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Dividing a circle into areas

In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = ${ n \choose 4 } + { n \choose 2 } + 1$, giving the sequence 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, .... Though the first five terms match the geometric progression 2n − 1, it deviates at n = 6, showing the risk of generalising from only a few observations.

Lemma
If there are n points on the circle and one more point is added, n lines can be drawn from the new point to previously existing points. Two cases are possible. In the first case (a), the new line passes through a point where two or more old lines (between previously existing points) cross. In the second case (b), the new line crosses each of the old lines in a different point. It will be useful to know the following fact.

Lemma. The new point A can be chosen so that case b occurs for each of the new lines.

Proof. For the case a, three points must be on one line: the new point A, the old point O to which the line is drawn, and the point I where two of the old lines intersect. There are n old points O, and hence finitely many points I where two of the old lines intersect. For each O and I, the line OI crosses the circle in one point other than O. Since the circle has infinitely many points, it has a point A which will be on none of the lines OI. Then, for this point A and all of the old points O, case b will be true.

This lemma means that, if there are k lines crossing AO, then each of them crosses AO at a different point and k + 1 new areas are created by the line AO.

Inductive method
The lemma establishes an important property for solving the problem. By employing an inductive proof, one can arrive at a formula for f(n) in terms of f(n − 1).

In the figure the dark lines are connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8). This figure illustrates the inductive step from n = 4 to n = 5 with the dashed lines. When the fifth point is added (i.e., when computing f(5) using f(4)), this results in four new lines (the dashed lines in the diagram) being added, numbered 1 through 4, one for each point that they connect to. The number of new regions introduced by the fifth point can therefore be determined by considering the number of regions added by each of the 4 lines. Set i to count the lines being added. Each new line can cross a number of existing lines, depending on which point it is to (the value of i). The new lines will never cross each other, except at the new point.

The number of lines that each new line intersects can be determined by considering the number of points on the "left" of the line and the number of points on the "right" of the line. Since all existing points already have lines between them, the number of points on the left multiplied by the number of points on the right is the number of lines that will be crossing the new line. For the line to point i, there are

 * n − i − 1

points on the left and

 * i − 1

points on the right, so a total of

 * (n − i  − 1) (i  − 1)

lines must be crossed.

In this example, the lines to i = 1 and i = 4 each cross zero lines, while the lines to i = 2 and i = 3 each cross two lines (there are two points on one side and one on the other).

So the recurrence can be expressed as

 * $$f(n) = f(n - 1) + \sum^{n-1}_{i=1} \big(1 + (n - i - 1)(i - 1)\big),$$

which can be easily reduced to

 * $$f(n) = f(n - 1) + \sum^{n-1}_{i=1} (2 - n + ni - i^2).$$

Using the sums of the first $$(n - 1)$$ natural numbers and the first $$(n - 1)$$ squares, this combines to

 * $$f(n) = f(n - 1) + \frac{1}{6} n^3 - n^2 + \frac{17}{6} n - 2.$$

Finally,

 * $$f(n) = \sum^{n}_{k=1} \left(\frac{1}{6} k^3 - k^2 + \frac{17}{6} k - 2\right) + 1,$$ with $$f(0) = 1,$$

which yields

 * $$f(n) = \frac{n}{24}(n^3 - 6n^2 + 23n - 18) + 1.$$

Combinatorics and topology method
The lemma asserts that the number of regions is maximal if all "inner" intersections of chords are simple (exactly two chords pass through each point of intersection in the interior). This will be the case if the points on the circle are chosen "in general position". Under this assumption of "generic intersection", the number of regions can also be determined in a non-inductive way, using the formula for the Euler characteristic of a connected planar graph (viewed here as a graph embedded in the 2-sphere S2).

A planar graph determines a cell decomposition of the plane with F faces (2-dimensional cells), E edges (1-dimensional cells) and V vertices (0-dimensional cells). As the graph is connected, the Euler relation for the 2-dimensional sphere S2
 * $$\, V-E+F=2 $$

holds. View the diagram (the circle together with all the chords) above as a planar graph. If the general formulas for V and E can both be found, the formula for F can also be derived, which will solve the problem.

Its vertices include the n points on the circle, referred to as the exterior vertices, as well as the interior vertices, the intersections of distinct chords in the interior of the circle. The "generic intersection" assumption made above guarantees that each interior vertex is the intersection of no more than two chords.

Thus the main task in determining V is finding the number of interior vertices. As a consequence of the lemma, any two intersecting chords will uniquely determine an interior vertex. These chords are in turn uniquely determined by the four corresponding endpoints of the chords, which are all exterior vertices. Any four exterior vertices determine a cyclic quadrilateral, and all cyclic quadrilaterals are convex quadrilaterals, so each set of four exterior vertices have exactly one point of intersection formed by their diagonals (chords). Further, by definition all interior vertices are formed by intersecting chords.

Therefore, each interior vertex is uniquely determined by a combination of four exterior vertices, where the number of interior vertices is given by
 * $$V_{\text{interior}} = { n \choose 4 },$$

and so
 * $$V = V_{\text{exterior}} + V_{\text{interior}} = n + { n \choose 4 }.$$

The edges include the n circular arcs connecting pairs of adjacent exterior vertices, as well as the chordal line segments (described below) created inside the circle by the collection of chords. Since there are two groups of vertices: exterior and interior, the chordal line segments can be further categorized into three groups:
 * 1) Edges directly (not cut by other chords) connecting two exterior vertices. These are chords between adjacent exterior vertices, and form the perimeter of the polygon. There are n such edges.
 * 2) Edges connecting two interior vertices.
 * 3) Edges connecting an interior and exterior vertex.

To find the number of edges in groups 2 and 3, consider each interior vertex, which is connected to exactly four edges. This yields
 * $$4{ n \choose 4 }$$

edges. Since each edge is defined by two endpoint vertices, only the interior vertices were enumerated, group 2 edges are counted twice while group 3 edges are counted once only.

Every chord that is cut by another (i.e., chords not in group 1) must contain two group 3 edges, its beginning and ending chordal segments. As chords are uniquely determined by two exterior vertices, there are altogether
 * $$2\left( { n \choose 2 } - n \right)$$

group 3 edges. This is twice the total number of chords that are not themselves members of group 1.

The sum of these results divided by two gives the combined number of edges in groups 2 and 3. Adding the n edges from group 1, and the n circular arc edges brings the total to
 * $$E = \frac{4{ n \choose 4 } + 2\left( { n \choose 2 } - n \right)}{2} + n + n = 2{ n \choose 4 } + { n \choose 2 } + n.$$

Substituting V and E into the Euler relation solved for F, $$\, F = E - V + 2, $$ one then obtains
 * $$ F = { n \choose 4 } + { n \choose 2 } + 2.$$

Since one of these faces is the exterior of the circle, the number of regions rG inside the circle is F − 1, or

 * $$ r_G={n \choose 4}+{n \choose 2}+1,$$

which resolves to

 * $$r_G=\frac{n!}{(n-4)! 4!}+\frac{n!}{(n-2)! 2!}+1$$

which yields the same quartic polynomial obtained by using the inductive method

 * $$r_G=\frac{1}{24}n(n^3-6n^2+23n-18)+1$$

The fifth column of Bernoulli's triangle (k = 4) gives the maximum number of regions in the problem of dividing a circle into areas for n + 1 points, where n ≥ 4.

Application to mathematical billiards inside the circle
Considering the force-free motion of a particle inside a circle it was shown (see D. Jaud) that for specific reflection angles along the circle boundary the associated area division sequence is given by an arithmetic series.

title: Dividing a circle into areas


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Liberal feminism

Liberal feminism, also called mainstream feminism, is a main branch of feminism defined by its focus on achieving gender equality through political and legal reform within the framework of liberal democracy and informed by a human rights perspective. It is often considered culturally progressive and economically center-right to center-left. As the oldest of the "Big Three" schools of feminist thought, liberal feminism has its roots in 19th century first-wave feminism seeking recognition of women as equal citizens, focusing particularly on women's suffrage and access to education, the effort associated with 19th century liberalism and progressivism. Liberal feminism "works within the structure of mainstream society to integrate women into that structure." Liberal feminism places great emphasis on the public world, especially laws, political institutions, education and working life, and considers the denial of equal legal and political rights as the main obstacle to equality. As such liberal feminists have worked to bring women into the political mainstream. Liberal feminism is inclusive and socially progressive, while broadly supporting existing institutions of power in liberal democratic societies, and is associated with centrism and reformism. Liberal feminism tends to be adopted by white middle-class women who do not disagree with the current social structure; Zhang and Rios found that liberal feminism with its focus on equality is viewed as the dominant and "default" form of feminism. Liberal feminism actively supports men's involvement in feminism and both women and men have always been active participants in the movement; progressive men had an important role alongside women in the struggle for equal political rights since the movement was launched in the 19th century.

Historically, liberal feminism largely grew out of and was often associated with social liberalism; the modern liberal feminist tradition notably includes both social liberal and social democratic streams, as well as many often diverging schools of thought such as equality feminism, social feminism, care-ethical liberal feminism, equity feminism, difference feminism, conservative liberal feminism, and liberal socialist feminism. Some forms of modern liberal feminism have been described as neoliberal feminism or "boardroom feminism". Liberal feminism is often closely associated with liberal internationalism. In many countries, particularly in the West but also in a number of secular states in the developing world, liberal feminism is associated with the concept of state feminism, and liberal feminism emphasizes constructive cooperation with the government and involvement in parliamentary and legislative processes to pursue reforms. Liberal feminism is also called "mainstream feminism", "reformist feminism", "egalitarian feminism", or historically "bourgeois feminism" (or bourgeois-liberal feminism), among other names. As one of the "Big Three" schools of feminist thought, liberal feminism is often contrasted with socialist/Marxist feminism and radical feminism: unlike them, liberal feminism seeks gradual social progress and equality on the basis of liberal democracy rather than a revolution or radical reordering of society. Liberal feminism and mainstream feminism are very broad terms, frequently taken to encompass all feminism that is not radical or revolutionary socialist/Marxist and that instead pursues equality through political, legal, and social reform within a liberal democratic framework. As such, liberal feminists may subscribe to a range of different feminist beliefs and political ideologies within the democratic spectrum from the centre-left to the centre-right.

Inherently pragmatic in orientation, liberal feminists have emphasized building far-reaching support for feminist causes among both women and men, and among the political centre, the government and legislatures. In the 21st century, liberal feminism has taken a turn toward an intersectional understanding of gender equality, and modern liberal feminists support LGBT rights as a core feminist issue. Liberal feminists typically support laws and regulations that promote gender equality and ban practices that are discriminatory towards women; mainstream liberal feminists, particularly those of a social democratic bent, often support social measures to reduce material inequality within a liberal democratic framework. While rooted in first-wave feminism and traditionally focused on political and legal reform, the broader liberal feminist tradition may include parts of subsequent waves of feminism, especially third-wave feminism and fourth-wave feminism. The sunflower and the color gold, taken to represent enlightenment, became widely used symbols of mainstream liberal feminism and women's suffrage from the 1860s, originally in the United States and later also in parts of Europe.

Terminology
The specific term "liberal feminism" is fairly modern, but its political tradition is much older. "Feminism" became the dominant term in English for the struggle for women's rights in the late 20th century, around a century after the organized liberal women's rights movement came into existence, but most western feminist historians contend that all movements working to obtain women's rights should be considered feminist movements, even when they did not (or do not) apply the term to themselves.

Historically, the bourgeois women's rights movement—the predecessor of modern liberal feminism—was mainly contrasted with the working-class or "proletarian" women's movements, which eventually developed into called socialist and Marxist feminism. Since the 1960s both liberal feminism and the "proletarian" or socialist/Marxist women's movements are also contrasted with radical feminism. Liberal feminism is usually included as one of the two, three, or four main traditions in the history of feminism.

Many liberal feminists embraced the term "feminism" in the 1970s or 1980s, although some initially expressed scepticism towards the term; for example the liberal feminist Norwegian Association for Women's Rights expressed scepticism towards the term "feminism" as late as 1980 because it could foster "unnecessary antagonism towards men", but accepted the term some years later as it increasingly became the mainstream general term for the women's rights struggle in the western world.

Movement
Liberal feminism ultimately has historical roots in classical liberalism and was often associated with social liberalism from the late 19th century. The goal for liberal feminists beginning in the late 18th century was to gain suffrage for women with the idea that this would allow them to gain individual liberty. They were concerned with gaining freedom through equality, diminishing men's cruelty to women, and gaining opportunities to become full persons. They believed that no government or custom should prohibit the due exercise of personal freedom. Early liberal feminists had to counter the assumption that only white men deserved to be full citizens. Pioneers such as Mary Wollstonecraft, Judith Sargent Murray, and Frances Wright advocated for women's full political inclusion. In 1920, after nearly 50 years of intense activism, women were finally granted the right to vote and the right to hold public office in the United States, and in much of the Western world within a few decades before or a few decades after this time.

Liberal feminism was largely quiet in the United States for four decades after winning the vote. In the 1960s during the civil rights movement, liberal feminists drew parallels between systemic race discrimination and sex discrimination. Groups such as the National Organization for Women, the National Women's Political Caucus, and the Women's Equity Action League were all created at that time to further women's rights. In the U.S., these groups have worked, thus far unsuccessfully, for the ratification of the Equal Rights Amendment or "Constitutional Equity Amendment", in the hopes it will ensure that men and women are treated as equals under the law. Specific issues important to liberal feminists include but are not limited to reproductive rights and abortion access, sexual harassment, voting, education, fair compensation for work, affordable childcare, affordable health care, and bringing to light the frequency of sexual and domestic violence against women.

Equal Rights Amendment
A fair number of American liberal feminists believe that equality in pay, job opportunities, political structure, social security, and education for women especially needs to be guaranteed by the U.S. Constitution.

Three years after women won the right to vote, the Equal Right Amendment (ERA) was introduced in Congress by Senator Charles Curtis Curtis and Representative Daniel Read Anthony Jr., both Republicans. This amendment stated that civil rights cannot be denied on the basis of one's sex. It was authored by Alice Paul, head of the National Women's Party, who led the suffrage campaign. Through the efforts of Alice Paul, the Amendment was introduced into each session of the United States Congress, but it was buried in committee in both Houses of Congress. In 1946, it was narrowly defeated by the full Senate, 38–35. In February 1970, twenty NOW leaders disrupted the hearings of the U.S. Senate Subcommittee on Constitutional Amendments, demanding the ERA be heard by the full Congress. In May of that year, the Senate Subcommittee began hearings on the ERA under Senator Birch Bayh. In June, the ERA finally left the House Judiciary Committee due to a discharge petition filed by Representative Martha Griffiths. In March 1972, the ERA was approved by the full Senate without changes, 84–8. Senator Sam Ervin and Representative Emanuel Celler succeeded in setting a time limit of seven years for ratification. The ERA then went to the individual states for approval but failed to win in enough of them (38) to become law. In 1978, Congress passed a disputed (less than supermajority) three-year extension on the original seven-year ratification limit, but the ERA could not gain approval by the needed number of states.

The state legislatures that were most hostile to the ERA were Utah, Florida, Illinois, North Carolina, and Oklahoma. The NOW holds that the single most obvious problem in passing the ERA was the gender and racial imbalance in the legislatures. More than 2/3 of the women and all of the African Americans in state legislatures voted for the ERA, but less than 50% of the white men in the targeted legislatures cast pro-ERA votes in 1982.

Equal rights
According to Anthony Giddens, liberal feminist theory "believes gender inequality is produced by reduced access for women and girls to civil rights and allocation of social resources such as education and employment." Catherine Rottenberg notes that the raison d'être of classic liberal feminism was "to pose an immanent critique of liberalism, revealing the gendered exclusions within liberal democracy’s proclamation of universal equality, particularly with respect to the law, institutional access, and the full incorporation of women into the public sphere." Rottenberg contrasts classic liberal feminism with modern neoliberal feminism which "seems perfectly in sync with the evolving neoliberal order."

At its core, liberal feminism believes in pragmatic "reforms against gender discrimination through the promotion of equal rights by engaging and formulating laws and policies that will ensure equality." Liberal feminists argue that society holds the false belief that women are, by nature, less intellectually and physically capable than men; thus it tends to discriminate against women in the academy, the forum, and the marketplace. Liberal feminists believe that "female subordination is rooted in a set of customary and legal constraints that blocks women's entrance to and success in the so-called public world", and strive for gender equality via political and legal reform. Cathrine Holst notes that "the bourgeois women's rights movement was liberal or liberal feminist. The bourgeois women's rights advocates fought for women’s civil liberties and rights: freedom of speech, freedom of movement, the right to vote, freedom of association, inheritance rights, property rights, and freedom of trade – and for women's access to education and working life. In short, women should have the same freedoms and rights as men."

Political liberalism gave feminism a familiar platform for convincing others that their reforms "could and should be incorporated into existing law". Liberal feminists argued that women, like men, be regarded as autonomous individuals, and likewise be accorded the rights of such. Inherently pragmatic, liberal feminists tend to focus on practical reforms of laws and policies in order to achieve equality; liberal feminism has a more individualistic approach to justice than left-wing branches of feminism such as socialist or radical feminism. Susan Wendell argues that "liberal feminism is an historical tradition that grew out of liberalism, as can be seen very clearly in the work of such feminists as Mary Wollstonecraft and John Stuart Mill, but feminists who took principles from that tradition have developed analyses and goals that go far beyond those of 18th and 19th century liberal feminists, and many feminists who have goals and strategies identified as liberal feminist ... reject major components of liberalism" in a modern or party-political sense; she highlights "equality of opportunity" as a defining feature of liberal feminism. Helga Hernes notes that liberal feminism has often been critical of liberalist political positions and that liberal feminism and liberalism in general are not necessarily the same.

Lucy E. Bailey notes that liberal feminism is characterized by "its focus on individual rights and reform through the state" and that it has "been instrumental in fueling women's rights movements in diverse contexts and remains a familiar and widespread form of feminist thought. Liberal feminism emerged as a distinct political tradition during the Enlightenment (...) Liberal feminist theory emphasizes women's individual rights to autonomy and proposes remedies for gender inequities through, variously, removing legal and social constraints or advancing conditions that support women's equality."

LGBT rights
Liberal feminist organizations are broadly inclusive and thus tend to support LGBT rights in the modern era. For example, the two largest American feminist organizations, the liberal feminist National Organization for Women (NOW) and the League of Women Voters (LWV) both regard LGBT rights as a core feminist issue and vehemently support trans rights and oppose transphobia. NOW president Terry O'Neill said the struggle against transphobia is a feminist issue. NOW has affirmed that "trans women are women, trans girls are girls." In a further statement NOW said that "trans women are women. They deserve equal opportunity, health care, a safe community & workplace, and they deserve to play sports. They have a right to have their identity respected without conforming to perceived sex and gender identity standards. We stand with you."

Similarly, the traditionally dominant liberal feminist international non-governmental organization, the International Alliance of Women (IAW) and its affiliates are trans-inclusive; IAW's Icelandic affiliate, the Icelandic Women's Rights Association, has stated that "IWRA works for the rights of all women. Feminism without trans women is no feminism at all." On Women's Rights Day in Iceland in 2020, the Icelandic Women's Rights Association organised an event together with Trans Ísland that saw several different feminist organisations in the country discuss strategies to stop anti-trans sentiment from increasing its influence in Iceland. Later that year, Trans Ísland was unanimously granted status as a member association of the Icelandic Women's Rights Association. In 2021 the International Alliance of Women and the Icelandic Women's Rights Association organized an event on how the women's movement could counter "anti-trans voices [that] are becoming ever louder and [that] are threatening feminist solidarity across borders." The Danish Women's Society supports LGBTQA rights, and has stated that it takes homophobia and transphobia very seriously, and that "we support all initiatives that promote the rights of gay and transgender people." The Norwegian Association for Women's Rights is trans-inclusive and supports legal protections against discrimination on the basis of sexual orientation, gender identity, and gender expression. The Deutscher Frauenring is intersectional and opposes transphobia. In November 2020, on Trans Day of Remembrance, the National Women's Council of Ireland and Amnesty International Ireland co-signed a statement along with a number of LGBT+ and human rights groups condemning trans-exclusionary feminism. The letter called upon the media and politicians "to no longer provide legitimate representation for those that share bigoted beliefs, that are aligned with far-right ideologies and seek nothing but harm and division" and stated that "these fringe internet accounts stand against affirmative medical care of transgender people, and they stand against the right to self-identification of transgender people in this country. In summation, they stand against trans, women’s, and gay rights by aligning themselves with far-right tropes and stances."

UN Women works to promote gender equality and the rights of women and LGBTIQ+ people, and "urgently calls on communities and governments around the world to stand up for LGBTIQ+ rights." The Association for Women's Rights in Development (AWID) supports LGBTIQ rights and opposes the anti-gender movement, and has described trans-exclusionary feminists as "trojan horses in human rights spaces" that seek to undermine human rights; AWID said that anti-trans activity is "alarming," that "the 'sex-based' rhetoric misuses concepts of sex and gender to push a deeply discriminatory agenda" and that "trans-exclusionary feminists (...) undermine progressions on gender and sexuality and protection of rights of marginalized groups." To be clear, while there are debates, UN Women is said to be a liberal feminist organization. As evidence, although they seem to acknowledge intersectionality, UN Women still evaluate gender equality in each country by looking at how integrated women are into hegemonic society, for example they measure how many women are in a position of CEO and politician.

Schools of thought
Liberal feminism as a broad school of thought and main tradition in feminism includes many different varieties, such as equality feminism, social feminism, equity feminism, and difference feminism. State feminism is often linked to liberal feminism, particularly in Western countries. Some forms of modern liberal feminism have been described as neoliberal feminism.

Neoliberal feminism
Neoliberal feminism emerged in the 2010s. In The Rise of Neoliberal Feminism, Rottenberg defines neoliberalism as a “new form of selfhood, which encourages people as individual subjects responsible for their own well-being” as well as it ensures the individual right to their own autonomous decision making (p. 421). The author argues that neoliberal feminism emerged from neoliberalism being espoused by “increasingly high-powered women”, for example Anne-Marie Slaughters and Sheryl Sandberg (p. 418). Even though Sandberg states in Lean In that she “supports who want to eliminate external barriers” so that every woman can lean in, she argues that as the first step, women should lean in so as to reform society (p. 3). Therefore, women who are worried about the possibility of having a child at the cost of her career should not “lean back” but keep leaning in (p. 51). Sandberg does not seek reformation of social system, which she even calls “the rat race” (p. 51). Neoliberal feminists apparently realize the gender inequality. However, they value women who accept the responsibility for taking balance between work and family following the theory of neoliberalism, in which they do not accuse the state but take care of their own well-being. As a political reason for emergence of neoliberal feminism, Rottenberg asserts that by “responsiblizing” women, neoliberalism feminism is useful for diffusing social issues (i.e., sexism, racism, capitalism).

Libertarian feminism
Individualist or libertarian feminism is sometimes grouped as one of many branches of feminism with historical roots in liberal feminism but tends to diverge significantly from mainstream liberal feminism on many issues. For example, "libertarian feminism does not require social measures to reduce material inequality; in fact, it opposes such measures ... in contrast, liberal feminism may support such requirements and egalitarian versions of feminism insist on them." Libertarian feminists tend to focus more on sexual politics, a topic traditionally of less concern to liberal feminists. Mainstream liberal feminists, such as the National Organization for Women, tend to oppose prostitution, but are somewhat divided on prostitution politics, unlike both libertarian and radical feminists.

Western feminism
Liberal feminist organizations such as the International Alliance of Women tend to be supportive of liberal democratic states' foreign and security policy, and maintained a clear pro-Western stance throughout the Cold War. From the second half of the 20th century women in development has increasingly become an important topic for liberal feminist organizations.

Hillary Clinton is often considered a liberal feminist, and has defined "feminist" in accordance with the liberal feminist definition as "someone who believes in equal rights." Some articles do not clearly describe her as a liberal feminist, yet argue that Clinton's policy and her white privilege ignore many women, for instance women of color, low-income women, and immigrants  while NOW (2015) admire her as “a trailblazer for women with an impressive record of public service where she put women’s rights at the forefront”.

Equity feminism
Equity feminism is a form of liberal feminism discussed since the 1980s, specifically a kind of classically liberal or libertarian feminism, emphasizing equality under law, equal freedoms, and rights, rather than profound social transformations.

The Stanford Encyclopedia of Philosophy refers to Wendy McElroy, Joan Kennedy Taylor, Cathy Young, Rita Simon, Katie Roiphe, Diana Furchtgott-Roth, Christine Stolba, and Christina Hoff Sommers as equity feminists. Steven Pinker, an evolutionary psychologist, identifies himself as an equity feminist, which he defines as "a moral doctrine about equal treatment that makes no commitments regarding open empirical issues in psychology or biology". Barry Kuhle asserts that equity feminism is compatible with evolutionary psychology, in contrast to gender feminism.

Writers
Feminist writers associated with this theory include Mary Wollstonecraft, John Stuart Mill, Helen Taylor, Elizabeth Cady Stanton, and Gina Krog; Second Wave feminists Betty Friedan, Gloria Steinem, Simone de Beauvoir; and Third Wave feminist Rebecca Walker.

Mary Wollstonecraft

Mary Wollstonecraft (1759–1797) has been very influential in her writings as A Vindication of the Rights of Woman commented on society's view of women and encouraged women to use their voices in making decisions separate from decisions previously made for them. Wollstonecraft "denied that women are, by nature, more pleasure seeking and pleasure giving than men. She reasoned that if they were confined to the same cages that trap women, men would develop the same flawed characters. What Wollstonecraft most wanted for women was personhood." She argued that patriarchal oppression is a form of slavery that could no longer be ignored. Wollstonecraft argued that the inequality between men and women existed due to the disparity between their educations. Along with Judith Sargent Murray and Frances Wright, Wollstonecraft was one of the first major advocates for women's full inclusion in politics.

Elizabeth Cady Stanton

Elizabeth Cady Stanton (1815–1902) was one of the most influential women in first wave feminism. An American social activist, she was instrumental in orchestrating the Seneca Falls Convention, the first women's rights convention, which was held in Seneca Falls, New York. Not only was the suffragist movement important to Stanton, she also was involved in women's parental and custody rights, divorce laws, birth control, employment and financial rights, among other issues. Her partner in this movement was the equally influential Susan B. Anthony. Together, they fought for a linguistic shift in the Fourteenth and Fifteenth Amendments to include "female". Additionally, in 1890 she founded the National American Woman Suffrage Association and presided as president until 1892. She produced many speeches, resolutions, letters, calls, and petitions that fed the first wave and kept the spirit alive. Furthermore, by gathering a large number of signatures, she aided the passage of the Married Women's Property Act of 1848 which considered women legally independent of their husbands and granted the property of their own. Together these women formed what was known as the NWSA (National Women Suffrage Association), which focused on working with legislatures and the courts to gain suffrage.

John Stuart Mill

John Stuart Mill (20 May 1806 – 7 May 1873) believed that both sexes should have equal rights under the law and that "until conditions of equality exist, no one can possibly assess the natural differences between women and men, distorted as they have been. What is natural to the two sexes can only be found out by allowing both to develop and use their faculties freely." Mill frequently spoke of this imbalance and wondered if women were able to feel the same "genuine unselfishness" that men did in providing for their families. This unselfishness Mill advocated is the one "that motivates people to take into account the good of society as well as the good of the individual person or small family unit". Similar to Mary Wollstonecraft, Mill compared sexual inequality to slavery, arguing that their husbands are often just as abusive as masters and that a human being controls nearly every aspect of life for another human being. In his book The Subjection of Women, Mill argues that three major parts of women's lives are hindering them: society and gender construction, education, and marriage. He also argues that sex inequality is greatly inhibiting the progress of humanity.

Betty Friedan

Betty Friedan (1921–2006) was a liberal feminist prominent in the 1960s. She was a co-founder and the first president of NOW, and contributed to the second wave feminism. Her book The Feminine Mystique, written in 1963, became a landmark bestseller and significantly influential by rebuking the fulfillment of middle-class women for domestic lives. In her book, Friedan reversed the discourse of American housewife as ideal and happy and pointed out dissatisfaction and loneliness which were faced by many American women in the 1950s and 1960s. She described these women's experience as a problem without name and called for financial independence of women for liberation. Many articles argue that Friedan was unaware of her white privilege and failed to realize intersectionality of women. For example, by stating that "only economic independence can free a woman to marry for love", Friedan attempted to encourage every woman not to "be afraid of flying" and seek their own lives outside of household. She also argued the necessity of a social and political women's movement by raising the black civil rights movement as a model. However, she did not try to combine those movements together, nor was black women's experience considered in feminist context. Instead, she presumed the separation of issues of race and sex.

Notable liberal feminists

 * 18th century

 * Judith Sargent Murray
 * Mary Wollstonecraft
 * Frances Wright

 * 19th century

 * Susan B. Anthony
 * Gina Krog
 * John Stuart Mill
 * Elizabeth Cady Stanton
 * Harriet Taylor
 * Harriet Tubman

 * 20th century

 * Margarete Bonnevie
 * Karin M. Bruzelius
 * Betty Friedan
 * Eva Kolstad
 * Martha Nussbaum
 * Gloria Steinem
 * Nadine Strossen
 * Rebecca Walker
 * Naomi Wolf

 * 21st century

 * Hillary Clinton
 * Kamala Harris
 * Sheryl Sandberg
 * Anne-Marie Slaughter

National Organization for Women
The National Organization for Women (NOW) is the largest liberal feminist organization in the United States. It supports the Equal Rights Amendment, reproductive rights including freer access to abortion, as well as lesbian, gay, bisexual, and transgender rights (LGBT rights), and economic justice. It opposes violence against women and racism.

Various other issues the National Organization for Women also deals with are:

 * Affirmative action
 * Disability rights
 * EcoFeminism
 * Family
 * Opposing right-wing causes contrary to NOW's interests
 * Global feminism
 * Women's health
 * Immigration
 * Promotion of nominating judges with feminist viewpoints
 * Legislation
 * Legal recognition of same-sex marriages
 * Media activism
 * Mothers' economic rights
 * Working for peace; opposition to conflicts such as the Iraq War
 * Social Security
 * Supreme Court
 * Title IX/Education
 * Welfare
 * Workplace discrimination
 * Women in the military
 * Young feminist programs

National Women's Political Caucus
The National Women's Political Caucus (NWPC), founded in 1971, is the only national organization in the U.S. dedicated exclusively to increasing women's participation in all areas of political and public life as elected and appointed officials, as delegates to national party conventions, as judges in the state and federal courts, and as lobbyists, voters and campaign organizers.

Founders of NWPC include such prominent women as Gloria Steinem, author, lecturer and founding editor of Ms. Magazine; former Congresswoman Shirley Chisholm; former Congresswoman Bella Abzug; Dorothy Height, former president of the National Council of Negro Women; Jill Ruckelshaus, former U.S. Civil Rights Commissioner; Ann Lewis, former Political Director of the Democratic National Committee; Elly Peterson, former vice-chair of the Republican National Committee; LaDonna Harris, Indian rights leader; Liz Carpenter, author, lecturer and former press secretary to Lady Bird Johnson; and Eleanor Holmes Norton, Delegate to the U.S. House of Representatives and former chair of the Equal Employment Opportunity Commission.

These women were spurred by Congress' failure to pass the Equal Rights Amendment in 1970. They believed legal, economic and social equity would come about only when women were equally represented among the nation's political decision-makers. Their faith that women's interests would best be served by women lawmakers has been confirmed time and time again, as women in Congress, state legislatures and city halls across the country have introduced, fought for and won legislation to eliminate sex discrimination and meet women's changing needs.

Women's Equity Action League
The Women's Equity Action League (WEAL) was a national membership organization, with state chapters and divisions, founded in 1968 and dedicated to improving the status and lives of women primarily through education, litigation, and legislation. It was a more conservative organization than NOW and was formed largely by former members of that organization who did not share NOW's the assertive stance on socio-sexual issues, particularly on abortion rights. WEAL spawned a sister organization, the Women's Equity Action League Fund, which was incorporated in 1972 "to help secure legal rights for women and to carry on educational and research projects on sex discrimination". The two organizations merged in 1981 following changes in the tax code. WEAL dissolved in 1989.

The stated purposes of WEAL were:
 * to promote greater economic progress on the part of American women;
 * to press for full enforcement of existing anti-discriminatory laws on behalf of women;
 * to seek correction of de facto discrimination against women;
 * to gather and disseminate information and educational material;
 * to investigate instances of, and seek solutions to, economic, educational, tax, and employment problems affecting women;
 * to urge that girls be prepared to enter more advanced career fields;
 * to seek reappraisal of federal, state, and local laws and practices limiting women's employment opportunities;
 * to combat by all lawful means, job discrimination against women in the pay, promotional or advancement policies of governmental or private employers;
 * to seek the cooperation and coordination of all American women, individually or as organizations *to attain these objectives, whether through legislation, litigation, or other means and by doing any and all things necessary or incident thereto.

Norwegian Association for Women's Rights

Norway has had a tradition of government-supported liberal feminism since 1884, when the Norwegian Association for Women's Rights (NKF) was founded with the support of the progressive establishment within the then-dominant governing Liberal Party (which received 63.4% of the votes in the election the following year). The association's founders included five Norwegian prime ministers, and several of its early leaders were married to prime ministers. Rooted in first-wave liberal feminism, it works "to promote gender equality and women's and girls' human rights within the framework of liberal democracy and through political and legal reform". NKF members had key roles in developing the government apparatus and legislation related to gender equality in Norway since 1884; with the professionalization of gender equality advocacy from 1970s, the "Norwegian government adopted NKF's [equality] ideology as its own" and adopted laws and established government institutions such as the Gender Equality Ombud based on NKF's proposals; the new government institutions to promote gender equality were also largely built and led by prominent NKF members such as Eva Kolstad, NKF's former president and the first Gender Equality Ombud. NKF's feminist tradition has often been described as Norway's state feminism. The term state feminism itself was coined by NKF member Helga Hernes. Although it grew out of 19th-century progressive liberalism, Norwegian liberal feminism is not limited to liberalism in a modern party-political sense, and NKF is broadly representative of the democratic political spectrum from the center-left to the center-right, including the social democratic Labour Party. Norwegian supreme court justice and former NKF President Karin Maria Bruzelius has described NKF's liberal feminism as "a realistic, sober, practical feminism".

Other organizations

 * Feminist Majority Foundation
 * Ms. Magazine
 * EMILY's List
 * Icelandic Women's Rights Association

Symbolism
The sunflower (and sometimes by analogy the Sun) and the color yellow/gold (Or in heraldry), taken to represent enlightenment, became widely used symbols of the mainstream liberal women's rights movement and women's suffrage from the 1860s, originally in the United States and later also in parts of Europe. The suffragists and liberal feminists Elizabeth Cady Stanton and Susan B. Anthony encouraged the use of the sunflower by wearing sunflower pins when campaigning for the right to vote in 1867 in Kansas. Hence the colors yellow and white became the main colors of the international liberal (also called mainstream or bourgeois) suffrage movement around the turn of the century, notably used by the International Woman Suffrage Alliance. Historians Cheris Kramarae and Paula A. Treichler noted that

"Colors were important in the iconography of the suffrage movement. The use of the color gold began with Elizabeth Cady Stanton and Susan B. Anthony’s campaign in Kansas in 1867 and derived from the color of the sunflower, the Kansas state symbol. Suffragists used gold pins, ribbons, sashes, and yellow roses to symbolize their cause. In 1876, during the U.S. Centennial, women wore yellow ribbons and sang the song “The Yellow Ribbon.” In 1916, suffragists staged “The Golden Lane” at the national Democratic convention; to reach the convention hall, all delegates had to walk through a line of women stretching several blocks long, dressed in white with gold sashes, carrying yellow umbrellas, and accompanied by hundreds of yards of draped gold bunting. Gold also signified enlightenment, the professed goal of the mainstream U.S. suffrage movement."

The sunflower and/or the color yellow/gold remain in use among the older liberal (bourgeois) feminist organizations such as the Norwegian Association for Women's Rights and the International Alliance of Women that were founded during the struggle for women's suffrage.

The color yellow is also widely used as a symbol of liberalism in general.

Gender roles
Critics of liberal feminism argue that its individualist assumptions make it difficult to see the ways in which underlying social structures and values disadvantage women. They argue that even if women are not dependent upon individual men, they are still dependent upon a patriarchal state. These critics believe that institutional changes, like the introduction of women's suffrage, are insufficient to emancipate women.

According to Zhang and Rios, "liberal feminism tends to be adopted by 'mainstream' (i.e., middle-class) women who do not disagree with the current social structure." They found that liberal feminist beliefs were viewed as the dominant and "default" form of feminism.

One of the more prevalent critiques of liberal feminism is that it, as a study, allows too much of its focus to fall on a "metamorphosis" of women into men, and in doing so, it disregards the significance of the traditional role of women. One of the leading scholars who have critiqued liberal feminism is radical feminist Catherine A. MacKinnon, an American lawyer, writer, and social activist. Specializing in issues regarding sex equality, she has been intimately involved in cases regarding the definition of sexual harassment and sex discrimination. She, among other radical feminist scholars, views liberalism and feminism as incompatible, because liberalism offers women a "piece of the pie as currently and poisonously baked".

Racial attitudes
bell hooks' main criticism of the philosophies of liberal feminism is that they focus too much on an equality with men in their own class. She maintains that the "cultural basis of group oppression" is the biggest challenge, in that liberal feminists tend to ignore it.

Another important critique of liberal feminism posits the existence of a "white woman's burden" or white savior complex. The phrase "white woman's burden" derives from "The White Man's Burden". Critics such as Black feminists and postcolonial feminists assert that mainstream liberal feminism reflects only the values of middle-class, heterosexual, white women and fails to appreciate the position of women of different races, cultures, or classes. With this, white liberal feminists reflect the issues that underlie the white savior complex. They do not understand women that are outside the dominant society but try to "save" or "help" them by pushing them to assimilate into their ideals of feminism. According to such critics, liberal feminism fails to recognize the power dynamics that are in play with women of color and transnational women which involve multiple sources of oppression.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Liberal feminism


text:
Sloth bear

The sloth bear (Melursus ursinus), also known as the Indian bear, is a myrmecophagous bear species native to the Indian subcontinent. It feeds on fruits, ants and termites. It is listed as vulnerable on the IUCN Red List, mainly because of habitat loss and degradation. It is the only species in the genus Melursus.

It has also been called "labiated bear" because of its long lower lip and palate used for sucking up insects. It has long, shaggy fur, a mane around the face, and long, sickle-shaped claws. It is lankier than brown and Asian black bears. It shares features of insectivorous mammals and evolved during the Pleistocene from the ancestral brown bear through divergent evolution.

Sloth bears breed during spring and early summer and give birth near the beginning of winter. When their territories are encroached upon by humans, they sometimes attack them. Historically, humans have drastically reduced these bears' habitat and diminished their population by hunting them for food and products such as their bacula and claws. Sloth bears have been tamed and used as performing animals and as pets.

Taxonomy
George Shaw in 1791 named the species Bradypus ursinus. In 1793, Meyer named it Melursus lybius, and in 1817, de Blainville named it Ursus labiatus because of its long lips. Illiger named it Prochilus hirsutus, the Greek genus name indicating long lips, while the specific name noted its long and coarse hair. Fischer called it Chondrorhynchus hirsutus, while Tiedemann named it Ursus longirostris.

Evolution
Sloth bears may have reached their current form in the Early Pleistocene, the time when the bear family specialised and dispersed. A fragment of fossilised humerus from the Pleistocene, found in Andhra Pradesh's Kurnool Basin is identical to the humerus of a modern sloth bear. The fossilised skulls of a bear once named Melursus theobaldi found in the Shivaliks from the Early Pleistocene or Early Pliocene are thought by certain authors to represent an intermediate stage between sloth bears and ancestral brown bears. M. theobaldi itself had teeth intermediate in size between sloth bears and other bear species, though its palate was the same size as the former species, leading to the theory that it is the sloth bear's direct ancestor. Sloth bears probably arose during the Middle Pliocene and evolved in the Indian subcontinent. The sloth bear shows evidence of having undergone a convergent evolution similar to that of other ant-eating mammals.

The sloth bear is one of eight extant species in the bear family Ursidae and of six extant species in the subfamily Ursinae.

Characteristics

Sloth bears adults are medium-sized bears. The typical weight range for females is from 55 to 105 kg, and for males is from 80 to 145 kg. Exceptionally large female specimens can reach 124 kg and males up to 192 kg. The average weight of sloth bears from the nominate subspecies in Nepal was 95 kg in females and 114 kg in males. Nominate bears in India were found to weigh average 93.2 kg in males and 83.3 kg in female per one study. Specimens from Sri Lanka (M. u. inornatus) may weigh up to 68.2 kg in females and 104.5 kg in males. However six Sri Lankan male sloth bears averaged only 74.8 kg, and 57.5 kg was the average for four females, so Sri Lankan bears could be around 30% lighter in body mass than nominate race bears and with more pronounced size sexual dimorphism. They are 60 – high at the shoulder, and have a body length of 1.4 –. Besides being smaller than males, females reportedly typically have more fur between their shoulders.

Sloth bear muzzles are thick and long, with small jaws and bulbous snouts with wide nostrils. They have long lower lips which can be stretched over the outer edge of their noses, and they lack upper incisors, thus allowing them to suck up large numbers of insects. The premolars and molars are smaller than in other bears, as they do not chew as much vegetation. In adults, the teeth are usually in poor condition, due to the amount of soil they suck up and chew when feeding on insects. The back of the palate is long and broad, as is typical in other ant-eating mammals. The paws are disproportionately large, and have highly developed, sickle-shaped, blunt claws which measure 4 in in length. Their toe pads are connected by a hairless web. They have the longest tail in the bear family, which can grow to 6 - 7 in. Their back legs are not very strong, though they are knee-jointed, and allow them to assume almost any position. The ears are very large and floppy. The sloth bear is the only bear with long hair on its ears.

Sloth bear fur is completely black (rusty for some specimens), save for a whitish Y- or V-shaped mark on the chest. This feature is sometimes absent, particularly in Sri Lankan specimens. This feature, which is also present in Asian black bears and sun bears, is thought to serve as a threat display, as all three species are sympatric with tigers (tigers usually do not carry out attacks on an adult bear if the bear is aware or facing the cat). The coat is long, shaggy, and unkempt, despite the relatively warm environment in which the species is found, and is particularly heavy behind the neck and between the shoulders, forming a mane which can be 30 cm long. The belly and underlegs can be almost bare. Sloth bears are usually about the same size as an Asian black bear but are immediately distinctive for their shaggier coat, whitish claws, as well as their typically rangier build. Their head and mouth is highly distinct from that of a black bear with a longer, narrower skull shape (particularly the snout), loose-looking, flappier lips and paler muzzle colour. In few areas of overlap, sloth bear confusion with sun bears is unlikely, given the latter species considerably smaller size, much shorter fur, wrinkled folding skin (especially around the back), bolder chest marking and drastically different, more compact head structure and appearance.

Distribution and habitat
The sloth bear's global range includes India, the Terai of Nepal, temperate climatic zones of Bhutan and Sri Lanka. It occurs in a wide range of habitats including moist and dry tropical forests, savannahs, scrublands and grasslands below 1500 m on the Indian subcontinent, and below 300 m in Sri Lanka's dry forests. It is regionally extinct in Bangladesh.

Behaviour and ecology
Adult sloth bears may travel in pairs. Males are often observed to be gentle with cubs. They may fight for food. They walk in a slow, shambling motion, with their feet being set down in a noisy, flapping motion. They are capable of galloping faster than running humans. Although they appear slow and clumsy, both young and adult sloth bears are excellent climbers. They occasionally will climb to feed and to rest, though not to escape enemies, as they prefer to stand their ground. Sloth bear mothers carry their cubs up trees as the primary defense against attacks by predators instead of sending them up trees. The cubs can be threatened by predators such as tigers, leopards, and other bears. They are adequate climbers on more accessible trees but cannot climb as quickly or on as varied surfaces as can black bears due to the sloth species' more elongated claw structure. Given their smaller size and still shorter claws, sloth bear cubs probably climb more proficiently than adults (much as brown bear cubs can climb well but not adults). They are good swimmers, and primarily enter water to play.

To mark their territories, sloth bears scrape trees with their forepaws, and rub against them with their flanks. Sloth bears are recorded to produce several sounds and vocals. Howls, squeals, screams, barks and trumpet-like calls are made during aggressive encounters while huffing is made as a warning signal. Chuffing calls are made when disturbed. Females keep in contact with their cubs with a grunt-whicker while cubs yelp when separated.

Reproduction
The breeding season for sloth bears varies according to location: in India, they mate in April, May, and June, and give birth in December and early January, while in Sri Lanka, it occurs all year. Sows gestate for 210 days, and typically give birth in caves or in shelters under boulders. Litters usually consist of one or two cubs, or rarely three. Cubs are born blind, and open their eyes after four weeks. Sloth bear cubs develop quickly compared to most other bear species: they start walking a month after birth, become independent at 24–36 months, and become sexually mature at the age of three years. Young cubs ride on their mother's back when she walks, runs, or climbs trees until they reach a third of her size. Individual riding positions are maintained by cubs through fighting. Intervals between litters can last two to three years.

Dietary habits
Sloth bears are expert hunters of termites, ants, and bees, which they locate by smell. On arriving at a mound, they scrape at the structure with their claws till they reach the large combs at the bottom of the galleries, and disperse the soil with violent puffs. The termites are then sucked up through the muzzle, producing a sucking sound which can be heard 180 m away. Their sense of smell is strong enough to detect grubs 3 ft below ground. Unlike other bears, they do not congregate in feeding groups. Sloth bears may supplement their diets with fruit, plant matter, carrion, and very rarely other mammals. In March and April, they eat the fallen petals of mowha trees and are partial to mangoes, maize, sugar cane, jackfruit, and the pods of the golden shower tree. Sloth bears are extremely fond of honey. When feeding their cubs, sows are reported to regurgitate a mixture of half-digested jack fruit, wood apples, and pieces of honeycomb. This sticky substance hardens into a dark yellow, circular, bread-like mass which is fed to the cubs. This "bear's bread" is considered a delicacy by some of India's natives. Rarely, Sloth bears can become addicted to sweets in hotel waste visiting rubbish bins even inside populated towns all year long. Their diet includes animal flesh.

In Neyyar Wildlife Sanctuary, Kerala, seeds of six tree species eaten and excreted by sloth bears (Artocarpus hirsuta, A. integrifolia, Cassia fistula, Mangifera indica, Zizyphus oenoplina) did not see significantly different percentages of germination (appearance of cotyledon) when compared to germinated seeds that had not been passed through the gut of the bears. However, seeds germinated much faster after being ingested by bears for three species, Artocarpus hirsuta, Cassia fistula, and Zizyphus oenoplina. This experiment suggests that sloth bears may play an important role in seed dispersal and germination, with effects varying by tree species.

Relationships with other animals
The large canine teeth of sloth bears, relative to both its overall body size and to the size of the canine teeth of other bear species, and the aggressive disposition of sloth bears, may be a defense in interactions with large, dangerous animals, such as the tiger, elephant, and rhinoceros, as well as prehistoric species such as Megantereon.

Bengal tigers occasionally prey on sloth bears. Tigers usually give sloth bears a wide berth, though some specimens may become habitual bear killers, and it is not uncommon to find sloth bear fur in tiger scats. Tigers typically hunt sloth bears by waiting for them near termite mounds, then creeping behind them and seizing them by the back of their necks and forcing them to the ground with their weight. One tiger was reported to simply break its victim's back with its paw, then wait for the paralysed bear to exhaust itself trying to escape before going in for the kill. When confronted by tigers face to face, sloth bears charge at them, crying loudly. A young or already sated tiger usually retreats from an assertive sloth bear, as the bear's claws can inflict serious wounds, and most tigers end the hunt if the bears become aware of the tiger's presence before the pounce. Sloth bears may scavenge on tiger kills. As tigers are known to mimic the calls of sambar deer to attract them, sloth bears react fearfully even to the sounds made by deer themselves. In 2011, a female bear with cubs was observed to stand her ground and prevail in a confrontation against two tigers (one female, one male) in rapid succession.

Besides tigers there are few predators of sloth bears. Leopards can also be a threat, as they are able to follow sloth bears up trees. Bear cubs are probably far more vulnerable and healthy adult bears may be avoided by leopards. One leopard killed a three-quarters grown female sloth bear in an apparently lengthy fight that culminated in the trees. Apparently, a sloth bear killed a leopard in a confrontation in Yala National Park, Sri Lanka, but was itself badly injured in the fight and was subsequently put down by park rangers. Sloth bears occasionally chase leopards from their kills. Dhole packs may attack sloth bears. When attacking them, dholes try to prevent the bear from retreating into caves. Unlike tigers which prey on sloth bears of all size, there is little evidence that dholes are a threat to fully-grown sloth bears other than exceptionally rare cases. In one case, a golden jackal (a species much smaller and less powerful than a sloth bear and not generally a pack hunter as is the dhole) was seen to aggressively displace an adult bear which passively loped away from the snapping canid, indicating the sloth bear does not regard other carnivores as competition.

Sloth bears are sympatric with Asiatic black bears in northern India, and the two species, along with the sun bear, coexist in some of the national parks and wildlife sanctuaries. They are also found together in Assam, Manipur, and Mizoram, in the hills south of the Brahmaputra River, the only places occupied by all three bear species. The three species do not act aggressively toward each other. This may be because the three species generally differ in habit and dietary preferences.

Asian elephants apparently do not tolerate sloth bears in their vicinity. The reason for this is unknown, as individual elephants known to maintain their composure near tigers have been reported to charge bears. The Indian rhinoceros has a similar intolerance for sloth bears, and will charge at them.

Status and conservation
IUCN estimates that fewer than 20,000 sloth bears survive in the wilds of the Indian subcontinent and Sri Lanka. The sloth bear is listed in Schedule I of the Indian Wildlife Protection Act, 1972, which provides for their legal protection. Commercial international trade of the sloth bear (including parts and derivatives) is prohibited as it is listed in Appendix I of the Convention on International Trade in Endangered Species.

To address the human-bear conflict, people may be educated about the conservation ethics, particularly among locals. To resolve this conflict, the basic issue of deteriorating habitat, which is the reason for the conflict between people and bears, improvements through government or community-based reforestation programmes, may be promoted.

The population of sloth bears grows when they live in high-profile reserves that protect species, such as tigers and elephants. Directly managed reserves could conserve the sloth bear, hence such reserves must be supported. Managing garbage, especially hotel waste with foods, is essential in situations where sloth bears get used to entering towns with an increase in the number of accidental attacks on humans.

The government of India has banned use of sloth bears for entertainment, and a 'Sloth Bear Welfare Project' in the country has the objective of putting an end to their use for entertainment. However, their number in such activity is still large. Many organisations are helping in the conservation and preservation of sloth bears in safe places. Sloth bears previously used for entertainment are being rehabilitated in facilities like Agra Bear Rescue Facility run by Wildlife SOS and others. Major sloth bear sanctuaries in India include the Daroji bear sanctuary, Karnataka.

Sloth bears have also been found dead in traps, electrocuted, or killed by other means by poachers, with body parts (i.e. canines, claws, gall bladder, paws, etc) usually removed for the illegal wildlife trade.

Attacks on humans
Sloth bears are one of the most aggressive extant bears and, due to large human populations often closely surrounding reserves that hold bears, aggressive encounters and attacks are relatively frequent, though in some places, attacks appear to be a reaction to encountering people accidentally. In absolute numbers, this is the species of bear that most regularly attacks humans. Only the Himalayan black bear subspecies of Asian black bear is nearly as dangerous. Sloth bears likely view humans as potential predators, as their reactions to them (roaring, followed by retreat or charging) are similar to those evoked in the presence of tigers and leopards. Their long claws, which are ideally adapted for digging at termite mounds, make adults less capable of climbing trees to escape danger, as are other bears such as Asian black bears. Therefore, sloth bears have seemingly evolved to deal with threats by behaving aggressively. For the same reason, brown bears can be similarly inclined, accounting for the relatively high incidence of seemingly nonpredatory aggression towards humans in these two bear species.

According to Robert Armitage Sterndale, in his Mammalia of India (1884, p. 62):

"[The sloth bear] is also more inclined to attack man unprovoked than almost any other animal, and casualties inflicted by it are unfortunately very common, the victim being often terribly disfigured even if not killed, as the bear strikes at the head and face. [William Thomas] Blanford was inclined to consider bears more dangerous than tigers..."

Captain Williamson in his Oriental Field Sports wrote of how sloth bears rarely killed their human victims outright, but would suck and chew on their limbs till they were reduced to bloody pulps. One specimen, known as the sloth bear of Mysore, was responsible for the deaths of 12 people and the mutilation of 24 others. It was shot by Kenneth Anderson. Although sloth bears have attacked humans, they rarely become man-eaters. Dunbar-Brander's Wild Animals of Central India mentions a case in which a sow with two cubs began a six-week reign of terror in Chanda, a district of the Central Provinces, during which more than one of their victims had been eaten, while the sloth bear of Mysore partially ate at least three of its victims. R.G. Burton deduced from comparing statistics that sloth bears killed more people than Asian black bears, and Theodore Roosevelt considered them to be more dangerous than American black bears. Unlike some other bear species, which at times make mock charges at humans when surprised or frightened without making physical contact, sloth bears frequently appear to initiate a physical attack almost immediately. When people living near an aggressive population of sloth bears were armed with rifles, it was found that it was an ineffective form of defense, since the bear apparently charges and knocks the victim back (often knocking the rifle away) before the human has the chance to defend themself. In Madhya Pradesh, sloth bear attacks accounted for the deaths of 48 people and the injuring of 686 others between 1989 and 1994, probably due in part to the density of population and competition for food sources. A total of 137 attacks (resulting in 11 deaths) occurred between April 1998 and December 2000 in the North Bilaspur Forest Division of Chhattisgarh. The majority of attacks were perpetrated by single bears, and occurred in kitchen gardens, crop fields, and in adjoining forests during the monsoon season. One Mr. Watts Jones wrote a first-hand account of how it feels to be attacked by a sloth bear, recalling when he failed to score a direct hit against a bear he had targeted:

"I do not know exactly what happened next, neither does my hunter who was with me; but I believe, from the marks in the snow, that in his rush the bear knocked me over backwards in fact, knocked me three or four feet away. When next I remember anything, the bear's weight was on me, and he was biting my leg. He bit two or three times. I felt the flesh crush, but I felt no pain at all. It was rather like having a tooth out with gas. I felt no particular terror, though I thought the bear had got me; but in a hazy sort of way I wondered when he would kill me, and thought what a fool I was to get killed by a stupid beast like a bear. The shikari then very pluckily came up and fired a shot into the bear, and he left me. I felt the weight lift off me, and got up. I did not think I was much hurt. ... The main wound was a flap of flesh torn out of the inside of my left thigh and left hanging. It was fairly deep, and I could see all the muscles working underneath when I lifted it up to clean the wound.'"

In 2016, according to a forest official, a female bear had killed three people, and hurt five others in Gujarat State's Banaskantha district, near Balaram Ambaji Wildlife Sanctuary, with some of the casualties being colleagues. At first, an attempt was made to trace and cage it, but this failed, costing the life of one official, and so a team of both officials and policemen shot the bear.

In Karnataka's Bellary district, most of the attacks by sloth bears occurred outside forests, when they entered settlements and farmlands in search of food and water.

In Mount Abu town in southern Rajasthan, sloth bears attacked people inside towns where they were seeking hotel waste in rubbish bins and encountered people by chance. Though such attacks were concomitant with increasing tourism activity, quite remarkably, local residents have not retaliated against the sloth bears. The absence of retaliation in many locations of India appears related to cultural norms and the dominant religion Hinduism where nature and animals are worshipped as deities.

Hunting and products
One method of hunting sloth bears involved the use of beaters, in which case, a hunter waiting on a post could either shoot the approaching bear through the shoulder or on the white chest mark if it was moving directly to him. Sloth bears are very resistant to body shots, and can charge hunters if wounded, though someone of steady nerves could score a direct hit from within a few paces of a charging bear. Sloth bears were easy to track during the wet season, as their clear footprints could be followed straight to their lairs. The majority of sloth bears killed in forests were due to chance encounters with them during hunts for other game. In hilly or mountainous regions, two methods were used to hunt them there. One was to lie in wait above the bear's lair at dawn and wait for the bear to return from its nocturnal foraging. Another was to rouse them at daytime by firing flares into the cave to draw them out. Sloth bears were also occasionally speared on horseback. In Sri Lanka, the baculum of a sloth bear was once used as a charm against barrenness.

Tameability
Officers in British India often kept sloth bears as pets. The wife of Kenneth Anderson kept an orphaned sloth bear cub from Mysore, which she named "Bruno". The bear was fed all sorts of things and was very affectionate toward people. It was even taught numerous tricks, such as cradling a woodblock like a baby or pointing a bamboo stick like a gun.

Dancing bears were historically a popular entertainment in India, dating back to the 13th century and the pre-Mughal era. The Kalandars, who practised the tradition of capturing sloth bears for entertainment purposes, were often employed in the courts of Mughal emperors to stage spectacles involving trained bears. They were once common in the towns of Calcutta, where they often disturbed the horses of British officers.

Despite a ban on the practice that was enacted in 1972, as many as 800 dancing bears were in the streets of India during the latter part of the 20th century, particularly on the highway between Delhi, Agra, and Jaipur. Sloth bear cubs, which were usually purchased at the age of six months from traders and poachers, were trained to dance and follow commands through coercive stimuli and starvation. Males were castrated at an early age, and their teeth were knocked out at the age of one year to prevent them from seriously injuring their handlers. The bears were typically fitted with a nose ring attached to a four-foot leash. Some were found to be blind from malnutrition.

In 2009, following a seven-year campaign by a coalition of Indian and international animal welfare groups, the last Kalandar dancing bear was set free. The effort to end the practice involved helping the bear handlers find jobs and education, which enabled them to reduce their reliance on dancing-bear income.

Cultural references
Charles Catton included the bear in his 1788 book Animals Drawn from Nature and Engraved in Aqua-tinta, describing it as an "animal of the bear-kind" and saying it was properly called the "Petre Bear".

In Rudyard Kipling's The Jungle Book, Baloo "the sleepy old brown bear" teaches the Law of the Jungle to the wolf cubs of the Seeonee wolf pack, as well as to his most challenging pupil, the "man-cub" Mowgli. Robert Armitage Sterndale, from whom Kipling derived most of his knowledge of Indian fauna, used the Hindustani word bhalu for several bear species, though Daniel Karlin, who edited the Penguin Classics reissue of The Jungle Book in 1989, stated, with the exception of colour, Kipling's descriptions of Baloo are consistent with the sloth bear, as brown bears and Asian black bears do not occur in the Seoni area where the novel takes place. Also, the name "sloth" can be used in the context of sleepiness. Karlin states, however, that Baloo's diet of ".. only roots and nuts and honey" is a trait more common to the Asian black bear than to the sloth bear.

Local names:

 * ভালুক, bhaluk
 * રીંછ, rīn̄ch; also rinchh
 * भालू, bhālū; रीछ
 * ଭାଲୁ, bhālu
 * শ্লথ ভালুক, ślath bhaluk; kālō bhāluk; also bhaluk
 * ऋक्ष, ṛkṣa; also rikspa
 * ಕರಡಿ, karaḍi; kaddi
 * கரடி, karaṭi; kaddi
 * കരടി, karaṭi
 * ఎలుగుబంటి, elugubaṇṭi; also elugu
 * अस्वल, asval; also aswal
 * Gond: yerid, yedjal and asol
 * Kol: bana
 * Oraon: bir mendi
 * වලසා, valasā; also usa
 * भालु, bhālu
 * ਰਿੱਛ, richh

title: Sloth bear


text:
Blue rock thrush

The blue rock thrush (Monticola solitarius) is a species of chat. This thrush-like Old World flycatcher was formerly placed in the family Turdidae. It breeds in southern Europe, northwest Africa, and from Central Asia to northern China and Malaysia. The blue rock thrush is the official national bird of Malta (the word for it in Maltese being Merill) and was shown on the Lm 1 coins that were part of the country's former currency.

Taxonomy
The blue rock thrush was described by Carl Linnaeus in 1758 in the 10th edition of his Systema Naturae under the binomial name Turdus solitarius. The scientific name is from Latin. Monticola is from mons, montis "mountain", and colere, "to dwell", and the specific epithet solitarius means "solitary".

The rock thrush genus Monticola was formerly placed in the family Turdidae but molecular phylogenetic studies have shown that the species in the genus are more closely related to members of the Old World flycatcher family Muscicapidae.

There are five recognised subspecies:

 * M. s. solitarius (Linnaeus, 1758) – northwest Africa, south Europe, north Turkey to Georgia and Azerbaijan.
 * M. s. longirostris (Blyth, 1847) – Greece and west and south Turkey through the Middle East to the northwest Himalayas to northeast Africa and India
 * M. s. pandoo (Sykes, 1832) – central Himalayas to east China and north Vietnam to Greater Sunda Islands
 * M. s. philippensis (Statius Müller, 1776) – east Mongolia to Sakhalin south to Japan, extreme north Philippines and northeast China to Indonesia
 * M. s. madoci Chasen, 1940 – Malay Peninsula and north Sumatra

There is a proposal to split Monticola solitarius into two species: a western taxon comprising M. s. solitarius and M. s. longirostris and an eastern taxon with M. s. philippensis, M. s. pandoo and M. s. madoci.

Description
The blue rock thrush is a starling-sized bird, 21 – in length with a long slim bill. The breeding male of the nominate subspecies is unmistakable, with all blue-grey plumage apart from its darker wings. Females and immatures are much less striking, with dark brown upperparts, and paler brown scaly underparts. The male of the subspecies M. s. philippensis has rufous-chestnut plumage from the mid-breast down to the undertail. Both sexes lack the reddish outer tail feathers of rock thrush.

The male blue rock thrush sings a clear, melodious call that is similar to, but louder than, the call of the rock thrush.

Distribution and habitat
The European, north African and southeast Asian birds are mainly resident, apart from altitudinal movements. Other Asian populations are more migratory, wintering in sub-Saharan Africa, India and southeast Asia. This bird is a very uncommon visitor to northern and western Europe. It has only known to have been spotted in North America twice: once in British Columbia in 1997 and once in Oregon in 2024.

Behaviour
Blue rock thrush breeds in open mountainous areas. It nests in rock cavities and walls, and usually lays 3-5 eggs. An omnivore, the blue rock thrush eats a wide variety of insects and small reptiles in addition to berries and seeds.

title: Blue rock thrush