Study on Sargent's "Poppies"

Flowers on the Deck Painting

I think it is finished. I need to look at it for about a week and then sign it.

My Paintings

I am actually quite pleased with my two current paintings. I am having to adapt my old painting style to one that requires less precise vision but overall, I think they are coming along nicely. I'll post the finished products, hopefully, in a few days!

Cezanne

I have begun to study Cezanne; not just his work but his life. Out of 559 paintings that have been identified as his, only 13 were signed. According to letters he wrote, he felt that many of them needed "further resolution". His work was so individualistic. I found it interesting that he excelled in mathematics and languages but chose to be an artist.

Flowers Painting

I think it will take approximately two weeks to complete my painting of the flowers on the back deck. So far, I am happy with how it is progressing.

In class, we finished the still life and now we are moving one to finding inspiration in other painters' paintings. we are to choose an Impressionist to do a study from. John Singer Sargent did some Impressionist pieces along with his portrait studies so i am choosing one -- "Poppies".

Painting On The Deck

Yesterday, I painted on the back deck. The weather was perfect and I love the flowers back there this year. I can't wait to see what the painting looks like when it is finished.

Painting and Engineering Math

After the long hiatus, doing paintings again feels good. I think I will start going to the studio between classes in addition to during class. I will end up doing extra paintings but that is okay. The teacher is very flexible.

I am also working through an engineering math book , too. Loads of fun and it makes a great review.

Next fall, I think I will take College Chemistry o I can start getting back int0o my biochemical research and the second painting class. It is all so incredibly cheap through the community college and the college itself is only five miles away; not even much gas required.

Angle Formed By Chord and Tangent

Prove that the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

Given circle O, tangent DA where point A is on circle O, and chord BA for circle O. To show that the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc, I will use proof by cases as the first case has already been proved.

Case 1 is where chord BA is a diameter so point O is on chord BA such that B-O-A. This makes OA and OB radii of circle O so according to Theorem 6.7, tangent DA would be perpendicular to radii OA. This means that the angle measure on both sides is 90 which is indeed, as proved earlier (problem 6.3.2), half of the intercepted arc.

Case 2 is where chord BA is smaller than the diameter. AP1 allows us to construct a line parallel to the tangent DA going through point B, line BC. This creates angle ABC with the intercepted arc, AC. Theorem 6.9 states that the measure of this angle, angle ABC is equal to half of the measure of arc AC.

As lines DA and BC are parallel and secant of chord AB is a transversal, then angles DAB and ABC are alternating interior angles (Definition 4.7) and they are congruent (Theorem 4.27). Therefore, as ABC is half the measure of the intercepted arc, then angle DAB is also half the measure of the intercepted arc; or the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

Proof In Progress

Here is the current proof:

Prove that the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

I will post my proof when I finish it.

Painting Class

I am now in a painting class. So far it is going okay even though my vision has gone to Hell. The next painting is going to be a still life and I am not sure how that will go but I will see. Today was not a good vision day so at one point I looked at my painting and went....oh well. I think for the still life I will have to do some rethinking of my techniques as I will not be able to rely on my vision. As I said earlier, I will find out.

Inscribed Quadrilateral

Prove that if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

Assume circle O has an inscribed quadrilateral, ABCD, where four inscribed angles are formed within circle O. In other words, chord AC creates two inscribed angles, ABC and CDB. Each angle equals half the measure of the arc intercepted by the angle (Theorem 6.9). The sum of the measure of the intercepted arcs of the opposite angles is the full circle or 360. That means the angles sum to half of this measure or 180. By Definition 4.14, this means that opposite angles are supplementary.

End

I am coming to the end of my geometry course. I will miss it. I am now on circles, arcs, inscribed angles.

Tangents to a Circle are Congruent

Prove that tangents to a circle from a point are congruent.

Circle O is given. Point P is outside of circle O. In accordance with Definition 6.3, construct segments PA and PB so they form tangents to circle O. Also construct radii AO and BO. Two triangles are now formed – triangle PAB and triangle OAB. As radii are congruent (Theorem 6.1) then AO and BO are congruent. The two radii intersect the two tangent lines perpendicularly (Theorem 6.5). Segment PO then becomes the hypotenuse for triangles PAO and PBO. Segments are also congruent to themselves (AC02) so in both triangles PO is congruent. According to Theorem 4.78, triangles PAO and PBO are congruent as they have congruent hypotenuses and congruent corresponding legs. Theorem 4.20 says that all sides of congruent triangles are congruent; therefore, it can be concluded that PA nd PB are congruent as they are corresponding sides.

Sugar Snap Peas

Tonight was my night to cook (yes, all three of us share making meals, even my 16 year old son). I went through the refrigerator in an attempt to use up remainders before they go bad. The sugar snap pea medley was a success! Snap peas, cherry tomatoes, scallions sauteed in olive oil on high heat. Then I added salt, pepper, capers, and pine nuts. Yum.

Next President

Lord, I hope McCain becomes president. If Obama gets voted in this country might as well place a sign at its door saying "Welcome Terrorist"! And there are already too many of them living here now!

Success

The asparagus was a success!

• Start at least three hours prior to serving so it will be well chilled.
  
• Wash and cut the asparagus into about 1/2 to 3/4 inch pieces.
  
• Boil water and then blanch the aspargus for about 45 seconds to a minute.
  
• Quickly drain asparagus and wash in cold water; place asparagus into a bowl used later for refrigerating.
  
• Add olive oil and lemon juice ; grind pepper on top. Add capers.
  
• Cut beef bratwurst into halves and then into 1/2 inch segments.
  
• Brown bratwurst on high heat in olive oil; then mix with aspargus.
  
• Chill at least three hours and serve.

Risk

I love risk; not reckless risk but well calculated risk. I love going 90 in my car with the top down. I do it on straight stretches when vision is clear and the speed limit is 65 or more. I only do it for short stretches.

I think risk is part of why I keep learning (risk adversity may be the reason why some people stop) and taking classes; forever stretching myself and trying to stretch to my limits. Part of it is risk; risk that I may do well and risk that I might struggle or even fail.

Perhaps that is also why the image of a perfect type of Heaven is revolting to me. There would be no risk and not learning; no growing and changing. I have zero desire to have life too safe. To me, a person might as well be dead as to have a completely safe life where everything is always under control and perfect; even of the perfection is an illusion.