
x = 70 : 4
x = 17.5
Answer: The cost is $17.5.
2 ) Mike`s weight - x
2 x - 3 = 215
2 x = 215 + 3
2 x = 218
x = 218 : 2
x = 109
Answer: Mike`s weight is 109 pounds.
3 ) Mr- Washington`s savings - x
5 x = 36,000
x = 36,000 : 5
x = 7,200
Answer: He has saved $7,200.

Why did the writings of the poet Virgil and the historian Livy focus on the rise and fall of Roman power?

Answers

 They wanted to arouse patriotism and restore traditional roman virtues      
Hope This Helps

Answer:

They wanted to arouse patriotism and restore traditional roman virtues. Some actions of roman emperors tended to flourish feelings against the republic; therefore people were not happy with their rulers’ values.

Explanation:

If 75% of India’s rural population lives in poverty, it most likely means that

Answers

Most of India's rural population is poor
They would live on less than 2 dollars a day

Which event is considered the beginning of the Civil War?
The Battle of Bull Run
The Battle of Fort Sumter
The standoff at Fort Pickens
The announcement of the Emancipation Proclamation

Answers

The Battle of Fort Sumter

The right answer would be the battle of fort Sumter because that was when the confederate attacked and stated the civil war.

I hope this helps

Well-educated people during the Renaissance learned

Answers

Final answer:

During the Renaissance, well-educated people learned about a variety of subjects including art, architecture, politics, science, and literature.

Explanation:

During the Renaissance, well-educated people learned about a variety of subjects including art, architecture, politics, science, and literature. They were influenced by the rediscovery of classical Greek philosophy and the revival of Greek statuary. The Renaissance was a time of intellectual growth and expansion of human knowledge.

Although horrific, the Japanese attack on Pearl Harbor was not reason enough for the United States to enter into World War II.

Answers

Hey!

 Your answer is false.

Although the war began with Adolf Hitler, the U.S ultimately did not decide to go to war until the Japanese bombed Pearl Harbor.

Hope this helps! :)


The US Constitution gives Congress the power to

Answers

Congress has the power to establish post offices and post roads, issue patents and copyrights, fix standards of weights and measures, establish courts inferior to the Supreme Court, and "To make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers"

What was the goal of Spanish missionaries in the new world

Answers

Gold - Find gold to bring back
God- spread religion 
Glory- basically wanted bragging rights to say they were the best because they were able to sail and find new land to claim and claim all the gold on the land

to teach the natives about christianity

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