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Maria’s Story

By Murray Bourne, 24 Jan 2009

Maria lived in an age when most people − especially women − received no education at all. She was a brilliant girl but painfully shy.

After her mother died, Maria had to take over the house and look after all her 20 younger brothers and sisters.

Maria had a fascination with mathematics and gained a reputation as a competent mathematician. She managed to find time to write a famous book, Analytic Institutions, which brought together the brilliant calculus discoveries of Isaac Newton and Gottfried Leibniz.

Being a known sleepwalker, Maria would get up in the middle of the night and write down the solution for a math problem she’d been struggling with − while asleep! She would get up the next morning to find her answer waiting for her.

She was also a linguist and could speak French, Italian, Greek, Hebrew, Spanish, German and Latin by the time she was 11.

At just 9 years of age, Maria wrote and delivered an hour-long speech in Latin on women's right to be educated.

Always being concerned for those less fortunate than her, Maria would help the poor and needy in her area. She worked in a small hospital that she’d set up in her father’s house until she died at 81.

Who am I talking about? Maria Gaetana Agnesi (1718-1799), a resident of Milan. In 18th century Italy, women had very limited opportunity for education and found it hard to be taken seriously. Maria’s accomplishments are all the more remarkable because of the other duties she had to perform. Can you imagine trying to write a book with all those kids running around?

Maria Agnesi's Mathematics

Apart from her book, Maria was famous for a curve known as "The Witch of Agnesi". The witch part was just a translation error (it was supposed to be "turn"), but the name has stuck. She didn’t create the curve, but she studied it.

The Witch of Agnesi is formed as follows.

Take a circle and draw a horizontal line through the top of it.

Witch of Agnesi - construction 1

From a point O directly below the intersection of the line and the circle, draw a segment OP to intersect the horizontal line. Q is the point where OP intersects the circle. Draw a horizontal segment QR which intersects the vertical dropped from the point P. Put a (blue) dot at R.

Witch of Agnesi - construction 2

Move the point P along the horizontal line and join the bottom of the circle and drop verticals and horizontals as follows. Put blue dots on each intersection point.

Witch of Agnesi - construction 3

If we draw enough of these and join the blue dots, we get the following curve, the Witch of Agnesi:

Witch of Agnesi

If the circle has radius a, then the equation of the Witch of Agnesi is given by:

Witch of Agnesi  formula

The shape is quite similar to the bell-shaped normal curve that we come across in probability and statistics.

See the 11 Comments below.

11 Comments on “Maria’s Story”

  1. Donne e matematica « In teoria says:

    [...] Per chi volesse saperne di più: sul personaggio, sulla curva, sul sito da dove traggo le informazioni. [...]

  2. Matt says:

    Yeah, she had some nice curves.

  3. Sigrid Rose says:


  4. Burton MacKenZie says:

    It's the reciprocal function of a parabola (quadratic function).

  5. kewani welay says:

    Really strong woman!!!!!!!

  6. svb subrahmanyeswara rao says:

    It's an interesting story about the great Agnesi...her efforts were inspiring.

  7. mhdsys says:

    its a very nice curve , very simple to be plot by using geogebra software,

  8. maricel says:

    Wow!!! I was really amazed in this person, Maria...
    She really has a great contribution not only to his neighbor but also to us, us future mathematics teachers...

  9. Enabudoso says:


    Am amaze for Maria taken responsibility of 20 children and being a Mathematician is worth emulating. I really envy her ability to give solution to mathematics problem, create and make researches.

    She is indeed a genuiues. There is one thing that was fascinating about her, she was not even mindful of her background, despite her background she was determined.

  10. hassan hejazi says:

    really wonderfull!
    but really woman must share in all scientific fields because it may have some talent that trespass that of man....

  11. jonouella says:

    only i can say is this is very
    nice story of maria and aside from that
    she is very thrifty and a good child....
    she have a great affinity for me
    and her prowess is undisputed and also
    her knowledge is very arcaneling.......

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